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

Asaf Khan; Gul Zaman; Roman Ullah; Nawazish Naveed; Asaf Khan; Gul Zaman; Roman Ullah; Nawazish Naveed

doi:10.3934/math.2021086

AIMS Mathematics

2021, Volume 6, Issue 2: 1377-1394. doi: 10.3934/math.2021086

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

1.
Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics, FATA University, Khyber Pakhtunkhwa, Pakistan
3.
Department of Computing, Muscat College, Muscat, Oman
4.
Department of Information Technology, University of Technology and Applied Sciences, CAS Ibri, Oman
Correction on: AIMS Mathematics 6: 7318-7319

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.
- heroin epidemics,
- age-structure,
- control theory,
- weak derivatives,
- adjoint equations
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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Abstract

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.

References

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