Age-Structured Heroin Transmission Model with Delay - Zirar, Imane Hana; Lakmeche, Abdelkader; Helal, Nacera; Djilali, Salih; Zeb, Anwar (Journal of Applied Nonlinear Dynamics, 2026)
This study investigates the outbreak of heroin addiction using a new model for heroin transmission with delay and a finite treatment period. The investigated model considers two different repulsion mechanisms, namely, repulsion from treatment to heroin addiction during treatment, and repulsion from treatment to potentially addicted individuals after treatment. These two repulsions make investigating the suggested age-structured model challenging. Indeed, we establish that the drug-free (resp. drug spread) equilibrium is locally asymptotically stable if the incidence rate β is less than a certain threshold value β^*, with additional assumptions on the parameters of the model. Moreover, we have demonstrated the global asymptotic stability of the drug-free equilibrium when β is less than another threshold value β^ (where β^** < β^*). Some numerical investigations of the model are conducted to identify effective measures for containing the epidemic.