Click to view posters for each subgroup
Adnan A Khan
(MEPI)
Lahore University of Management Sciences
"Understanding the COVID-19 Outbreak in Pakistan"
We present a study of the transmission dynamics of the COVID-19 outbreak in Pakistan. Important transmission pathways such as the role of Asymptomatic, Quarantined and Isolated individuals are incorporated in the model. The model is then used to study the outbreak in Pakistan, considering the different lockdown and social distancing measures taken at different times by the health authorities noting that the epidemic curve in Pakistan has been quite different from those in Europe and the US, with a significantly lower disease burden and mortality rate.
Akhil Kumar Srivastav
(MEPI)
Vellore Institute of Technology
"Mathematical Modeling of Malaria with Saturated Treatment-A Case Study of India"
Malaria is a life-threatening mosquito-borne disease. It is transmitted through the bite of an infected Anopheles mosquito. People who get infected with malaria become very sick with high fevers, chills, and flu-like symptoms. Malaria may be fatal if not treated promptly. Here we propose an SIS model to study the trans- mission dynamics of malaria with saturated treatment. We assume that the mosquito population is growing logistically in the environment. Here we include a saturated type treatment function which is more suitable for the regions with limited resources. We discuss the existence and stability of different equilibria of the proposed model. We also compute the basic reproduction number R0 which plays an important role in existence and stability of equilibria of the model. We estimate the parameter corresponding to transmission of malaria using real data from different states of India by least square method. We also perform sensitivity analysis using PRCC to identify the key parameters which influence the basic reproduction number and system both, hence regulate the transmission dynamics of malaria. Numerical simulations are presented to illustrate the analytic findings.
Alexis Erich S Almocera
(MEPI)
Univ. of the Philippines Visayas
"Modeling the viral infectious disease from infection to epidemic"
Mathematical models can integrate different components of an infectious disease to reveal novel insights into the long-term effects. Conventional models focus either on pathogen infection (in-host scale) or pathogen transmission (between-host scale). However, we have yet to establish a framework that unites the two scales. We employ a conceptual modeling approach, where the standard transmission parameter becomes a function of the viral load, coupling in-host virus kinetics with an immune response to a compartmental disease model. The stability of the steady states with simulations cast light on the extent of a chronic host infection to influence the severity of an outbreak. Our results lend support to the 'multiscale' paradigm of disease modeling, which can inform long-term, personalized, and data-driven strategies in disease control and healthcare.
Angelo J Zorn
(MEPI)
Occidental College
"An Epidemic Mobility Model with Symptomatic and Asymptomatic Individuals Allowing Variation of Contact Rates Between Individuals and Across Regions"
The control of contacts among individuals and across regions is of paramount importance to understand the dynamics of infectious diseases. In the current COVID-19 pandemic, many infectious individuals are asymptomatic, thereby raising the question as to whether limiting contacts with infected individuals displaying symptoms is sufficient to control the spread of the disease.
To this end, we have developed a mathematical model, called SAIRD model, that includes susceptible individuals (S), asymptomatic infectious individuals (A), infectious individuals displaying symptoms (I), individuals who recovered (R) and deceased individuals (D). The model also includes mobility of individuals across geographic regions that accounts for inter-region travel patterns.
We have considered 3 regions characterized by different inter-individual contacts. Specifically, no limitations are adopted in region 1, limitations are adopted only for symptomatic individuals in region 2, and limitations are adopted for both asymptomatic and symptomatic infectious individuals in region 3. In the absence of inter-region connection, the model predicts similar disease dynamics in regions 1 and 2, whereas region 3 experiences a notable lower number of infections and death. These results suggest that controlling inter-individual contacts in both asymptomatic and symptomatic cases is essential to contain the disease dynamics. Furthermore, the model predicts that controlling inter-individual contacts without controlling inter-region connections may nullify the gains.
Aniruddha Deka
(MEPI)
Shiv Nadar University
"Optimal public health strategy during an influenza outbreak"
Although vaccine has proven to be the best preventive method to reduce risk of flu infection, the coverage often remains below the herd-immunity level due to individuals’ perceptions towards the vaccination and the severity of disease outbreak. This, however, brings challenges to public health for strategic decision-making in controlling flu outbreak every year. To understand the impact of behavioral issues on public health decision-making to control flu, we define vaccination decision in population as a two-strategy pairwise-contest game and integrate with the disease process model to consider vaccination during a flu outbreak. We use optimal control theory to identify the best possible strategy for public health to reduce infection at a minimum cost. Our analysis shows that the cost of public health initiatives can be minimized by putting the effort in the beginning and end of the outbreak rather than during the peak. We also consider vaccination with evolving risk perception and infection with high severity such as disease-induced death. Our model demonstrates a feed-forward mechanism in the dynamics of vaccination and exhibits an increase in vaccine uptake as the risk perception decreases with more coverage. It confers that public health effort towards disseminating disease severity or actual vaccination risk might accelerate the vaccination coverage and mitigate the infection faster.
Augustine Okebunor Okolie
(MEPI)
Technical University of Munich
"Exact and approximate formulas for contact tracing on random trees"
We consider a stochastic susceptible-infected-recovered (SIR) model with contact tracing on random trees and on the configuration model. On a rooted tree, where initially all individuals are susceptible apart from the root which is infected, we are able to find exact formulas for the distribution of the infectious period. Thereto, we show how to extend the existing theory for contact tracing in homogeneously mixing populations to trees. Based on these formulas, we discuss the influence of randomness in the tree and the basic reproduction number. We find the well known results for the homogeneously mixing case as a limit of the present model (tree-shaped contact graph). Furthermore, we develop approximate mean field equations for the dynamics on trees, and – using the message passing method – also for the configuration model. The interpretation and implications of the results are discussed.
Beryl O Musundi
(MEPI)
Technical University of Munich
"An immuno-epidemiological model linking within-host and between-host dynamics of cholera"
Cholera, an acute gastrointestinal disease caused by the bacterium Vibrio cholerae, continues to be a major threat to public health with an estimated 1.3 - 4 million cases reported annually. The majority of existing cholera models focus on the between-host dynamics independent of within-host dynamics, a factor that downplays the interdependence of the two processes on the spread of the infection. In this study, an immuno-epidemiological model for cholera is formulated to analyze the effect of within- host dynamics on the population. The model is an adaptation of the immuno-epidemiological models reviewed by M. Martcheva, N. Tuncer, C. St Mary (2015). We use time-scale methods to distinguish the dynamics of the immune response and the parasite load of an individual. A thorough bifurcation analysis reveals the existence of a saddle node and Hopf bifurcation. In contrast to other immunological models, the present approach allows for clearance of the pathogen after a finite time. The between- host system is represented by a size structured model with the pathogen load considered as the linking mechanism. We derive expressions for the reproduction number and conduct stability analysis of the equilibria. Conclusions about the interdependence of the two dynamics on disease spread are drawn from the analysis.
Bhattacharyya Samit
(MEPI)
Shiv Nadar University
"Evolutionary game models to explain the potential interactions among Adverse events, Vaccine scares and Individual vaccination choice"
Rumours on adverse health outcomes either from infection or vaccination have strong impact on vaccination uptake. Understanding human behavioral responses during a vac- cine scare and its interactions with the population dynamics of disease play key role in predicting the dynamics of disease, designing intervention strategies and policymaking in public health program. Mathematical modelling is an important tool for investigating and quantifying such effects in infectious disease and control. In the first part of my talk, I will introduce evolutionary game models of vaccination dynamics in homogeneous population to describe how human attitude changes towards vaccination during a scare using empirical data of several vaccination coverage. In the second part, I will introduce vaccination game on social network to discuss how rare but severe events can impact the vaccination dynamics.
