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Allali, Karam
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Mathematics

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GLOBAL STABILITY OF SPATIO-TEMPORAL MODEL WITH QUARANTINE AND VACCINATION Yaagoub, Zakaria; Sadki, Marya; Allali, Karam
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1452.321-337

Abstract

In this paper, we suggest a spatio-temporal epidemic model for coronavirus. Our model will be represented by a system of six partial differential non-linear equations that describe the dynamics of susceptible, exposed, infected, quarantined, removed, and vaccinated individuals. We will start the study of this model by presenting some results of the existence and uniqueness to the solution of our suggested model. By using the method of next-generation matrix, we obtain the basic reproduction number. The model has one disease-free equilibrium point and another endemic steady state. The global stability of these steady states is proved by using some Lyapunouv functions. Finally, different numerical simulations are given to confirm our results given in the theoretical part of the paper.
ABUSE OF PSYCHOACTIVE DRUGS AND ITS PREVENTION IN A HOST COMMUNITY: MATHEMATICAL ANALYSIS Fadugba, S.E.; Elkaf, Mariem; Allali, Karam
Journal of the Indonesian Mathematical Society Vol. 30 No. 3 (2024): NOVEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.3.1458.385-397

Abstract

In this paper, psychoactive drug abuse and prevention in a host community is illustrated by a mathematical model, studying the human population into four groups: those who are at risk of being initiated into psychoactive drug abuse, those who are currently abusing psychoactive drugs, those who are undergoing treatment for psychoactive drug abuse, and those who give up drug abuse through willingness or therapy. The positivity and invariant region of the model are investigated. The basic reproduction number $R_drg$ was also obtained. The numerical simulations were performed using the computer software MATLAB. The dynamics of variables and the sensitivity of parameters are displayed graphically to demonstrate that treatment and willingness to stop drug abuse are effective ways to reduce the threat of psychoactive drug abuse in a host community.
Co-Authors Elkaf, Mariem Fadugba, S.E. Sadki, Marya Yaagoub, Zakaria