Narrow Results

In this paper, we propose a stochastic cholera model that incorporates media coverage and two time delays driven by Lévy noise in order to deeply understand the propagation process of cholera in the real world, generalized nonlinear incidence rates ${\beta }_1(M)$ and ${\beta }_2(M)$ are also introduced. First, we discuss the existence and uniqueness of the global positive solution of the stochastic model by using the Lyapunov method. Moreover, the dynamic properties of stochastic solution around the disease-free and endemic equilibria are demonstrated. At last, we present numerical simulation results to reveal how Lévy jumps, time delays and media coverage affect the asymptotic properties of the stochastic model.

We propose a multi-scale modeling framework to investigate the transmission dynamics of cholera. At the population level, we employ a SIR model for the between-host transmission of the disease. At the individual host level, we describe the evolution of the pathogen within the human body. The between-host and within-host dynamics are connected through an environmental equation that characterizes the growth of the pathogen and its interaction with the hosts outside the human body. We put a special emphasis on the within-host dynamics by making a distinction for each individual host. We conduct both mathematical analysis and numerical simulation for our model in order to explore various scenarios associated with cholera transmission and to better understand the complex, multi-scale disease dynamics.