Cameline Nafula
(MEPI)
Maseno University
"Modelling the spatio-temporal risk of measles outbreaks and options for their control in Kenya"
The measles control programme in Kenya is considered to be at it end phase. There has been long-term high level coverage of measles containing vaccine (MCV) at 9m reaching around 90% in 2010-12. Supplementary immunization activities (SIAs) are undertaken periodically (last done in 2016) to reduce the build-up of susceptibles in the age range 9m to 14 years. However, sporadic outbreaks continue, and data suggests vaccine uptake of MCV dose 1 has decreased over the last 5 years (WHO & UNICEF 2017, Manakongtreecheep & Davis 2017). A second dose of MCV was introduced in 2013 at 18months of age, but coverage is only at around 35%, and there is little confidence that this can easily be improved. There is national case-based surveillance, with follow up, through IgM serology from cases of rash illness. This study seeks to understand the possible reasons for continued outbreaks and to predict the implications of various vaccine strategies by modelling the Spatio-temporal risk of measles outbreaks and options for their control in Kenya.
Carlos Enrique Bustamante-Orellana
(MEPI)
Arizona State University
"Modeling and Preparedness: The Transmission Dynamics of COVID19 Outbreak in Provinces of Ecuador"
COVID-19 disease has become a pandemic just a few months after it was first detected. Ecuador has reported one of the highest rates of COVID-19 in Latin America, with more than 62,000 cases and 8,500 deaths in a country of approximately 17 million people. The dynamics of the outbreak is being observed quite different in different provinces of Ecuador with high reported prevalence in some low population density provinces. In this study, we aim to understand the variations in outbreaks between provinces and provide assistance in essential preparedness planning in order to respond effectively to ongoing COVID-19 outbreak. This study estimated the critical level of quarantine rate along with corresponding leakage in order to avoid overwhelming the local health care system. The results suggest that provinces with high population density can avoid a large disease burden provided they initiate early and stricter quarantine measures even under low isolation rate. To best of our knowledge, this study is first from the region to determine which provinces will need much preparation for current outbreak in fall and which might need more help.
Caroline Franco
(MEPI)
Institute of Theoretical Physics - Sao Paulo State University
"Modelling non-pharmaceutical interventions to mitigate COVID-19 in Sao Paulo"
The SARS-CoV-2 pandemic has had an unprecedented impact on multiple levels of society. Not only has the pandemic completely overwhelmed some health systems but it has also changed how scientific evidence is shared and increased the pace at which such evidence is published and consumed, by scientists, policymakers and the wider public. With very little experimental scientific evidence, predictive mathematical models have played an increasingly prominent role advising policymakers, even in low- and middle-income countries, such as Brazil. Through the COVID-19 Modelling (CoMo) Consortium, an international group of infectious disease modellers and public health experts collaborated to create a modelling interface that could help simulating the effect of different non-pharmaceutical interventions on mitigating the epidemic in numerous locations. Here, we describe how we adapted this modelling framework to the Brazilian context and, more specifically, to the city of Sao Paulo.
Cristian C. E. Espitia
(MEPI)
University of Campinas
"A mathematical model of HIV/AIDS Spread in human population, the triangle transmission case."
There exist individuals that change their sexual behavior depending on the situation or at different stages in their life. A possibly common and transient example of situational sexuality is the person who self-identifies as heterosexual, but will sexually interact with a member of the same sex when lacking other opportunities. Less transient but also possibly common, a person who self-identifies as gay or lesbian (either at the time, or later) may sexually interact with a member of the opposite sex if a same-sex relationship seems unfeasible, Thompson 2008, [1]. HIV/AIDS transmission usually considers sexual contact in heterosexual and homosexual population separately, besides in sexual transmission the same format for men and women is assumed. Thus, Can the population be split in heterosexuals and homosexual and thus the group of bisexuals be ignored? Can the sexual transmission form be equal for men and women? What is the contribution of a bisexual group in the HIV transmission? and, How to consider sexual transmission in men and women according to sexual behavior? To try to answer these questions we proposed an original mathematical model considering bisexuals in the HIV transmission. Mathematical analysis undertaken and stationary points, stability analysis of disease free equilibrium and boundary equilibrium, the basic reproductive number is obtained and discussed through the next generation method; numerical simulations show that these casual contacts between bisexuals has less influence than homosexual case.
Darwin Bandoy
(MEPI)
University of California,Davis
"Pandemic dynamics of COVID-19 using epidemic stage, instantaneous reproductive number and pathogen genome identity (GENI) score: modeling molecular epidemiology"
Background: Global spread of COVID-19 created an unprecedented infectious disease crisis that progressed to a pandemic with >180,000 cases in >100 countries. Reproductive number (R) is an outbreak metric estimating the transmission of a pathogen. Initial R values were published based on the early outbreak in China with limited number of cases with whole genome sequencing. Initial comparisons failed to show a direct relationship viral genomic diversity and epidemic severity was not established for SARS-Cov-2. Methods: Each country's COVID-19 outbreak status was classified according to epicurve stage (index, takeoff, exponential, decline). Instantaneous R estimates (Wallinga and Teunis method) with a short and standard serial interval examined asymptomatic spread. Whole genome sequences were used to quantify the pathogen genome identity score that were used to estimate transmission time and epicurve stage. Transmission time was estimated based on evolutionary rate of 2 mutations/month. Findings: The country-specific R revealed variable infection dynamics between and within outbreak stages. Outside China, R estimates revealed propagating epidemics poised to move into the takeoff and exponential stages. Population density and local temperatures had variable relationship to the outbreaks. GENI scores differentiated countries in index stage with cryptic transmission. Integration of incidence data with genome variation directly increases in cases with increased genome variation. Interpretation: R was dynamic for each country and during the outbreak stage. Integrating the outbreak dynamic, dynamic R, and genome variation found a direct association between cases and genome variation. Synergistically, GENI provides an evidence-based transmission metric that can be determined by sequencing the virus from each case. We calculated an instantaneous country-specific R at different stages of outbreaks and formulated a novel metric for infection dynamics using viral genome sequences to capture gaps in untraceable transmission. Integrating epidemiology with genome sequencing allows evidence-based dynamic disease outbreak tracking with predictive evidence.
David Gurarie
(MEPI)
CWRU
"Individual-based modeling of Covid-19 in local community settings"
Individual based modeling of disease transmission (IBM) offers an attractive alternative to population based approaches e.g. (continuous DE), as it allows a detailed account of biological (risk) factors, environment, and behavior. This is particularly relevant in local community settings (hospital, workplace, school, city district or county), where finite population size and host heterogeneity, in terms social interactions and disease progression, make a ‘continuous approach’ impractical. We develop such IBM methodology to simulate Covid-19 outbreaks in local settings, and explore different control-mitigation strategies. Our models feature multiple disease pathways (asymptomatic, mild and severe) typical of Covid-19, as well as heterogeneous host communities with different susceptibility levels and structured social contacts. Individual hosts undergo SEIR disease progression (Susceptible, Exposed - presymptomatic, Infected-symptomatic, Recovered) of variable stage-duration and infectivity. The crucial (S->E) transition is determined by host ‘contact-pool’ on daily basis. Unlike conventional social-contact network (‘one-to-one’ transmission), our setup features ‘many-to-many’ (multigraph) transmission. Two typical IBM examples include (i) hospital, made of interacting healthcare workers (HCW) and patients, (ii) school/college, where students + staff aggregate in classrooms, dorms and engage in other (social, sport) activities. In both cases, we used available data (a hospital in Wuhan, a college in US) to set up and calibrate our models. Different control/mitigation strategies were explored, including symptomatic and asymptomatic testing and isolation, use of PPE (hospital), social distancing, and contact tracing (college). We assessed the efficacy of each intervention, and resources required to prevent or mitigate the outbreak.
