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)
Maku Vyambwera, Sibaliwe and Witbooi, Peter
"A Two-Group Model of TB in a Crowded Environment,"
Applied Mathematics & Information Sciences: Vol. 15
, Article 15.
Available at: https://dc.naturalspublishing.com/amis/vol15/iss4/15