The effect of population migration on the diffusion of cholera outbreaks in metapopulations

Abstract

AbstractIn this study, an improved Susceptible-Infected-Recovered (SIR) epidemic diffusion model for cholera is extended by including migration for susceptible people. This model is applied to a metapopulation that consists of two isolated cities where just susceptible individuals can migrate between the cities. The disease-free equilibrium, the endemic equilibrium points, and the basic reproductive number with unequal migration rates are analyzed for this metapopulation. Firstly, the study showed that the basic reproductive number depends on the migration rates between the cities. Then, showed that when the epidemic SIR system is stable, then the infected cases for cholera outbreak can reach zero in one city, but the infected cases in the other city still can stay positive. Finally, discussed three scenarios that depend on population sizes and migration rates of susceptible people between the cities and showed how important the migration rates are in the diffusion of the cholera outbreak by visualizing these three scenarios.Mathematics Subject ClassificationPrimary: 92B05; Secondary: 92D40