Deena Schmidt
(MEPI)
University of Nevada, Reno
"Building age-structured network models from interaction data"
Many methods exists for generating networks with certain pre-specified properties. However, there are network properties that arise in certain applications for which we don't have standard methods. For example, age or sub-population structure in biological applications can be a very important determinant of node connectivity, but methods for constructing networks with a given structure are still being developed. In this talk, I will discuss a method we developed for generating an age-structured human interaction network using survey data that summarizes the number of interactions between individuals within and between different age groups. We do this using the well-known POLYMOD dataset to construct an age-structured infectious disease transmission network.
Dhiraj Kumar Das
(MEPI)
Indian Institute of Engineering Science and Technology, Shibpur
"Influence of the smear-microscopy in global dynamics of tuberculosis transmission"
Tuberculosis, a lethal infectious disease attribute among the top 10 causes of death globally and leading cause of death from a single infectious pathogen (rank before HIV). The sputum smear-microscopy and chest X-ray are the key TB diagnosis methods available in resource-constrained health settings of many developing countries. The specificity of the diagnostic method is satisfactory whereas, sensitivity is limited and cannot detect pulmonary tuberculosis (PTB) cases below a bacterial load of 1000 organism/ml. According to the sensitivity of this diagnostic method, PTB patients are categorized into two kinds: (a) smear-positive and (b) smear-negative. Interestingly, this categorization also scales the infectivity of PTB patients in the community. Our current study addresses this heterogeneity in the infectiousness of PTB individuals to investigate its consequences in disease dynamics.
A five-dimensional compartmental model is formulated considering the infectivity of both the smear-positive and negative PTB individuals. The expression of the basic reproduction number ($R_0$) is obtained through the next-generation matrix method. The asymptotic behaviour of the model is thoroughly discussed around the steady states of the proposed model. The global asymptotic stability of the equilibrium points is established using suitably constructed Lyapunov functions. It is observed that the disease-free equilibrium is globally asymptotically stable for $R_0<1$ and the disease-persistent equilibrium point is the same whenever $R_0>1$. The study also provides a list of normalized forward sensitivity indices of $R_0$ with respect to the involved parameters. This list showcases the influential level of the associated parameters in determining the size of the threshold quantity $R_0$. It has been found that neglecting the transmission capacity of the smear-negative individuals underestimates the value of $R_0$ whereas, ignoring the smear-negative compartment overestimates the same quantity. We also implement numerical simulations whenever necessary, using a suitable TB parameter set to visualize the obtained analytical results.
Emma L Fairbanks
(MEPI)
University of Nottingham
"Re-parameterisation of a mathematical model of AHSV using data from literature"
Midge-borne arboviruses were once restricted to other geographical regions; however due to climate change and increased globalisation these diseases now pose a threat to the UK, with outbreaks having already occurred. African horse sickness virus (AHSV) is endemic in parts of Africa. An outbreak in Spain 1987-1990, which spread to Portugal and Morocco, demonstrated the ability of this virus to spread within Europe.
A previously published model suggested an ordinary differential equation model for AHSV in which parameters were derived from three published studies. In order to better inform the model studies documenting experimental infection of equids in vaccination trials were systematically reviewed. As we were interested in modelling emergence of AHSV in a naive population, only experimental infections of control (i.e. naive) animals were considered. Parameters derived from the systematic review were the time until the onset of viraemia, clinical signs and death after experimental infection of a naive equid. The mean latent period of horses was found to be 4.6 days, longer than previously estimated (3.7 days). The infectious periods of dying and surviving hosts were found to be 3.9 and 8.7 days, whereas previous estimations where 4.4 and 6 days, respectively. The host mortality rate was also found to be higher than previous estimations. Model simulations were compared for the previously published models parameters and an updated set of parameter values derived from the systematic review and other literature. The updated parameter values resulted in an increase in the number of host deaths and decrease in the duration of the outbreak. We also observed many more vector infections in simulations using the updated parameters. Sensitivity analysis showed that the host latent period and vector to host ratio had the greatest impact on simulation outputs.
The vector parameters in this model were also updated using literature. However, many of these were from studies on american vector species. Therefore, the stages of this work involve fitting a model developed for the vector populations to UK trap data.
Emma Southall
(MEPI)
University of Warwick
"Identifying indicators of critical transitions in epidemiological data"
A challenging problem in infectious disease modelling is assessing when a disease has been eliminated. Control campaigns have substantial economic consequences; as such there are high demands to reduce costs and reallocate resources. However, if campaigns are stopped prematurely it can result in disease resurgence and subsequently put control efforts back by decades. Early-warning signals offer a computationally inexpensive technique to monitor the progress towards elimination, using statistical indicators calculated on time series data.
Early-warning signals are widely used in many fields to anticipate a critical threshold prior to reaching it. A system undergoes the phenomenon known as critical slowing down as it crosses through a threshold. Theory predicts that fluctuations away from the mean will recover more slowly as the system approaches a critical transition (Scheffer et al., 2009). This is key in infectious disease modelling to assess when the basic reproduction number is reduced below the threshold of one.
Recent theoretical advances have shown indicators of critical transitions in epidemiology such as measuring the variance in synthetic disease data. Our work highlights several challenges when applying this theory in practice. One potential problem is known as 'detrending' the data, which can be difficult to achieve in a single time series (Dessavre & Southall et al., 2019). Accurately detrending the signal removes the mean to obtain the fluctuations, whilst preserving any statistical properties. We present a novel approach using a metapopulation framework to successfully detrend data using the mean of different geographical subpopulations.
A second limitation is that often only incidence-level data is available publicly. However, current theoretical analyses of statistical indicators concentrate on prevalence data, instead of new cases. We demonstrate that indicators calculated on simulated incidence time series data exhibit vastly different behaviours to those previously studied on prevalence data (Southall et al., 2020). Inconsistencies in time series traits between different diseases systems and a variety of disease data types could lead to misleading results when applied to collected data.
In this talk we present methods for dealing with the typical data collected and our results show promising methods for calculating early-warning signals of elimination on real-world noisy data.
Estadilla S Carlo Delfin
(MEPI)
Ateneo de Manila University
"Optimal Strategies for Mitigating the COVID-19 Epidemic in the Philippines"
With one of the longest lockdowns in the world and over 50,000 cases and 1,600 deaths, the Philippines is one of the hardest hit countries of the COVID-19 pandemic in the Southeast Asian region as of July 2020. The country continues to realign its lockdown policies and increase its test-trace-and-treat capacity to control the epidemic while trying to ease the burden on the national economy. In this study, we identify the best strategy to mitigate the spread of COVID-19 for the regions with the highest cases in the Philippines by applying optimal control theory to a nonlinear dynamical model fitted to local epidemiological data. Furthermore, long-term viability of different levels of community quarantine, testing, and combinations of these two strategies to minimize the number of infectious individuals are examined through cost effectiveness analysis given the limited resources available to the country.
