### AIMS Mathematics

2021, Issue 2: 1377-1394. doi: 10.3934/math.2021086
Research article

# Optimal control strategies for a heroin epidemic model with age-dependent susceptibility and recovery-age

• Received: 01 September 2020 Accepted: 11 November 2020 Published: 19 November 2020
• MSC : 49J20, 00A72, 49J50, 35B50, 37M05

• In the present manuscript, an age-structured heroin epidemic model is formulated with the assumption that susceptibility and recovery are age-dependent. Keeping in view some control measures for heroin addiction, a control problem for further analysis is presented. The main results are the existence of control variables, sensitivities, adjoint system and the setting of an optimal control problem. We used the techniques of weak derivatives and a general principle of Pontryagin's type for obtaining the optimal control problem. To compare our results, we demonstrated sample simulations which show the effect of control on the entire population.

Citation: Asaf Khan, Gul Zaman, Roman Ullah, Nawazish Naveed. Optimal control strategies for a heroin epidemic model with age-dependent susceptibility and recovery-age[J]. AIMS Mathematics, 2021, 6(2): 1377-1394. doi: 10.3934/math.2021086

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• In the present manuscript, an age-structured heroin epidemic model is formulated with the assumption that susceptibility and recovery are age-dependent. Keeping in view some control measures for heroin addiction, a control problem for further analysis is presented. The main results are the existence of control variables, sensitivities, adjoint system and the setting of an optimal control problem. We used the techniques of weak derivatives and a general principle of Pontryagin's type for obtaining the optimal control problem. To compare our results, we demonstrated sample simulations which show the effect of control on the entire population.

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