Modeling the within-host dynamics of cholera: bacterial–viral interaction

Abstract

Novel deterministic and stochastic models are proposed in this paper for the within-host dynamics of cholera, with a focus on the bacterial–viral interaction. The deterministic model is a system of differential equations describing the interaction among the two types of vibrios and the viruses. The stochastic model is a system of Markov jump processes that is derived based on the dynamics of the deterministic model. The multitype branching process approximation is applied to estimate the extinction probability of bacteria and viruses within a human host during the early stage of the bacterial–viral infection. Accordingly, a closed-form expression is derived for the disease extinction probability, and analytic estimates are validated with numerical simulations. The local and global dynamics of the bacterial–viral interaction are analysed using the deterministic model, and the result indicates that there is a sharp disease threshold characterized by the basic reproduction number R0: if R0 < 1, vibrios ingested from the environment into human body will not cause cholera infection; if R0 > 1, vibrios will grow with increased toxicity and persist within the host, leading to human cholera. In contrast, the stochastic model indicates, more realistically, that there is always a positive probability of disease extinction within the human host.