References: Philippine Department of Health - Epidemiology Bureau (2020), COVID-19 Tracker Philippines (accessed July 15, 2020). https://www.doh.gov.ph/covid19tracker L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelize, and E. F. Mishchenko,The Mathematical Theory of Optimal Processes, Wiley, 1962.
Fatima Sulayman
(MEPI)
Universiti Sains Malaysia
"Dynamical systems analysis of tuberculosis with the impact of transmission rate and vaccination."
This paper examine the impact of transmission rate and vaccination on the dynamics of tuberculosis infection. Model analysis is established, the existence of hopf-bifurcation is analytically shown which deduces the oscillatory persistence of the infection in the population. The stability properties of the steady states and its bifurcation structures are investigated. We illustrate that there exist threshold values for the transmission rate and vaccination which corresponds to saddle node, transcritical and subcritical hopf bifurcation.
Gemma Massonis
(MEPI)
CSIC
"Structural Identifiability and Observability of Compartmental Models of the COVID-19 Pandemic"
The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from out-put measurements, its ability to yield correct insights – as well as the possibility of controlling the system – maybe compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider boththe constant and time-varying parameter assumptions. We analyse the structural identifiability and observability ofall of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing themost informative model for each purpose, taking into account the available knowledge and measurements.
Gilberto C Gonzalez-Parra
(MEPI)
New Mexico Tech
"Forecasting cases of RSV using artificial neural networks and mechanistic models"
We study and present an approach based on artificial neural networks to forecast the number of cases with the Respiratory Syncytial Virus (RSV). The number of cases of RSV in most of the countries around the world present a seasonal type behavior. We construct and develop several multilayer perceptron models that intend to forecast appropriately the number of cases of RSV. We compared our approach with a classical technique for time series, and our results are more accurate. The adjusted MLP network that we find has a fairly high accuracy of forecast. Finally, we compare empirical and mechanistic models applied to forecasting and prediction.
Gustavo J Sibona
(MEPI)
FAMAF - Universidad Nacional de Córdoba
"SIRS dynamics on a diffusive agent system"
Since its introduction in 1927 by Kermack and McKendrick, SIR compartmental models have been the basis of mathematical epidemiology. In this work we consider a SIRS epidemics on a system of mobile agents, which can interact during a finite period of time that depends on their dynamics. Thus, as the probability of disease transmission depends on this contact time, the spatial dynamics will strongly influence the disease evolution. By combining individual-based simulations and mean-field arguments, we study the dependency of the equilibrium populations on motility parameters, specifically the active speed and tumbling frequency. We find that the equilibrium epidemic size exhibits two very distinct, non-trivial scaling regimes with the motility parameters, depending on whether the system is in the ballistic or diffusive regime. Our mean-field estimates lead to an effective renormalization of the transition rates that allow building a phase-diagram that separates endemic and disease free phases. We find an excellent agreement between numerical simulations and mean-field estimates.
Hana Dobrovolny
(MEPI)
Texas Christian University
"SARS-CoV-2 coinfections: Implications for the second wave"
Researchers have noted that there are unexpectedly few SARS-CoV-2 coinfections with other circulating respiratory viruses. We use an in host mathematical model to examine interaction of SARS-CoV-2 with other respiratory viruses, finding that SARS-CoV-2 growth tends to be blocked by the presence of other viruses. We then formulate an epidemiological model to determine how this blocking effect might influence the impending second wave of SARS-CoV-2 infections.
Himanshu Aggarwal
(MEPI)
Indian Institute of Science Education and Research (IISER) Mohali
"Impact of temperature change on Malaria incidence in high altitude regions of India"
Malaria is a vector (mosquito)-borne parasitic disease, which is a major cause of death and disability in the world around the equatorial belt. The mosquitoes require a range of temperature and humidity to reproduce and persist, and the Malaria parasite (species of Plasmodium) uses both mosquito and human as their host for growth and reproduction. The cooler regions, such as the cold high altitude mountainous areas, therefore, witness fewer Malaria cases. An increase in temperature, as a possible consequence of global warming, is hypothesized to drive the spread of the malarial vectors to higher altitudes, by rendering these regions suitable for their growth, and consequent increase in Malaria incidence. But this view is hotly debated with evidence existing both against and in favour. Therefore, there is a need for more empirical evidence covering a wide variety of regions all around the world. A detailed study is performed, on a historical dataset (1975-1995) of Malaria cases in 19 contiguous districts from the three north-western states of India having an altitude higher than 1000 meters, for the analysis of the impact of temperature changes on Malaria incidence in these high altitude regions. In reality, the mean temperatures do not show a consistent increase over the years, and the vegetation, rainfall, and other environmental and demographic factors also differ among the regions and years. Using different data analytic and statistical measures, the results, though collectively do not provide a definite evidence for climate change-induced increase in Malaria in the high altitude regions under study, yet they do point towards increased malaria cases with an increase in temperature. It also points out that many other drivers may be responsible for the spread of an infectious disease like Malaria (e.g., population density, tourism, water bodies, agricultural land-use, etc.), which needs to be considered. This argues in favour of considering epidemiological data from a more interdisciplinary perspective by including demographic, environmental, social and economic driving factors in analysis and modelling.
Iulia Martina Bulai
(MEPI)
University of Basilicata
"Modeling COVID-19 considering asymptomatic cases and avoid contacts"
World Health Organization (WHO) defined coronaviruses (CoV) as a large family of viruses that cause illness ranging from the common cold to more severe diseases such as Middle East Respiratory Syndrome (MERS-CoV) and Severe Acute Respiratory Syndrome (SARS CoV).The novel coronavirus (Covid-19) is a new strain that has not been previously identified in humans. Coronaviruses are zoonotic, meaning they are transmitted between animals and people. In this work is presented a mathematical model that describes the transmission of Covid-19. The model considers both symptomatic and asymptomatic cases. Several studies showed the importance of asymptomatic people in the disease transmission. This is a predictive model, we look at different scenarios, first of all assuming any prevention to avoid the diffusion of the virus is taken and secondly different scenarios where precautionary measures to avoid contact between people are taken, such as quarantine and social distancing. We consider a measures to contain the disease, already studied for a predator-prey systems with the disease in the prey population assuming that the infection rate can be decreased avoiding contacts between preys (people in our case). From the numerical results we get that avoiding contacts helps to delay the peak of the maximum number of infected people, that is important in those cases where the hospital system does not have enough seats in the intensive care unit. Furthermore we studied how the reproduction number depends on the parameters values of the model. Some of the parameters are fixed, as found in literature for Italy, while other are used as control parameters.
