Models of Infectious Diseases and Control

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Aurelio de los Reyes, Jonggul Lee

Hyojung Lee

National Institute for Mathematical Sciences, Korea
"Transmission dynamics of Coronavirus disease (COVID19) in Korea"
The novel coronavirus outbreak has rapidly spread out from Wuhan, Hubei Province, China to other countries since December, 2019. More than 2,000 cases have confirmed since the first case was reported on 20 January, 2020 in South Korea. . The aim of this research is to analyze the transmission dynamics of COVID-19 in South Korea during the early phase of the outbreak. To do so, first, using the 30 confirmed cases, we estimated the basic epidemiological parameters from the data of the symptom onset dates by employing maximum likelihood estimation. Second, super-spreading events were occurred in Daegu, Korea from 31 January, 2020. Accounting for the heterogeneous transmission dynamics, we construct the mathematical model to estimate the geographic reproduction number. Finally, we assess the effect of the control interventions by simulating the various control scenarios to suggest the most effective intervention to halt the transmission

Robert Smith?

University of Ottawa
"Assessing potential COVID-19 outcomes for a university campus with and without physical distancing"
By early March of 2020, it became apparent that COVID-19 was going to have a significant impact on institutions throughout society. On March 12, the University of Ottawa commissioned an informal modeling study to aid in their decision-making process. Here we present the results from that study: a differential-equation model was created in order to describe the states of susceptibility, exposure, infection, asymptomatic individuals, recovery and death. Our results shows that, in the worst-case scenario, the epidemic would peak at 7000 cases on campus with 63 dead, starting 115 days after the first case. Reducing contacts by 50% could lower the number of cases and fatalities, but it would expand the timeframe by several years. One day after this modeling study was completed, the University of Ottawa closed campus entirely. It follows that modeling and simulation in the midst of a fast-moving pandemic can be valuable tools for decision-makers.

Aurelio A de los Reyes

Institute of Mathematics, University of the Philippines Diliman
"Intervention strategies to mitigate HIV/AIDS transmission in the Philippines"
Human Immunodeficiency Virus (HIV) impairs a person’s immune system leading to Acquired Immunodeficiency Syndrome (AIDS) – a condition characterized by severe illnesses. The number of HIV infections has more than doubled in the Philippines within the last decade, prompting the need to develop a model of disease transmission in the country. In this study, disease-free and endemic equilibria are obtained, stability analysis is performed, and the basic reproduction number is computed. Available data is utilized to identify model parameters giving insights on the trend of the disease in the country. Furthermore, effectiveness of control measures including precaution, HIV screening, Anti-Retroviral Treatment, and Pre-Exposure Prophylaxis (PrEP) are investigated in the framework of optimal control theory. These various control efforts are compared with regard to cost efficiency and effectivity in minimizing the number of infected individuals. Given limited available control measures, PrEP-only scenario is shown to be most cost effective.

Jonggul Lee

National Institute of Mathematical Sciences, South Korea
"Spatial heterogeneity and control measures during avian influenza epidemic 2014-2015 in Korea"
During the winter of 2014-2015, an epidemic of highly pathogenic avian influenza (HPAI) led to high mortality in poultry and put a serious burden on the poultry industry of the Republic of Korea. Effective control measures considering spatial heterogeneity to mitigate the HPAI epidemic is still a challenging issue. Here we develop a farm-based HPAI model to analyze the spatiotemporal evolution of the epidemic and assess the impact of control strategies. The epidemiological and geographical data of the domestic poultry farms in South Korea are used to find the best-fitted parameters of the model. We investigate potential for two control measures against HPAI: preemptive culling and farm rest. The best culling radius to maximize the final size of the susceptible farms and minimize the total number of culled farms is calculated from the model. The reproductive number of a farm is calculated as an indicator of virus transmission in a given area. Simulation results indicate that this parameter is strongly influenced not only by epidemiological factors such as transmissibility and/or susceptibility of poultry species but also by geographical and demographical factors such as the distribution of poultry farms (or density) and connectivity (or distance) between farms. Based on this result, we suggest the optimal culling radius and number of resting farms with respect to the reproductive number in a targeted area.

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