Mathematical analysis, forecasting and optimal control of HIV/AIDS spatiotemporal transmission with a reaction diffusion SICA model

AIMS Mathematics

article

Houssine Zine¹  Abderrahim El Adraoui²  Delfim F. M. Torres¹ 

[1] Center for Research and Development in Mathematics and Applications ,(CIDMA), Department of Mathematics, University of Aveiro;Laboratory of Analysis Modeling and Simulation ,(LAMS), Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan Ⅱ University of Casablanca

关键词: HIV/AIDS epidemiology;    reaction-diffusion;    spatiotemporal SICA model;    optimal control strategies;    necessary optimality conditions;   

DOI  :  10.3934/math.2022904

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

We propose a mathematical spatiotemporal epidemic SICA model with a control strategy. The spatial behavior is modeled by adding a diffusion term with the Laplace operator, which is justified and interpreted both mathematically and physically. By applying semigroup theory on the ordinary differential equations, we prove existence and uniqueness of the global positive spatiotemporal solution for our proposed system and some of its important characteristics. Some illustrative numerical simulations are carried out that motivate us to consider optimal control theory. A suitable optimal control problem is then posed and investigated. Using an effective method based on some properties within the weak topology, we prove existence of an optimal control and develop an appropriate set of necessary optimality conditions to find the optimal control pair that minimizes the density of infected individuals and the cost of the treatment program.

【 授权许可】

CC BY