Jahedi Sana
(MEPI)
University of New Brunswick
"When the best pandemic models are the simplest"
As a pandemic of coronavirus spreads across the globe, people debate policies to mitigate its severity. Many complex, highly detailed models have been developed to help policy setters make better decisions. However, the basis of these models is unlikely to be understood by non-experts. We describe the advantages of simple models for covid-19. We say a model is ' simple' if its only parameter is the rate of contact between people in the population. This contact rate can vary over time, depending on choices by policy setters. Such models can be understood by a broad audience, and thus can be helpful in explaining the policy decisions to the public. They can be used to evaluate outcomes of different policy strategies. However, simple models have a disadvantage when dealing with inhomogeneous populations. To augment the power of a simple model to evaluate complicated situations, we add what we call 'satellite' equations that do not change the original model. For example, with the help of a satellite equation, one could know what his/her chance is of remaining uninfected through the end of epidemic. Satellite equations can model the effect of the epidemic on high-risk individuals, or death rates, or on nursing homes, and other isolated populations. To compare simple models with complex models, we introduce our 'slightly complex' Model J. We find the conclusions of simple and complex models can be quite similar. But, for each added complexity, a modeler may have to choose additional parameter values describing who will infect whom under what conditions, choices for which there is often little rationale but that can have a big impact on predictions. Our simulations suggest that the added complexity offers little predictive advantage.
Jayrah Bena E Riñon
(MEPI)
University of the Philippines Diliman and Bicol University
"A Mathematical Model and Optimal Control of Schistosomiasis in Agusan del Sur, Philippines"
Schistosomiasis, a parasitic disease caused by extit{Schistosoma japonicum}, is one of the neglected tropical diseases and remains endemic in the Philippines, covering 28 provinces in 12 regions. Unlike other species of extit{Schistosoma}, extit{Schistosoma japonicum} is a zoonotic parasite which infects other mammalian hosts aside from humans. With that nature of the parasite, we construct a mathematical model to study the transmission dynamics of schistosomiasis in Agusan del Sur, Philippines. Here, we consider humans and carabaos as definitive hosts, and snails as intermediate hosts. We conduct stability analysis on the proposed model, and calculate for the basic reproduction number, $R_0$. We also perform sensitivity analysis using the Latin hypercube sampling combined with partial rank correlation coefficient technique to investigate how the number of infected humans is affected by the changes in model parameters. Using the available Philippine schistosomiasis data from the Department of Health, we estimate some model parameters. Finally, we apply optimal control theory to determine optimal strategies to control and prevent the spread of schistosomiasis in the country, which may eventually lead to the elimination of the disease.
Jim Greene
(MEPI)
Clarkson University
"A novel COVID-19 model reveals unexpected consequences of social distancing strategies"
Early 2020 saw the onset of the COVID-19 pandemic. As of July 14, 2020, there have been over 13 million confirmed cases worldwide, which have caused over 570K fatalities; in reality, the numbers are almost certainly much higher. As a vaccine has yet to be developed, social distancing as a form of a Nonpharmaceutical Intervention (NPI) has been enacted in many countries as a means of reducing the spread of the virus. Understanding the effects of social distancing to hopefully “flatten the curve” is fundamentally important in the design of reopening policies. In this work, we introduce a framework which explicitly models socially distanced populations via separate compartments: distancing regulations are modeled by flow rates between the distanced and non-distanced populations, and the overall reduction in transmissions due to distancing is also incorporated. In this way, both the response to distancing guidelines and their stringency can be explicitly modeled, and thus the control problem can be thought of as having two inputs from a policy-design perspective. We note that many authors have studied the control problem via reduction in transmission rate, whereas flow rate control has not been sufficiently analyzed; the latter is a focus of the current work. We compute the basic reproduction number R0, which characterizes the initial outbreak of the infection, and demonstrate that at sufficiently early stages of the pandemic when there is little immunity in the population, a quick implementation of social distancing is required in order for R0<1. We also find that R0 is sensitive to the fraction of infected individuals who become symptomatic (currently highly uncertain), illustrating the importance of obtaining a confident measurement of this value before quantitative model predictions can be trusted. Similarly, as it is currently unknown how infective asymptomatic carriers are, we investigate the dependence of R0 on distancing regulations (both flow rate and transmission reduction) as a function of the asymptomatic infection rate. Dynamic simulations of time-varying distancing guidelines also provide surprising results. We discover a critical implementation delay in issuing separation mandates. That is, there is a nontrivial but tight “window of opportunity” for commencing social distancing in order to meet the capacity of healthcare resources. Different relaxation strategies are also simulated. Periodic relaxation policies suggest a schedule which may significantly inhibit peak infective load, but that this schedule is very sensitive to parameter values and the schedule’s frequency. Furthermore, we consider the impact of steadily reducing social distancing measures over time. We find that a too-sudden reopening of society may negate the progress achieved under initial distancing guidelines (which is unfortunately playing out in real-time in the U.S.), but the negative effects can be mitigated if the relaxation strategy is carefully designed.
Jordy Jose Cevallos Chavez
(MEPI)
Arizona State University
"Mobility impact in the spreading of COVID-19 in Ecuador "
Ecuador has reported one of the highest per capita death rates of COVID-19 in the world, with more than 5000 deaths in a country of approxi-mately 17 million people. Transmission of COVID-19 infection in Ecuador has been the result of contact patterns, mobility structure of the population, regional epidemiology, and efficacy of public health interventions. In this study, we link provincial-level demographic, epidemiological, and transportation information with the spread of COVID-19 outbreak to understand the role of local patterns of low and high-density provinces on the infection growth rate at the country level. The analysis is carried out using best (with no interprovincial movement) and worst (with movement patterns similar to before COVID-19 outbreak) case scenarios in Ecuador. The results suggest that human movement (instead of local epidemiology) has primarily been shaping transmission dynamics of COVID-19 in Ecuador by introducing infected individuals regularly into low-risk provinces.
Kellen Myers
(MEPI)
Tusculum University
"Resource Limitations and Household Economics in Outbreaks"
Epidemiological models have been employed with great success to explore the efficacy of alternative strategies at combating disease outbreaks. These models have often incorporated an understanding of age-based susceptibility and severity of outcome, considering how to limit the adverse outcomes or disease burden relative to an age structure. Such models frequently recommend the preferential treatment/vaccination of children or elderly, demonstrating how prevention of serious disease within these etiological subgroups can provide both protection within the subgroup itself and indirect protection to the broader population.
However, it is most frequently the case that these target populations are consumers, rather than providers, of household resources. In areas of the globe where continued health of household members relies on continued provision of resources, these models may fail to provide the most effective overall strategies for health outcomes in both target populations and overall. This is particularly important for tropical diseases impacting rural and low-income areas in which the disease may be endemic or newly emergent, particularly in the wake of natural disasters.
We propose a modified SIR model with targeted treatment in resource-limited populations. We evaluate the model over a broad parameter space. This model demonstrates how economic limitations may shift the optimal strategy. It may be advantageous to treat populations at lesser direct risk if they are responsible for providing secondary protection to higher-risk population(s) by producing household resources. Evaluation of this model over the parameter space reveals that, in some cases, targeting treatment towards consumers may result in greater numbers of consumer infections.
Our results demonstrate how household resource limitation can, in certain regions of the parameter space, drastically affect the impact of targeted treatment strategies for limiting epidemics. Depending on the economic circumstances, it is possible that focusing treatment on consumers such as children can produce a counter-intuitive outcome in which more children contract the disease.
Kelly R Buch
(MEPI)
University of Tennessee Knoxville
"Mathematical Model of Basal Sprout Production in Response to Laurel Wilt"
Laurel wilt is fatal fungal tree disease vectored by the invasive Redbay Ambrosia Beetle (RAB). Redbay trees and sassafrass trees are both susceptible to the fungal disease, and upon infection both provide suitable host material for RAB. Each of these two species responds differently to the fungal infection, with only redbay trees producing shoots that grow from the root system, called basal sprouts, and thus providing further potential host material for RAB. Using a stage structured SI model, we will explore the effect of basal sprout production on boom and bust disease cycles and the establishment of RAB. We interpret our results to provide insight on the circumstances which lead to Laurel wilt becoming endemic or local extinction of Sassafras and Redbay trees, which is vital for disease control.
