Tuberculosis Model with Exogenous Reinfection and Treatment
Ebenezer Appiagyei *
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P.R. China and Department of Mathematics, Valley View University, Techiman Campus, P.O. Box 183 B/A, Ghana.
Mojeeb Al-Rahman El-Nor Osman
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P.R. China and Department of Mathematics and Computer Science, International University of Africa, P.O. Box 2469, Khartoum, Sudan.
Isaac Kwasi Adu
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P.R. China and Department of Mathematics, Valley View University, Techiman Campus, P.O. Box 183 B/A, Ghana.
*Author to whom correspondence should be addressed.
Abstract
The epidemiology of tuberculosis model, which includes exogenous reinfection and treatment, is analyzed. We consider both the diagnosed and the undiagnosed individuals as infectious. Since tuberculosis is treatable, we also included the treatment for diagnosed infective. We presented the basic reproduction number and the stability of the disease-free and endemic equilibria. We also analyzed the model when the exogenous re-infection is set to zero. The exogenous re-infection is shown to be capable of supporting multiple equilibria. Lastly, we presented the global stability and numerical simulations of the model.
Keywords: Next-generation matrix, stability, backward bifurcation, reproduction number