A Two-Group Model of TB in a Crowded Environment

Authors

Sibaliwe Maku Vyambwera, Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South AfricaFollow
Peter Witbooi, Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South AfricaFollow

Author Country (or Countries)

Republic of South Africa

Abstract

In this paper, we introduce a two-group epidemic model of the dynamics of tuberculosis in a prison system. The total population of inmates consists of two groups: The sentenced inmates and those inmates who are awaiting trial. The threshold parameter for local stability is computed and analysed. We also prove the global stability of the disease free equilibrium using a Lyapunov function. We apply the model to South African data on tuberculosis and we observe consistency between the model prediction and the data. Numerical results are presented to illustrate the analytical results.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/150415

Recommended Citation

Maku Vyambwera, Sibaliwe and Witbooi, Peter (2021) "A Two-Group Model of TB in a Crowded Environment," Applied Mathematics & Information Sciences: Vol. 15: Iss. 4, Article 15.
DOI: http://dx.doi.org/10.18576/amis/150415
Available at: https://digitalcommons.aaru.edu.jo/amis/vol15/iss4/15