Koushik Garain
(MEPI)
"Treatment control is one of the most important factor to reduce the spread of COVID-19 epidemic"
On 31st December 2019, China first reported WHO about a unknown disease and on 11th February 2020, WHO announced the name COVID-19. On 11th March 2020, WHO declared COVID-19 (Novel Coronavirus) as a pandemic. It is the global health crisis in this time and is the biggest challenge we have faced since world war two. To curb the spread of COVID-19, most of the countries implemented lockdown but the pandemic is still growing significantly. Our aim is to show that lockdown is one factor only to reduce transmission of the diseases but one more important factor is treatment control. In this paper, we propose a SIRS model with a treatment function. In this model, we have determined the basic reproduction number R0, which is inversely proportional to the treatment capacity. We can control the outbreak of COVID-19 when the basic reproduction number is less than one. We will show that increasing the maximum capacity we can stop the disease. Example of China shows that treatment is playing a bigger role, China set up a special 1000 bed hospital in just 10 days. Lockdown and quarantine are not sufficient and increasing the capacity of treatment to maximum is suggested to decrease the infective population.
Lucas Boettcher
(MEPI)
UCLA
"Unifying continuous, discrete, and hybrid susceptible-infected-recovered processes on networks"
Waiting times between two consecutive infection and recovery events in spreading processes are often assumed to be exponentially distributed, which results in Markovian (i.e., memoryless) continuous spreading dynamics. However, this is not taking into account memory (correlation) effects and discrete interactions that have been identified as relevant in social, transportation, and disease dynamics. We introduce a framework to model continuous, discrete, and hybrid forms of (non-)Markovian susceptible-infected-recovered (SIR) stochastic processes on networks. The hybrid SIR processes that we study in this paper describe infections as discrete-time Markovian and recovery events as continuous-time non-Markovian processes, which mimic the distribution of cell cycles. Our results suggest that the effective-infection-rate description of epidemic processes fails to uniquely capture the behavior of such hybrid and also general non-Markovian disease dynamics. Providing a unifying description of general Markovian and non-Markovian disease outbreaks, we instead show that the mean transmissibility produces the same phase diagrams independent of the underlying inter-event-time distributions.
Marilin Nathalya Guerrero Laos
(MEPI)
Universidad de Nariño
"Approach and analysis of a mathematical model in ordinary differential equations, applied to HIV transmission, considering protection strategies."
Throughout the years, since 1981 approximately, the virus HIV marked its presence in the humanity razing with a large number of lives in which children, teenagers, and adults were involved. Although the rates of death caused by HIV have reduced notably because of antiretroviral drugs, the HIV continues spreading in the population. Due to above, in this research HIV spreading is modelled, in special in the city of Pasto, Nariño in Colombia, where thanks to the review of data provided by the NDHI (Nariño departmental health institute) was evident that in recent years, exactly between 2008 and 2018 the number of infected people increased. Then, this fact lead the study of the dynamics of HIV transmission in Pasto, where is necessary a search for information of strategies applied to control the infection, which give bases to propose a mathematical model which initially describes the dynamics of transmission of said epidemic and, finally, it will have a theoretical control incorporated based on sex education campaigns, which pretends to maximize the number of protected people against HIV and clearly avoid the number of people with HIV increases.
Martin Lopez-Garcia
(MEPI)
School of Mathematics, University of Leeds
"Exact approaches for the analysis of stochastic epidemic processes on small networks"
This research work is framed within the area of modelling hospital-acquired infections. I will introduce a number of existing compartmental-based approaches for modelling the spread of (typically antibiotic resistant) bacteria in hospital settings. Mathematical models with a relatively small number of compartments can be used for representing the spread of bacteria across patients and healthcare workers (HCWs), including relevant factors such as environmental contamination. However, more complex approaches (i.e., models with a large number of compartments, or network-based representations) are needed for example when introducing spatial considerations or HCW-patient contact network structures. When looking at network-based approaches, I will show some recent work on analysing exactly these epidemic dynamics on small networks. When considering an SIR epidemic process on a network, this analytic and computational approach amounts to the analysis of the exact 3^N-states continuous-time Markov chain (CTMC), and makes special focus on algorithmic aspects and the organisation of the space of states S=(S,I,R)^N. Finally, I will present some recent results on the applicability of graph-automorphism lumping techniques in these systems.
Michael Pablo
(MEPI)
University of California, San Francisco | Gladstone Institutes
"Early-phase decoupling between population mobility and death rates"
Reductions in human mobility have been a major strategy in controlling COVID-19 transmissions. However, analysis of publicly available data has revealed decreases in COVID-19 death rates that precede mobility changes. This suggests that, in some regions, there are mobility-independent factor(s) slowing COVID-19 deaths. Given the disproportionate impact that COVID-19 has had among nursing homes both in the US and in other countries, we hypothesized that this high-risk population might have dominated early changes in mortality rate. Simulations of a two-population SEIRD model, where one population is more vulnerable, reveal that early-phase decoupling may occur if susceptible individuals in the more vulnerable population are depleted before mobility changes can occur. More work is needed to determine whether mortality in nursing homes explains regional early-phase decoupling.
Miller Orlando Cerón
(MEPI)
Universidad de Nariño
"Mathematical model with carriers and general non-linear incidence rate"
We analyzed a mathematical model with asymptomatic and a general incidence. We show that there are two equilibrium points and by means of conditions imposed on the functions involved in the non-linear incidence we show the global stability of the equilibrium points by Lyapunov direct method.
Moacyr A H B Silva
(MEPI)
EMAp/FGV
"A death-based mathematical model of the ongoing COVID-19 pandemic"
ASICRD model —Susceptible, Infectious, Critically infectious, Removed and Dead was employed to model COVID-19. While the model is certainly very simple, it captures important early dynamics of diseases such as Covid-19. The model is calibrated for the deaths in the linear phase, which turns out to be a 2x2 linear system. The calibration can be done without any knowledge of the model parameters and allows for a universal fitting over the linear phase.As expected the fitted linear model has the first eigenvalue positive, while the second eigenvalue λ 2 is negative, but otherwise free. It turns out, however, that λ 2 ∈ B ⊂ (−∞,0), where B is a compact interval. For each choice of λ 2 we have a distinct value of0. For this model0(λ2) is monotonic in B. This allows for a bracketing of the possible values of 0. For all choices of the remaining free parameters, the linear dynamics is indistinguishable — though the nonlinear dynamics will be different. Another interesting point is that, once the fitting is done, the non-linear dynamics can be described by a one parameter family of sub-models. This allows for a convenient description of the epidemic evolution scenarios. (This is a joint work by Moacyr Silva, Helio Schechtman and Max O Souza)
Muhammad Said
(MEPI)
"Sensitivity and stability analysis of an Ebola Virus disease and GB virus C co-infection."
