Modelling the influence of awareness programs by media on the drinking dynamics. (English) Zbl 1474.91129

Summary: We develop a nonlinear mathematical model with the effect of awareness programs on the binge drinking. Due to the fact that awareness programs are capable of inducing behavioral changes in nondrinkers, we introduce a separate class by avoiding contacts with the heavy drinkers. Furthermore we assume that cumulative density of awareness programs increases at a rate proportional to the number of heavy drinkers. We establish some sufficient conditions for the stability of the alcohol free and the alcohol present equilibria and give some numerical simulations to explain our main result. Our results show that awareness programs is an effective measure in reducing alcohol problems.


91D10 Models of societies, social and urban evolution
34C60 Qualitative investigation and simulation of ordinary differential equation models
Full Text: DOI


[1] Rehm, J., The risks associated with alcohol use and alcoholism, Alcohol Research & Health, 34, 2, 135-143, (2011)
[2] Rehm, J.; Mathers, C.; Popova, S.; Thavorncharoensap, M.; Teerawattananon, Y.; Patra, J., Global burden of disease and injury and economic cost attributable to alcohol use and alcohol-use disorders, The Lancet, 373, 9682, 2223-2233, (2009)
[3] Ribes, J.; Clèries, R.; Esteban, L.; Moreno, V.; Bosch, F. X., The influence of alcohol consumption and hepatitis B and C infections on the risk of liver cancer in Europe, Journal of Hepatology, 49, 2, 233-242, (2008)
[4] Wechsler, H.; Nelson, T. F., Focusing attention on college student alcohol consumption and the environmental conditions that promote it, Journal of Studies on Alcohol and Drugs, 69, 4, 481-490, (2008)
[5] Powell, L. M.; Williams, J.; Wechsler, H., Study habits and the level of alcohol use among college students, Education Economics, 12, 2, 135-149, (2004)
[6] Wechsler, H.; Moeykens, B.; Davenport, A.; Castillo, S.; Hansen, J., The adverse impact of heavy episodic drinkers on other college students, Journal of Studies on Alcohol and Drugs, 56, 6, 628-634, (1995)
[7] Mushayabasa, S.; Bhunu, C. P., Modelling the effects of heavy alcohol consumption on the transmission dynamics of gonorrhea, Nonlinear Dynamics, 66, 4, 695-706, (2011) · Zbl 1242.92041
[8] Ormerod, P.; Wiltshire, G., ‘Binge” drinking in the UK: a social network phenomenon, Mind & Society, 8, 2, 135-152, (2009)
[9] Sanchez, F.; Wang, X. H.; Castillo-Chavez, C.; Gorman, D. M.; Gruenewald, P. J.; Witkiewitz, K. A.; Marlatt, G. A., Drinking as an epidemica simple mathematical model with recovery and relapse, Therapists Guide to Evidence-Based Relapse Prevention: Practical Resources for the Mental Health Professional, 353-368, (2007), Burlington, Canada: Academic Press, Burlington, Canada
[10] Mulone, G.; Straughan, B., Modeling binge drinking, International Journal of Biomathematics, 5, 1, (2012) · Zbl 1297.92079
[11] Huo, H.-F.; Song, N.-N., Global stability for a binge drinking model with two stages, Discrete Dynamics in Nature and Society, 2012, (2012) · Zbl 1253.91157
[12] Huo, H. F.; Zhu, C. C., Modeling the effect of constant immigration on drinking behaviour
[13] Huo, H. F.; Zhu, C. C., Stability of a quit drinking model with relapse
[14] Huo, H.-F.; Zhu, C.-C., Influence of relapse in a giving up smoking model, Abstract and Applied Analysis, 2013, (2013) · Zbl 1402.92241
[15] Schwitzer, G.; Mudur, G.; Henry, D.; Wilson, A.; Goozner, M.; Simbra, M.; Sweet, M.; Baverstock, K. A., What are the roles and responsibilities of the media in disseminating health information?, PLoS Medicine, 2, 7, article e215, (2005)
[16] Jaramillo, E., The impact of media-based health education on tuberculosis diagnosis in Cali, Colombia, Health Policy and Planning, 16, 1, 68-73, (2001)
[17] Liu, R.; Wu, J.; Zhu, H., Media/psychological impact on multiple outbreaks of emerging infectious diseases, Computational and Mathematical Methods in Medicine, 8, 3, 153-164, (2007) · Zbl 1121.92060
[18] Palfai, T. P.; Zisserson, R.; Saitz, R., Using personalized feedback to reduce alcohol use among hazardous drinking college students: the moderating effect of alcohol-related negative consequences, Addictive Behaviors, 36, 5, 539-542, (2011)
[19] Tchuenche, J. M.; Bauch, C. T., Dynamics of an infectious disease where media coverage influences transmission, ISRN Biomathematics, 2012, (2012) · Zbl 1269.92052
[20] Xiang, H.; Song, N. N.; Huo, H. F., Modelling effects of public health educational campaigns on drinking dynamics
[21] Misra, A. K.; Sharma, A.; Singh, V., Effect of awareness programs in controlling the prevalence of an epidemic with time delay, Journal of Biological Systems, 19, 2, 389-402, (2011) · Zbl 1228.92067
[22] Misra, A. K.; Sharma, A.; Shukla, J. B., Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases, Mathematical and Computer Modelling, 53, 5-6, 1221-1228, (2011) · Zbl 1217.34097
[23] WHO Report of Alcohol in developing societies summary
[24] Chisholm, D.; Rehm, J.; van Ommeren, M.; Monteiro, M., Reducing the global burden of hazardous alcohol use: a comparative cost-effectiveness analysis, Journal of Studies on Alcohol, 65, 6, 782-793, (2004)
[25] van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180, 29-48, (2002) · Zbl 1015.92036
[26] Li, J.-Q.; Yang, Y.-L.; Zhou, Y.-C., Global stability of an epidemic model with latent stage and vaccination, Nonlinear Analysis: Real World Applications, 12, 4, 2163-2173, (2011) · Zbl 1220.34069
[27] LaSalle, J. P., Stability theory for ordinary differential equations, Journal of Differential Equations, 4, 1, 57-65, (1968) · Zbl 0159.12002
[28] