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2018 A Stochastic TB Model for a Crowded Environment
Sibaliwe Maku Vyambwera, Peter Witbooi
J. Appl. Math. 2018: 1-8 (2018). DOI: 10.1155/2018/3420528

Abstract

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

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Sibaliwe Maku Vyambwera. Peter Witbooi. "A Stochastic TB Model for a Crowded Environment." J. Appl. Math. 2018 1 - 8, 2018. https://doi.org/10.1155/2018/3420528

Information

Received: 19 February 2018; Accepted: 12 May 2018; Published: 2018
First available in Project Euclid: 11 July 2018

zbMATH: 07132101
MathSciNet: MR3817715
Digital Object Identifier: 10.1155/2018/3420528

Rights: Copyright © 2018 Hindawi

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