In this work, we propose a nonlinear mathematical model to study the transmission dynamics of the Ebola Virus Disease(EVD) and the Hepatitis G virus (GBV) co-infection. The basic reproductive number is found by the next-generation matrix method. Then the infectious free and endemic equilibrium of the system is computed. The local and global stability of the system is presented as well. For local asymptotical stability, linearization, and Routh-Hurwitz criterion and show that if R_0<1, then the system is locally asymptotically stable otherwise unstable. The global asymptotical stability is found out by the Lyapunov function method. Finally, we present a numerical simulation of the proposed model.
Muhammad Humayun Kabir
(MEPI)
Jahangirnagar University
"Model-aided Understanding of the Outbreak of COVID-19 in Bangladesh"
In this talk, we focus on a seven compartmental model to understand the infectious dynamics of COVID-19 pandemic. We show the boundedness and non-negativity of solutions of the model. We analytically calculate the basic reproduction number of the model and perform the stability analysis at all equilibrium points to understand the epidemic and endemic cases based on the results of the basic reproduction number. Our results reveal that regional lockdown and social awareness (e.g., wearing a face mask, washing hands, social distancing) can reduce the pandemic of the current outbreak of novel coronavirus in a most densely populated country like Bangladesh.
Pamela Kim N Salonga
(MEPI)
University of the Philippines Diliman
"A mathematical model of the dynamics of lymphatic filariasis in Caraga Region, The Philippines"
Despite being one of the first countries to implement mass drug administration (MDA) for elimination of lymphatic filariasis (LF) in 2001 after a pilot study in 2000, the Philippines is yet to eliminate the disease as a public health problem with 6 out of the 46 endemic provinces still implementing MDA for LF as of 2018. In this work, we propose a mathematical model of the transmission dynamics of LF and its elimination using MDA in the Philippines. Using the computed basic reproduction number R0, we show that the disease-free equilibrium E0 of the model system is locally asymptotically stable when R0 < 1 and unstable when R0 > 1, whereas the endemic equilibrium E* is locally asymptotically stable when R0 > 1. Sensitivity analysis using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient method suggests that the infected human population is most sensitive to the treatment parameters. Using the available LF data in Caraga Region from the Philippine Department of Health (DOH), we estimate the treatment rates r1, r2 using the least squares parameter estimation technique. Finally, we apply optimal control theory with the objective of minimizing the infected human population and the corresponding implementation cost of MDA, using the treatment coverage γ as the control parameter. Simulation results highlight the importance of maintaining a high MDA coverage per year to effectively minimize the infected population by the year 2030. This work is envisioned to be protocol-directing and policy-making. As there are still several endemic areas in the Philippines and other tropical countries in the Southeast Asia and Western Pacific regions, this study could help the DOH and other ministries of health in designing more effective implementation approaches for MDA to achieve LF elimination in the near future.
Paul D Alexander
(MEPI)
"Treatment of Viral Co-Infections"
Previous reports show that it is not uncommon for patients to have two viruses at the same time. At the current time, we do not know how to treat co-infections. In order to test the effects of having these concurrent infections, we simulate the two infections using a mathematical model. We use our model to simulate influenza A virus (IAV) coinfected with respiratory syncytial virus (RSV) and parainfluenza virus (PIV) coinfected with human rhinovirus (hRV). Using the model, we can estimate the co-duration of the viruses, the individual duration, and the peak virus amount for both viruses, both with and without drug treatment of the infections to figure out the best treatment strategies for co-infections. We find that sometimes treating one infection can lead to the lengthening of the other infection.
Paul J Hurtado
(MEPI)
University of Nevada, Reno
"Reproduction Numbers for ODE Models of Arbitrary Finite Dimension: An Application of the Generalized Linear Chain Trick"
The Generalized Linear Chain Trick (GLCT) is a conceptually and practically useful approach for deriving mean field ODE models, since it describes how the structure of mean-field ODE models (and quantities like the basic reproduction number) reflect the assumptions of an often unspecified underlying continuous-time, stochastic state-transition model. In this talk, I will first describe how to generalize an existing ODE model -- such as the SEIR model or Rosenzweig-MacArthur consumer-resource model -- using the GLCT to incorporate non-exponential dwell times (e.g., latent periods in SEIR models, or predator maturation times in consumer-resource models) that are Erlang distributed or, more generally, are phase-type distributed. The phase-type family of distributions are the absorption time distributions for continuous time Markov chains, and include exponential, Erlang, generalized Erlang, and Coxian distributions. Second, I will show how the structure of the resulting ODE model, which is of arbitrary finite dimension, can be exploited to obtain a general expression for the (basic) reproduction number. These results illustrate the utility of the GLCT, not just for model derivation, but also for model analysis and interpretation.
Perminov Dmitrievich Valeriy
(MEPI)
New bandage's materials, Ltd.
"Agent-based models for influenza epidemic dynamics and its decision-making capability"
Agents-based models (ABM) become more and more popular in applied mathematics. During last 15 years a large number of ABM have been created and used in different scientific area (ecology, economy, epidemiology, human behavior to name a few), but in this paper, only ABM for influenza epidemic/pandemic dynamics in cities are considered in detail. Based on a critical review of currently accepted ABM of such special type new ABM has been proposed. Unlike the old ABM, it can be used for analysis of efficiency and cost of all interventions (how for ones had been carried out before and during epidemic or pandemic under consideration and ones that could be implemented but had not been carried out for some reasons). Moreover, under some conditions, new ABM gives us an opportunity to analyze efficiency and cost of different interventions for future oncoming epidemics (first of all pandemics) and to select its optimal combination.
Phebe M. A Havor
(MEPI)
Kwame Nkrumah University of Science and Technology
"Dynamics of disease models with self-diffusion: Case study of Cholera in Ghana"
Modeling with reaction-diffusion systems involves constituents locally transformed into each other by chemical reactions and transported in space by diffusion. With this in mind, the attention to mathematical and disease epidemiology has increased, as disease epidemics have become a predominant worldwide health issue. The case of Vibrio Cholerae (blue-death) is no different especially in a country like Ghana. Factors that affect the transmission of such a disease includes mainly both human and environmental factors. Proposing a Reaction-Diffusion SIR-B mathematical model for Cholera with proliferate stability analysis on the epidemic and endemic equilibrium, that incorporates an environmental reservoir is formulated to capture the movement of human hosts and host organisms in a heterogeneous environment. Findings here are supported by the results of numerical simulations and based on these results, an evolutionary process that involves organism distribution and their interaction of spatially distributed population with local diffusion is presented. Results show that the model dynamics exhibit a diffusion-controlled formation of patterns which attribute to diffusion having a great influence on the spread of the disease.
Prashant K Srivastava
(MEPI)
IIT Patna
"The impact of information and saturated treatment with time delay in an Infectious disease model"
Here we propose a mathematical model with a saturated treatment rate in the presence of information. We consider that the information about the disease affects the transmission rate of infection and hence the transmission rate is corrected. We also assume that people are losing their immunity against disease and the model is of SIRS type. We analyse the stability of the model system and our analysis shows that the model possesses the existence of backward bifurcation and multiple endemic steady states. Various situations of multiple endemic equilibrium points are explored numerically. Further, we extend the model to include the time lags in information and we found that in presence of time delay, the endemic steady state destabilizes and oscillations are observed. Thus, we conclude that if information dissemination is delayed beyond a threshold time then the infection oscillates in population and it may lead to difficulty in controlling the disease. Also, nonlinear incidence rate and saturated treatment may cause the existence of multiple endemic equilibrium and hence leads to complex dynamics.
