Dynamical study of addiction modelling under some control strategies

Arif, Sarah Jafar; Al-Husseiny, Hassan Fadhil

doi:10.22075/ijnaa.2022.6778

Dynamical study of addiction modelling under some control strategies

Document Type : Research Paper

Authors

Sarah Jafar Arif

Hassan Fadhil Al-Husseiny

Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

10.22075/ijnaa.2022.6778

Abstract

In this work, a paradigm for drugs and addiction is put forth and examined. It is a given that the model took the impact of governmental policies and the addict's control into account. The designer's solution's availability, uniqueness, and bounds should be first addressed. Second, we investigated each equilibrium pointe's existence and localized stability. Additionally, some of the prerequisites for the optimistic equilibrium's global stability are identified. Finally, a computational domain is used to illustrate the theoretical result.

Highlights

[1] I.K. Adu, M. AL-Rahman and C. Yang, Mathematical model of drinking epidemic, Br. J. Math. Comput. Sci. 22
(2017), no. 5, 1–10.
[2] S. Cole and S. Wirkus, Modeling the dynamics of heroin and illicit opioid use disorder, treatment, and recovery,
Bull. Math. Bio. 84 (2022), no. 4, 1–49.
[3] M. Hafiruddin, Fatmawati and Miswanto, Mathematical model analysis of a drug ransmission with criminal law
and its optimal control, AIP Conf. Proc. 2192 (2019), no. 1, 060010.
[4] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
[5] R. Jason and R. Miranda, Alcohol craving in adolescents: Bridging the laboratory and natural environment,
Psychopharmacology 231 (2014), no. 8, 1841–1851.
[6] G. Johan, R.P. Grasman and H.L. van der Maas, The dynamics of addiction: craving versus self-control, PLoS
One 11 (2016), no. 6, e0158323.
[7] F. L. Matonya and D. Kuznetsov, Mathematical modelling on the effects of drug abuse to the societies, Ann. Pure
Appl. Math. 19 (2019), no. 1, 21–35.8] A.A. Mohsen and R.K. Naji, The role of media coverage on the dynamical behavior of smoking model with and
without spatial diffusion, J. Phys.: Conf. Ser. 1591 (2020), no. 1.
[9] T.O. Orwa and F. Nyabadza, Mathematical modelling and analysis of alcohol-methamphetamine co-abuse in the
Western Cape province of South Africa, Cogent Math. Statist. 6 (2019), no. 1, 1641175.
[10] L. Pengyan, L. Zhang and Y. Xing, Modelling and stability of a synthetic drugs transmission model with relapse
and treatment, J. Appl. Math. Comput. 60 (2018), no. 1, 465–484.
[11] X. Pengcheng, Z. Zhang and X. Sun, Smoking dynamics with health education effect, AIMS Math. 3 (2018), no.
4, 584–599.
[12] R. Resmawan, N. Supu and N. Achmad, Dynamic model analysis of the spread of drug addicts with educational
effects, 1st Int. Conf.. Math. Math. Educ., Atlantis Press, 2021.
[13] E.P. Reyes, Mathematical modeling of the spread of alcoholism among colombian college students, Ingen. Ciencia
16 (2020), no. 32, 92–223.
[14] S. Swarnali and G.P. Samanta, Analysis of a drinking epidemic model, Int. J. Dyn. Control 3 (2015), no. 3,
288–305
[15] UNODC, World Drug Report 2019; Sales No. E.19.XI.8, United Nations Publication: New York, NY, USA, 2019.

Keywords

locally segment-dense set

vector equilibrium problem

C-sequentially sign property

[1] I.K. Adu, M. AL-Rahman and C. Yang, Mathematical model of drinking epidemic, Br. J. Math. Comput. Sci. 22
(2017), no. 5, 1–10.
[2] S. Cole and S. Wirkus, Modeling the dynamics of heroin and illicit opioid use disorder, treatment, and recovery,
Bull. Math. Bio. 84 (2022), no. 4, 1–49.
[3] M. Hafiruddin, Fatmawati and Miswanto, Mathematical model analysis of a drug ransmission with criminal law
and its optimal control, AIP Conf. Proc. 2192 (2019), no. 1, 060010.
[4] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
[5] R. Jason and R. Miranda, Alcohol craving in adolescents: Bridging the laboratory and natural environment,
Psychopharmacology 231 (2014), no. 8, 1841–1851.
[6] G. Johan, R.P. Grasman and H.L. van der Maas, The dynamics of addiction: craving versus self-control, PLoS
One 11 (2016), no. 6, e0158323.
[7] F. L. Matonya and D. Kuznetsov, Mathematical modelling on the effects of drug abuse to the societies, Ann. Pure
Appl. Math. 19 (2019), no. 1, 21–35.[8] A.A. Mohsen and R.K. Naji, The role of media coverage on the dynamical behavior of smoking model with and
without spatial diffusion, J. Phys.: Conf. Ser. 1591 (2020), no. 1.
[9] T.O. Orwa and F. Nyabadza, Mathematical modelling and analysis of alcohol-methamphetamine co-abuse in the
Western Cape province of South Africa, Cogent Math. Statist. 6 (2019), no. 1, 1641175.
[10] L. Pengyan, L. Zhang and Y. Xing, Modelling and stability of a synthetic drugs transmission model with relapse
and treatment, J. Appl. Math. Comput. 60 (2018), no. 1, 465–484.
[11] X. Pengcheng, Z. Zhang and X. Sun, Smoking dynamics with health education effect, AIMS Math. 3 (2018), no.
4, 584–599.
[12] R. Resmawan, N. Supu and N. Achmad, Dynamic model analysis of the spread of drug addicts with educational
effects, 1st Int. Conf.. Math. Math. Educ., Atlantis Press, 2021.
[13] E.P. Reyes, Mathematical modeling of the spread of alcoholism among colombian college students, Ingen. Ciencia
16 (2020), no. 32, 92–223.
[14] S. Swarnali and G.P. Samanta, Analysis of a drinking epidemic model, Int. J. Dyn. Control 3 (2015), no. 3,
288–305
[15] UNODC, World Drug Report 2019; Sales No. E.19.XI.8, United Nations Publication: New York, NY, USA, 2019.