Controlling heroin addiction via age-structured modeling

Advances in Difference Equations

Anwarud Din¹  Yongjin Li¹ 

[1] Department of Mathematics, Sun Yat-sen University, 510275, Guangzhou, P.R. China;

关键词: Epidemic;    Age-structure;    Weak derivatives;    Optimal control;    49J20;    49J50;    65M06;   

DOI  :  10.1186/s13662-020-02983-5

来源: Springer

【 摘 要 】

The aim of the present study is to consider a heroin epidemic model with age-structure only in the active heroin users. The model was formulated with the help of available literature on heroin epidemic. Instead of treatment as a class, we incorporated recovered population and considered treatment as a control variable and thus a control problem is presented for further analysis. The techniques of weak derivatives and sensitivities were used for obtaining the adjoint equations. The maximum principle of Pontryagin’ type was used for obtaining the optimal value of the control variable. Sample simulations are presented at the end of the study in order to show the effectiveness of the treatment.

【 授权许可】

CC BY