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has been cited by the following article:

• TITLE: Stability and Optimal Control of Tuberculosis Spread with an Imperfect Vaccine in the Case of Co-Infection with HIV

  AUTHORS: Leontine Nkague Nkamba, Thomas Timothee Manga, Noboru Sakamoto

  KEYWORDS: Tuberculosis, Basic Reproduction Number, Global Stability, Prevalence, CD4 Cells, Immune Deficiency, Optimal Control, Optimality, HIV

  JOURNAL NAME: Open Journal of Modelling and Simulation, Vol.7 No.2, March 7, 2019

  ABSTRACT: This paper focuses on the study and control of a non-linear mathematical epidemic model ( SSvihVELI ) based on a system of ordinary differential equation modeling the spread of tuberculosis infectious with HIV/AIDS coinfection. Existence of both disease free equilibrium and endemic equilibrium is discussed. Reproduction number R0 is determined. Using Lyapunov-Lasalle methods, we analyze the stability of epidemic system around the equilibriums (disease free and endemic equilibrium). The global asymptotic stability of the disease free equilibrium whenever Rvac is proved, where R0 is the reproduction number. We prove also that when R0 is less than one, tuberculosis can be eradicated. Numerical simulations are conducted to approve analytic results. To achieve control of the disease, seeking to reduce the infectious group by the minimum vaccine coverage, a control problem is formulated. The Pontryagin’s maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the Runge Kutta fourth procedure.