Main Article Content
Mycobacterium tuberculosis is the causative agent of Tuberculosis in humans [1,2]. A mathematical model that explains the transmission of Tuberculosis is developed. The model consists of four compartments; the susceptible humans, the infectious humans, the latently infected humans, and the recovered humans. We conducted an analysis of the disease-free equilibrium and endemic equilibrium points. We also computed the basic reproduction number using the next generation matrix approach. The disease-free equilibrium was found to be asymptotically stable if the reproduction number was less than one. The most sensitive parameter to the basic reproduction number was also determined using sensitivity analysis. Recruitment and contact rate are the most sensitive parameter that contributes to the basic reproduction number. Ordinary Differential Equations is used in the formulation of the model equations. The Tuberculosis model is analyzed in order to give a proper account of the impact of its transmission dynamics and the effect of the latent stage in TB transmission. The steady state's solution of the model is investigated. The findings showed that as more people come into contact with infectious individuals, the spread of TB would increase. The latent rate of infection below a critical value makes TB infection to persist. However, the recovery rate of infectious individuals is an indication that the spread of the disease will reduce with time which could help curb TB transmission.
Chavez C, et al. Dynamical models of tuberculosis Castillo and their applications. Math Biosciences and Engineering. 2004;1(2):361-404.
Okosun KO, Makinde OD. A co-infection model of malaria and cholera diseases with optimal control. Mathematical Biosciences. 2014;258:19–32.
Nidhi Nirwani, Badshash VH, Khandelwal R, Porwal P. A model for transmission dynamics of Tuberculosis with endemic equilibrium. International Journal of Mathematical Achieve. 2014;5(5): 47-50.
Kazeem Oare Okosun, Mukamuri M, Daniel Oluwole Makinde. Global stability analysis and control of leptospirosis. Open Mathematics. 2016;14(1):567–585.
Nyabadza F, Winkler D. A simulation age-specificc tuberculosis model for the cape town metropole. South African Journal of Science. 2013;109(910): 1-7.
Kalu AU, Inyama SC. Mathematical model of the role of vaccination and treatment on the transmission dynamics of tuberculosis. Gen. Math Notes. 2012;11(1):10-23.
WHO. Reports on guidelines on the management of latent TB infection, 2014 Barcelona.
Yali Yang, Jianquan Li, Zhien Ma, Luju Liu. Global stability of two models within complete treatment for tuberculosis. Chaos, Solitons & Fractals. 2010;43(1-12):79–85.
Herbert W. Hethcote. The mathematics of infectious diseases. SIAM Review. 2000;42(4):599–653.
Pauline Van den Dries Sche, James Watmough. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences. 2002;180(1): 29–48.
Shaibu Osman, Oluwole Daniel Makinde, David Mwangi Theuri. Stability analysis and modelling of listeriosis dynamics in human and animal populations. Global Journal of Pure and Applied Mathematics. 2018;14(1):115–137.
Castillo-Chavez C, et al. Computation of and its role in global stability. In: Castillo-Chavez C et al (Eds) Mathematical approaches for emerging and re-emerging Infectious diseases: An introduction. IMA. 2002;125:229-250.