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Memarbashi, Reza, Ghasemabadi, Atena, Ebadi, Zahra. (1401). Backward bifurcation in a two strain model of heroin addiction. سامانه مدیریت نشریات علمی, 10(3), 656-673. doi: 10.22034/cmde.2021.44619.1881
Reza Memarbashi; Atena Ghasemabadi; Zahra Ebadi. "Backward bifurcation in a two strain model of heroin addiction". سامانه مدیریت نشریات علمی, 10, 3, 1401, 656-673. doi: 10.22034/cmde.2021.44619.1881
Memarbashi, Reza, Ghasemabadi, Atena, Ebadi, Zahra. (1401). 'Backward bifurcation in a two strain model of heroin addiction', سامانه مدیریت نشریات علمی, 10(3), pp. 656-673. doi: 10.22034/cmde.2021.44619.1881
Memarbashi, Reza, Ghasemabadi, Atena, Ebadi, Zahra. Backward bifurcation in a two strain model of heroin addiction. سامانه مدیریت نشریات علمی, 1401; 10(3): 656-673. doi: 10.22034/cmde.2021.44619.1881

Backward bifurcation in a two strain model of heroin addiction

Computational Methods for Differential Equations
مقاله 7، دوره 10، شماره 3، مهر 2022، صفحه 656-673    اصل مقاله (1.36 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.44619.1881
نویسندگان
Reza Memarbashi* 1؛ Atena Ghasemabadi2؛ Zahra Ebadi1
1Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
2Esfarayen University of Technology, Esfarayen, North Khorasan, Iran.
چکیده
Among the various causes of heroin addiction, the use of prescription opioids is one of the main reasons. In this article, we introduce and analyze a two-strain epidemic model with the superinfection for modeling the effect of prescribed opioids abuse on heroin addiction. Our model contains the impact of relapse of individuals under treatment/rehabilitation to drug abuse in each strain. We extract the basic reproductive ratio, the invasion numbers and study the occurrence of backward bifurcation in strain dominance equilibria, i.e., boundary equilibria. Also, we explore both the local and global stability of DFE and boundary equilibria under suitable conditions. Furthermore, we study the existence of the coexistence equilibrium point. We prove that when R0 < 1, the coexistence equilibrium point can exist, i.e., backward bifurcation occurs in coexistence equilibria. Finally, we use numerical simulation to describe the obtained analytical results. 
کلیدواژه‌ها
Epidemic model؛ Multiple strain؛ Superinfection؛ Global stability؛ Backward bifurcation
مراجع
  • [1]         J. Alidousti and E. Ghaffari, Stability and bifurcation of fractional tumor-immune model with time delay. Comput. Meth. Diff. Eq., 9(3) (2021), 692-709.
  • [2]         J. Arino, C. C. McCluskey, and P. Van den Driessche, Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM Journal on Applied Mathematics, 64(1) (2003), 260-276.
  • [3]         N. R. Badurally Adam, M. Z. Dauhoo, and O. Kavian, An analysis of the dynamical evolution of experimental, recreative and abusive marijuana consumption in the states of colorado and washington beyond the implementation of I–502, J. Math. Socio. 39(4) (2015), 257-279.
  • [4]         P. Balland and E. Su¨li, Analysis of the cell-vertex finite volume method for hyperbolic problems with variable coefficients, SIAM J. Numer. Anal., 34 (1997), 1127–1151. Doi: 10.1137/S0036142994264882.
  • [5]         A. Baveja, R. Batta, J. P. Caulkins, and M. H. Karwan, Modeling the response of illicit drug markets to local enforcement. Socio-Economic Plan. Sci. 27(2) (1993), 73-89.
  • [6]         S. Bonhoeffer and M. Nowak, Mutation and the evolution of parasite virulence, Proc. R. Soc. London. B, 258 (1994), 133-140.
  • [7]         C. P. Bhunu and W. Garira, A two strain tuberculosis transmission model with therapy and quarantine, Math. Mod. Anal., 14(3) (2009), 291-312.
  • [8]         R. G. Carlson, R. W. Nahhas, S. S. Martins, and R. Daniulaityte, Predictors of transition to heroin use among non-opioid dependent illicit pharmaceutical opioid users: A natural history study, Drug Alcohol Depend. 160 (2016), 127-134.
  • [9]         Center for Behavioral Health Statistics and Quality, Table 7.50A. 2014 National Survey on Drug Use and Health: Detailed Tables. Substance Abuse and Mental Health Services Administration, Rockville, MD. 2015.
  • [10]       C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 2 (2004), 361-404.
  • [11]       J. P. Caulkins, Mathematical models of drug markets and drug policy, Math. Comput. Model., 17 (1993), 1-115. Special Issue.
  • [12]       W. Chen, W. X. Wu, and Z. D. Teng, Complete Dynamics in a Nonlocal Dispersal Two-Strain SIV Epidemic Model with Vaccinations and Latent Delays, Applied and Computational Mathematics, 19(3) (2020), 360-391.
  • [13]       T. J. Cicero, M. S. Ellis, and Z. A. Kasper, Increased use of heroin as an initiating opioid of abuse, Addict Behav, 74 (2017), 63-66.
  • [14]       M. Z. Dauhoo, B. S. N. Korimboccus, and S. B. Issack, On the dynamics of illicit drug consumption in a given population, IMA J. Appl. Math., 78(3) (2013), 432-448.
  • [15]       S. Ghersheen, V. Kozlov, V. G. Tkachev, and U. Wenergren, Dynamical behavior of SIR model with coinfection: The case of finite carrying capacity. Math. Meth. Appl. Sci., 2019, Doi: 10.1002/mma.5671.
