A stochastic TB model for a crowded environment
Loading...
Date
2018
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi
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 thebasic reproductionnumber andprove the stabilityof thedisease-free equilibriumwhen it
is below unity or slightly higher than unity and the perturbation is small. Ourmain 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.
Description
Keywords
Population dynamics, Tuberculosis, Crowded environments, Camps, Prisons
Citation
Vyambwera, S.M. & Witbooi, P. (2018). A stochastic TB model for a crowded environment. Journal of Applied Mathematics, 2018: 3420528