Stability and Optimal Control of an Mathematical Model of Tuberculosis/AIDS Co-infection with Vaccination | Chapter 3 | New Ideas Concerning Science and Technology Vol. 11

 The analysis and control of a nonlinear mathematical epidemic model (S S_vih V E LI ) based on a system of ordinary differential equations modelling the spread of tuberculosis infectious with VIH/AIDS coinfection are the subject of this paper. The existence of both disease-free and endemic equilibrium is debated. R₀ is the reproduction number that has been calculated. We investigate the stability of epidemic systems around equilibriums using Lyapunov-Lasalle methods (Disease free and endemic equilibrium). The disease-free equilibrium's global asymptotic stability is proven whenever R_vac < 1, where R₀ is the reproduction number. We also show that Tuberculosis can be eradicated when R0 is less than one. To validate analytic data, numerical simulations are used. To achieve disease prevention by reducing the infectious group to the lowest level of vaccine coverage possible. There is a formulation of a control problem. The optimal control is defined using the Pontryagin's maximum theory. The Runge Kutta fourth method is used to extract and solve the optimality system numerically.

Author (s) Details

Leontine Nkague Nkamba
Department of Mathematics, University of Yaound´e I, Higher Teacher Training College, P.O. Box 47 Yaound´ e, Cameroon and AIDEPY Association des Ing ´enieurs Diplom´es de l’Ecole Polytechnique de Yaound´ e, Cameroon.

Thomas Timothee Manga
AIDEPY Association des Ing ´enieurs Diplom´es de l’Ecole Polytechnique de Yaound´ e, Cameroon.

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