Stochastic Mathematical Modelling Study for Understanding the Extinction, Persistence and Control of SARS-CoV-2 Virus at the Within-host Level

Abstract: Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the system or the environmental noise. In this paper, we analyze the stochastic within host compartment model for SARS-CoV-2 virus and explore its dynamics. We first examine the existence and positivity of the solution of the model using Ito's formula and the establish the stochastic boundedness and permanence of the model. Exponential stability of the infection free equilibrium state is established. Numerical simulations are conducted to complement the theoretical results. Environmental noise is found to play a crucial role in the dynamics of the disease and can even lead to the extinction of the disease. The model is also extended to a stochastic optimal control problem and the effectiveness of control measures, such as antiviral drugs and immunomodulators is investigated.