Stability and Optimal Control of Tuberculosis Spread with an Imperfect Vaccine in the Case of Co-Infection with HIV
Stability and Optimal Control of Tuberculosis Spread with an Imperfect Vaccine in the Case of Co-Infection with HIV作者机构：Department of Mathematics Higher Teacher Training College University of Yaoundé I Yaoundé Cameroon Deustotech Laboratory Chair of Computational Mathematics University of Deusto Bilbao Spain AIDEPY Association des Ingénieurs Diplomés de l’Ecole Polytechnique de Yaoundé Yaoundé Cameroon Faculty of Science and Engineering Department of Mechatronics Nanzan University Nagoya Japan
出 版 物：《Open Journal of Modelling and Simulation》 (建模与仿真（英文）)
年 卷 期：2019年第7卷第2期
页 面：97-114页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Tuberculosis Basic Reproduction Number Global Stability Prevalence CD4 Cells Immune Deficiency Optimal Control Optimality HIV
摘 要：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.
维普期刊数据库