Mathematical modelling and analysis of stochastic cholera and HIV co-infection model

Cholera and HIV are two major infectious diseases that often coexist and result in severe health outcomes. In this paper, we propose a co-infection model for the transmission dynamics of cholera and HIV to explore the distinctive correlation between these two diseases. Firstly, we analyze the sub-models at their steady states and calculate the basic reproduction number of the sub-models and co-infection model. Secondly, the proposed stochastic co-infection model has been investigated for the existence and uniqueness of a global solution, stationary distribution and ergodicity for the co-infection stochastic model are also studied by constructing stochastic Lyapunov candidates. At last, numerical simulations are carried out to validate theoretical results.