Global Transmission Dynamics of a Schistosomiasis Model and Its Optimal Control
Global Transmission Dynamics of a Schistosomiasis Model and Its Optimal Control作者机构：Laboratoire d’Analyse Numérique et d’Informatique (LANI) UFR SAT Université Gaston Berger de Saint-Louis Saint-Louis Sénégal UFR AGRO Université Gaston Berger de Saint-Louis Saint-Louis Sénégal LANI Pô le STN MAI (Mathématiques Appliquées et Informatique) Université Virtuelle du SENEGAL Dakar-Fann Sénégal
出 版 物：《Applied Mathematics》 (应用数学（英文）)
年 卷 期：2019年第10卷第6期
页 面：397-418页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Schistosomiasis Models Nonlinear Dynamical Systems Global Stability Reproduction Number Optimal Control Sensitivity Analysis
摘 要：Drug treatment, snail control, cercariae control, improved sanitation and health education are the effective strategies which are used to control the schistosomiasis. In this paper, we consider a deterministic model for schistosomiasis transmission dynamics in order to explore the role of the several control strategies. The global stability of a schistosomiasis infection model that involves mating structure including male schistosomes, female schistosomes, paired schistosomes and snails is studied by constructing appropriate Lyapunov functions. We derive the basic reproduction number R0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R0. We show that the disease can be eradicated when R0?≤1;otherwise, the system is persistent. In the case where ?R0?1, we prove the existence, uniqueness and global asymptotic stability of an endemic steady state. Sensitivity analysis and simulations are carried out in order to determine the relative importance of different control strategies for disease transmission and prevalence. Next, optimal control theory is applied to investigate the control strategies for eliminating schistosomiasis using time dependent controls. The characterization of the optimal control is carried out via the Pontryagins Maximum Principle. The simulation results demonstrate that the insecticide is important in the control of schistosomiasis.
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