Impact of Hygiene, Famine and Environment on Transmission and Spread of Cholera

Cholera is a bacterial disease caused by the bacterium Vibrio cholerae that requires optimal temperature and environmental conditions to survive. It is well known that climate change, influence of ecology, flood and droughts can affect the concentration of the bacterium in the environment. The goal of this article is to establish the effects of hygiene, famine, climate and environment on the transmission and spread of cholera. The transmission dynamics of the disease are modeled with a non-autonomous system of ordinary differential equations that is coupled to a model of intra-annual variation of Vibrio cholerae in the environment. When the intra-annual variation of Vibrio cholerae is not incorporated into the model, this latter becomes autonomous and we then give an explicit formulation of the basic reproductive number. In the non-autonomous case, we make analytically explicit two thresholds that allow to exhibit cases where disease extinction otherwise disease uniform persistence may occur. Finally, some numerical simulations allow to study the evolution of the cholera spread according the different environmental factors.