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A Stochastic TB Model for a Crowded Environment
Joint Authors
Maku Vyambwera, Sibaliwe
Witbooi, Peter J.
Source
Journal of Applied Mathematics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-06-13
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Maku Vyambwera, Sibaliwe& Witbooi, Peter J.. 2018. A Stochastic TB Model for a Crowded Environment. Journal of Applied Mathematics،Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1176003
Modern Language Association (MLA)
Maku Vyambwera, Sibaliwe& Witbooi, Peter J.. A Stochastic TB Model for a Crowded Environment. Journal of Applied Mathematics No. 2018 (2018), pp.1-8.
https://search.emarefa.net/detail/BIM-1176003
American Medical Association (AMA)
Maku Vyambwera, Sibaliwe& Witbooi, Peter J.. A Stochastic TB Model for a Crowded Environment. Journal of Applied Mathematics. 2018. Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1176003
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176003