دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,428
تعداد مقالات17,578
تعداد مشاهده مقاله57,058,950
تعداد دریافت فایل اصل مقاله18,951,585
Memarbashi, Reza, Ebadi, Zahra. (1401). An epidemic model for drug addiction. سامانه مدیریت نشریات علمی, 10(4), 876-893. doi: 10.22034/cmde.2021.47532.1989
Reza Memarbashi; Zahra Ebadi. "An epidemic model for drug addiction". سامانه مدیریت نشریات علمی, 10, 4, 1401, 876-893. doi: 10.22034/cmde.2021.47532.1989
Memarbashi, Reza, Ebadi, Zahra. (1401). 'An epidemic model for drug addiction', سامانه مدیریت نشریات علمی, 10(4), pp. 876-893. doi: 10.22034/cmde.2021.47532.1989
Memarbashi, Reza, Ebadi, Zahra. An epidemic model for drug addiction. سامانه مدیریت نشریات علمی, 1401; 10(4): 876-893. doi: 10.22034/cmde.2021.47532.1989

An epidemic model for drug addiction

Computational Methods for Differential Equations
مقاله 3، دوره 10، شماره 4، دی 2022، صفحه 876-893    اصل مقاله (685.94 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.47532.1989
نویسندگان
Reza Memarbashi* ؛ Zahra Ebadi
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.
چکیده
The two most common ways to prevent spreading drug addiction are counseling and imprisonment. In this paper, we propose and study a model for the spread of drug addiction incorporating the effect of consultation and incarceration of addicted individuals. We extract the basic reproductive ratio and study the occurrence of backward bifurcation. Also, we study the local and global stability of drug-free and endemic equilibria under suitable conditions. Finally, we use numerical simulations to illustrate the obtained analytical results. 
کلیدواژه‌ها
Epidemic model؛ Drug addiction؛ Backward bifurcation؛ Global Stability
مراجع
  • [1]          J. O. Akanni et al., Global asymptotic dynamics of a nonlinear illicit drug use system, J. Appl. Math. Comput., 2020, DOI:10.1007/s12190-020-01423-7.
  • [2]          R. M. Anderson and R. M. MAY, Infectious Diseases of Humans, Dynamics and Control, Oxford University Press, 1991.
  • [3]          J. Arino C. C. Mccluskey and P. Van den Driessche, Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM J. Appl. Math., 64(1) (2003), 260-276.
  • [4]          N. R. Badurally Adam et al., 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.
  • [5]          N. Bailey, The Mathematical Theory of Infectious Diseases, Charles Griffin, 1975.
  • [6]          N. A. Battista, A Comparison of Heroin epidemic models, School of Mathematical Sciences, 85 (2009), 1-12.
  • [7]          A. Bajeva et al., Modeling the response of illicit drug markets to local enforcement, Socio-Economic Plan. Sci., 27(2) (1993), 73-89.
  • [8]          F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, 2000.
  • [9]          B. Buonomo and D. Lacitignola, Global stability for a four dimensional epidemic model, Note di Matematica, 30(2) (2011), 83-96.
  • [10]        B. Buonomo and D. Lacitignola, On the use of the geometric approach to global stability for three dimensional ODE systems: a bilinear case, Journal of Mathematical Analysis and Applications, 348(1) (2008), 255-266.
  • [11]        C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 2 (2004), 361-404.
  • [12]        J. P. Caulkins, Mathematical models of drug markets and drug policy, Math. Comput. Model.,Special Issue, 17, (1993), 1-115.
  • [13]        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.
  • [14]        R. K. Chandler, B. W. Fletcher, and N. D. Volkow, Treating Drug Abuse and Addiction in the Criminal Justice System: Improving Public Health and Safety, JAMA. Author manuscript, 301(2) (2009), 183-200.
  • [15]        M. Z. Dauhoo et al., On the dynamics of illicit drug consumption in a given population, IMA J. Appl. Math., 78(3) (2013), 432-448.
  • [16]        P. V. D. Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compart- mental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
  • [17]        D. Grass et al., Optimal control of non-linear processes with applications in drugs, corruption and terror, Berlin, Germany, Springer, 2008.
  • [18]        A. B. Gumel, C. C. Mccluskey, and J. Watmough, An SVEIR model for assessing potential impact of an imperfect anti-SARS vaccine, Math. Biosci. Eng., 3 (2006), 485-512.
  • [19]        S. D. Hove-Musekwa and F. Nyabadza, From heroin epidemics to methamphetamine epidemics: Modelling sub- stance abuse in a South African province, Mathematical Biosciences, 225 (2010), 132–140.
  • [20]        J. Kaplan, The hardest drug: heroin and public policy, University of Chicago Press, Chicago, 1983.
  • [21]        J. P. Lassalle, The stability of dynamical systems, SIAM Publication, 1976.
  • [22]        M. Y. Li and J. S. Muldowney, A geometric approach to global-stability problems, SIAM J. Math. Anal., 27(4) (1996), 1070-1083.
  • [23]        M. Y. Li and J. S. Muldowney, On RA Smith’s autonomous convergence theorem, Rocky Mt. J. Math., 25(1) (1995), 365-378.
  • [24]        M. Martcheva, An introduction to mathematical epidemiology, Springer, New York, 2015.
  • [25]        R. Memarbashi and E. Pourhosseieni, Global dynamic of a heroin epidemic model, U.P.B. Sci. Bull., Series A, 81(3) (2019), 115-126.
  • [26]        R. Memarbashi and E. Sorouri, Modeling the effect of information transmission on the drug dynamic, Eur. Phys. J. Plus, 135(54) (2020) doi:10.1140/epjp/s13360-019-00064-5.
  • [27]        G. Mulone and B. Straughan, A note on heroin epidemic models, Math. Biosci., 218(2) (2009), 138-141.
  • [28]        J. D. Murray, Mathematical Biology I and II, Springer, 2004.
  • [29]        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.
  • [30]        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), 1-11.
  • [31]        F. Nyabadza et al., 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.
  • [32]        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.
  • [33]        J. D. Unodc, International standards on drug prevention, UNODC, New York, 2013.
  • [34]        L. Wiessing et al., The epidemiology of drug use at macro level:Indicators, models and policy-making, Bulletin on Narcotics, 53 (2001), 119-133.
  • [35]        E. White and C. Comiskey, Heroin epidemics, treatment and ODE modeling, Mathematical Biosciences, 208(1) (2007), 312-324.
آمار
تعداد مشاهده مقاله: 552
تعداد دریافت فایل اصل مقاله: 521


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب