Mathematical modelling of the impact of poverty on cholera outbreaks

Abstract

In this paper, we propose and analyze a coupled disease‐economic model to study the impact of poverty on cholera outbreaks. We consider the stock of capital per effective units of labor, reflecting the effect of the stock of capital on cholera outbreak and transmission. The system has positive bounded solutions. We show that the disease‐free equilibrium is globally asymptotically stable whenever , while when , the disease‐free equilibrium is unstable. The sensitivity analysis of the model has been performed in order to determine the impact of related parameters on outbreak severity. We further study various cases for the investment rate upon critical value of the investment in order to describe the effect of poverty on the infected individuals over time. The results we obtained show that increasing of the stock of capital per effective units of labor and the implementation of strategies combining awareness programs and therapeutic treatments will reduce the proportion of the infected population. To verify our analytical results, the numerical simulations on the model are performed.