  • [16]       J. M. Ginoux, R. Naeck, Y. B. Ruhomally, M. Z. Dauhoo, and M. Perc, Chaos in a predator-prey-based mathe- matical model for illicit drug consumption, Appl. Math. Comp., 347 (2019), 502-513.
  • [17]       D. Grass, J. P. Caulkins, G. Feichtinger, G. Tragler, and D. A. Behrens, Optimal control of non-linear processes with applications in drugs, corruption and terror, Berlin, Germany, Springer, 2008.
  • [18]       A. Haji Badali, M. S. Hashemi, and M. Ghahremani, Lie symmetry analysis for kawahara-kdv equations, Comput. Methods Differ. Equ., 1 (2013), 135–145.
  • [19]       M. Jafari, H. Kheiri, and A. Jabbari, Backward bifurcation in a fractional-order and two-patch model of tuberculosis epidemic with incomplete treatment, Int. J. Biomath, 14(02) (2020), 2150007.
  • [20]       C. M. Jones, J. Logan, R. M. Gladden, and M. K. Bohm, Vital signs: demographic and substance use trends among heroin users – United States, 2002-2013, Morbidity and Mortality Weekly Report (MMWR). Atlanta, GA: Centers for Disease Control and Prevention, 2015.
  • [21]       A. S. Kalula and F. Nyabadza, A theoretical model for substance abuse in the presence of treatment. South African Journal of Science. 108(3-4) (2012), 1-12.
  • [22]       K. Kane-Willis, S. J. Schmitz, M. Bazan, V. F. Narloch, and C. B. Wallace, Understanding suburban heroin use. Roosevelt University. https : //www.robertcrown.org/files/Understanding suburban heroin use.pdf. 2015.
  • [23]       J. Kaplan, The hardest drug: heroin and public policy, University of Chicago Press, Chicago, 1983.
  • [24]       Z. Lajmiri, I. Orak, and R. Fereidoni, Global dynamics and numerical bifurcation of a bioeconomic system, Comput. Meth. Diff. Eq., 9(2) (2021), 427-445.
  • [25]       R. J. LeVeque, Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics, Cam- bridge University Press, Cambridge, 2002. Doi: 10.1017/CBO9780511791253.
  • [26]       M. Y. Li and J. S. Muldowney, A geometric approach to global-stability problems. SIAM Journal on Mathematical Analysis. 27(4) (1996), 1070-1083.
  • [27]       J. A. Mackenzie, T. Sonar, and E. Su¨li, Adaptive finite volume methods for hyperbolic problems, in The mathe- matics of finite elements and applications (Uxbridge, 1993), Wiley, Chichester, 1994, 289–297.
  • [28]       M. Martcheva, An introduction to mathematical epidemiology, Springer, New York, 2015.
  • [29]       R. Memarbashi and E. Pourhosseieni, Global dynamic of a heroin epidemic model, U.P.B. Sci. Bull., Series A, 81(3), (2019), 115-126.
  • [30]       R. Memarbashi and E. Sorouri, Modeling the effect of information transmission on the drug dynamic, Eur. Phys. J. Plus, 135(1) (2020), 1-20.
  • [31]       P. K. Muhuri, J. C. Gfroerer, and M. C. Davies, Associations of Nonmedical Pain Reliever Use and Initiation of Heroin Use in the United States, Rockville, MD: Substance Abuse and Mental Health Services Administration., 2013.
  • [32]       G. Mulone and B. Straughan, A note on heroin epidemic models. Math. Biosci. 218(2) (2009), 138-141.
  • [33]       NIH, Prescription opioids, Drug Facts, National Institute on Drug Abuse, 2019.
  • [34]       H. J. B. Njagarah and F. Nyabadza, Modeling the impact of rehabilitation, amelioration, and relapse on the prevalence of drug epidemics. Journal of Biological Systems. 21(01) (2013), 135-145.
  • [35]       K. Y. Ng and M. M. Gui, COVID-19: Development of a robust mathematical model and simulation package with consideration for ageing population and time delay for control action and resusceptibility, Physica D, 411 (2020), 132599.
  • [36]       F. Nyabadza, J. B. Njagarah, and R. J. Smith, Modeling the dynamics of crystal meth (‘tik’) abuse in the presence of drug-supply chains in South Africa. Bull. Math. Biol. 75(1) (2013), 24-48.
  • [37]       F. Nyabadza and S. D. Hove-Musekwa, From heroin epidemics to methamphetamine epidemics: modeling sub- stance abuse in a South African province, Math. Biosci., 225 (2010), 132-140.
  • [38]       V. Sivakumar, D. Baleanu, J. Thippan, and P. B. Dhandapani, Analysis of time delay model for drug therapy on HIV dynamics, Comput. Meth. Diff. Eq., 9(2) (2021), 577-588.
  • [39]       B. Unal, Doubly warped products, ProQuest LLC, Ann Arbor, MI, 2000. Thesis (Ph.D.)–University of Missouri - Columbia.
  • [40]       P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compart- mental models of disease transmission, Math Biosci, 180 (2002), 29-48.
  • [41]       E. White and C. Comiskey, Heroin epidemics, treatment and ODE modeling, Mathematical Biosciences, 208(1) (2007), 312-324.
  • [42]       L. Wiessing, R. Hartnoll, and C. Rossi, The epidemiology of drug use at macro level: Indicators, models and policy-making, Bulletin on Narcotics, 53 (2001), 119-133.
  • [43]       X. Zhou, Stability and Bifurcation Analysis for an Epidemic Model with Vaccination and Nonlinear Incidence Rate, Applied and Computational Mathematics, 18(1) (2021), 22-40.
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