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.