Rebecca H Chisholm
(MEPI)
La Trobe University
"A model of population dynamics with complex household structure and mobility: implications for transmission and control of communicable diseases"
Households are known to be high-risk locations for the transmission of communicable diseases. Numerous modelling studies have demonstrated the important role of households in sustaining both communicable diseases outbreaks and endemic transmission, and as the focus for control efforts. However, these studies typically assume that households are associated with a single dwelling and have static membership. This assumption does not appropriately reflect households in some populations, such as those in remote Australian Indigenous communities, which can be distributed across more than one physical dwelling, leading to the occupancy of individual dwellings changing rapidly over time. In this study, we developed an individual-based model of an infectious disease outbreak in communities with demographic and household structure reflective of a remote Australian Indigenous community. We used the model to compare the dynamics of unmitigated outbreaks, and outbreaks constrained by a household-focused prophylaxis intervention, in communities exhibiting fluid versus stable dwelling occupancy. Our findings suggest that fluid dwelling occupancy can lead to larger and faster outbreaks, interfere with the effectiveness of household-focused interventions, and may contribute to the considerable burden of communicable diseases in communities exhibiting this type of structure.
Roxana López Cruz
(MEPI)
Universidad Nacional Mayor de San Marcos
"A Coupled Mathematical Model Introducing Biological Control of Dengue"
This work aims to study the dynamical behavior of a dengue epidemics model by introducing biological control. The first model represents the SEIR-SEI model of dengue epidemics and the second model corresponds to coupling a model of biological control. Controlling mosquitoes is considered by an infestation of bacteria that inhibit the transmission of dengue in humans. We determine an analytic expression of replacement ratios that depends on biological control. The results obtained show that the global stability of the disease-free equilibrium is determined by the value of a certain threshold parameter called the basic reproductive number R0 and of the replacement ratios of the biological model RU, RW. The sensitivity analysis shows that the vector to human transmission rate promotes more changes to the biological control system than other parameters. The simulation analysis of the last model showed the efficiency of the biologic control of dengue transmission.
Shohel Ahmed
(MEPI)
University of Alberta
"Global Asymptotic Stability for a Diffusive Opportunistic Diseases Model"
In this study, we consider a spatial infectious disease model under Opportunistic epidemics which allows for the continuous contribution of extracellular compartments. We show that the proposed model has a unique steady state that is asymptotically stable. Using an appropriately constructed Lyapunov functional, we establish its global asymptotic stability. Numerical results obtained through MATLAB simulations are presented to confirm the theoretical findings of this study.
Suzanne Sindi
(MEPI)
UC Merced
"Multiscale Modeling of Protein Aggregation"
Protein aggregation poses major health challenges for humans, but instead confer beneficial phenotypes for yeast. However, experiments on yeast systems necessarily involve multiple scales cell/colony. In this talk, I describe efforts towards linking these scales with mathematical models.
More specifically, propagon counting assays reflect the intracellular amplification process of prion aggregation coupled with cell-division. We model these experiments with generation and aggregate structured population models. Through an inverse problem formulation we attempt to infer the intracellular replication rates of these aggregates.
Thi Minh Thao Le
(MEPI)
Université de Tours
"Quasi-neutral dynamics in a co-infection system with N strains"
Understanding the interplay of different traits in a co-infection system with multiple strains has many applications in ecology and epidemiology. Because of high dimensionality and complex feedbacks between traits, manifested in infection and co-infection, the study of such systems remains a challenge. In the case where the strains are similar (quasi-neutrality assumption), we can model trait variation as perturbations in parameters, which simplifies analysis. Applying perturbation to many parameters at the same time is mathematically not easy. In this study, we advance in this direction. We consider and study such a quasi-neutral model of susceptible-infected-susceptible (SIS) type with N strains and variation in transmission, clearance, and co-colonization traits. The slow-fast dynamics and the Tikhonov's theorem are essential approaches that we use to analyze the system, under the perspective of the replicator equation, where the variables are frequencies of N strains. Coefficients of this replicator system, that inherently are pairwise invasion fitnesses of strains, characterize not only pairwise outcomes but also determine collective behavior. We illustrate the model framework by investigating particularly dynamics with two strains (N=2), and explicitly analyzing different fitness dimensions and their interplay for maintenance and stabilization of diversity.
Thomas N Vilches
(MEPI)
UNICAMP-Brazil
"Assessing the effects of the diagnostic methods on the schistosomiasis dynamics"
Schistosomiasis is a neglected tropical disease that affects around 200 million people worldwide. It is a macroparasite infection, caused by trematode from genus Schistosoma, whose intermediate host is a snail from genus Biomphalaria that is caracteristic of places with fresh water. Moreover, it is estimated that, every year, 100 thousand individuals die due to schistosomiasis-related causes. In Brazil, schistosomiasis is endemic in 13 states and affects around 25 million people that live in risk areas, with 6 million infected individuals (estimated).
Its biological cycle is very complex, having five different life stages: egg, miracidium, sporocyst, cercaria and schistosomula, which makes its control even more difficult. The recomended diagnostic method, named Kato-Katz, seeks for eggs in the individual's feces and does not have a high sensitivity. In 2007, a group of researchers developed a new method, named Helmintex, that uses paramagnetic markers to find the eggs in feces and showed to be three times more sensitive than Kato-Katz.
We sought to investigate the effects on the schistosomiasis dynamics of applying a mass diagnostic strategy, the idea is that infected individuals, who are diagnosed, are treated. In order to do that, we build an ordinary differential equations model that considers: a human population divided in susceptible individuals and three classes of infected people that represent different levels of worm burden; a snail population, susceptible and infected, and a miracidium reservoir, that is important in order to take in to account the reinfection effects of the highest level of worm burden. The cercaria dynamics is implicitly considered through the human infection parameters.
We performed the equilibrium and local stability analysis for different scenarios in order to compare the results. (i) First, considering that a more sensitive diagnostic method, the Helmitex, is applyed, setting to zero the human population in the two highest levels of worm burden; (ii) considering that a less sensitive method, the Kato-Katz, is applyed, setting to zero only the highest level of worm burden; and the last case, (iii) the complete model that represents the scenario in which there is no treatment/diagnostic strategy.
Our results, besides the conditions for existence and local stability of the endemic equilibrium points, suggest that the low sensitivity of the classic method can explain the why it is so difficult to control the infections and why, usually, after stop the treatment on a population, or precaution strategies, the infection prevalences returns to a high level.
Tiffany Leung
(MEPI)
Fred Hutch
"Evaluating the effectiveness of social distancing interventions: delaying the epidemic or flattening the curve?"
In March 2020, the World Health Organization declared coronavirus disease a pandemic. We used a mathematical model to investigate the effectiveness of social distancing interventions in a mid-sized city. Interventions reduced contacts of adults >60 years of age, adults 20–59 years of age, and children <19 years of age for 6 weeks. Our results suggest interventions started earlier in the epidemic delay the epidemic curve and interventions started later flatten the epidemic curve. We noted that, while social distancing interventions were in place, most new cases, hospitalizations, and deaths were averted, even with modest reductions in contact among adults. However, when interventions ended, the epidemic rebounded. Our models suggest that social distancing can provide crucial time to increase healthcare capacity but must occur in conjunction with testing and contact tracing of all suspected cases to mitigate virus transmission.
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Virtual conference of the Society for Mathematical Biology, 2020.
