Threshold dynamics of stochastic cholera epidemic model with direct transmission

This paper extends the cholera human-to-human direct transmission model from a deterministic to a stochastic framework. This is expressed as mixed system of stochastic and deterministic differential equations. A Lyapunov function is created to investigate the global stability of the stochastic cholera epidemic, which shows the existence of global positivity of the solution using the theory of stopping time. We then find the threshold quantity of the extended stochastic cholera epidemic model. We derive a parametric condition Re0, and for additive white noise, we establish sufficient conditions for the extinction and the persistence of the cholera infection. Finally, for a suitable choice of the parameter of the system for Re0, we perform numerical simulations for both scenarios of extinction and persistence of the dynamic of the cholera infection.

Automated summary

This paper extends the cholera human-to-human direct transmission model to a stochastic framework. A Lyapunov function is used to investigate the global stability of the stochastic cholera epidemic, and the threshold quantity of the extended model is found. Sufficient conditions for the extinction and persistence of the cholera infection are established using the theory of stopping time. Numerical simulations are performed to analyze the scenarios of extinction and persistence of the dynamic of the cholera infection.