Mathematical spatial compartmental epidemic models for the infectious disease cholera

Abstract

Cholera is an infectious disease caused by the bacterium Vibrio cholerae. Infections can occur directly via contact with infected people, but also indirectly via infected water. Because of these direct, but especially indirect infections, it is useful to investigate the spread of the disease using mathematical epidemic models. In this report a compartmental epidemic model for cholera is discussed: the SIRB model. This model consists of four compartments: susceptibles, infected, recovered and the bacterial concentration in water. The interaction between the groups is given by a system of differential equations. The equilibrium solutions and their stabilityare mathematically analysed. The main focus of this report, however, is on two different spatial models. The patches model consists of multiple patches connected by migration of people. Different measures against cholera are studied using this model. The second spatial model that has been numerically implemented is a diffusion SIRB model. The influence of the diffusion coefficients on the solution patterns will be researched for different initial conditions. The results presented in this report are building blocks for further research into compartmental models that simulate the spatial dynamics of cholera.