https://doi.org/10.1140/epjp/s13360-023-04122-x
Regular Article
Modeling the mechanisms of methamphetamine abuse transmission with immigration impact and relapse
1
Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Multan, Pakistan
2
CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
3
Department of Mathematics and Statistics, University of Swat, District Swat, Swat, Khyber Pakhtunkhwa, Pakistan
Received:
5
April
2023
Accepted:
20
May
2023
Published online:
1
June
2023
Drug addiction is a neurological disorder, and it can be studied using mathematical modeling and computer simulations. The usage of methamphetamine is on the rise globally and has reached an epidemic level. Researchers have focused a lot of attention on the epidemic’s social repercussions. A model describing the dynamics of methamphetamine is introduced in the present research endeavor. The process of the abuse extinction is investigated using the harmonic mean kind of uptake function. Both local and global dynamics near feasible equilibrium points have been explored. The obtained results are illustrated via some examples equipped with graphical expressions. Also, sensitivity analysis for the basic reproduction number is presented. Additionally, the second model examines the impact of immigrants on each compartment of the problem under consideration. The subsequent model takes the immigrant effect into account, so there is no disease-free equilibrium in this case, as the system allows for the immigration of infected individuals. Lastly, the effect of relapse in the susceptible class from the recovered class is also studied in the succeeding third new model. The stability analysis-related results are demonstrated analytically as well as graphically.
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