A stochastic model for COVID-19 with a highly effective vaccine

Mozart Umba Nsuami, Peter Joseph Witbooi

Abstract


We propose a stochastic model for the population dynamics of COVID-19 with vaccine. The model allows for waning immunity. We start off with a deterministic model in terms of ordinary differential equations (ODEs), which afterwards are stochastically perturbed to form a system of stochastic differential equations (SDEs). The ODE system and the SDE system have global positive solutions. We discuss the equilibrium points of the ODE system. For the SDE model we obtain a stability result in terms of almost sure exponential stability theorem for the disease-free equilibrium of the stochastic model. Our theoretical results are illustrated by numerical simulations.

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Published: 2021-10-04

How to Cite this Article:

Mozart Umba Nsuami, Peter Joseph Witbooi, A stochastic model for COVID-19 with a highly effective vaccine, J. Math. Comput. Sci., 11 (2021), 7754-7772

Copyright © 2021 Mozart Umba Nsuami, Peter Joseph Witbooi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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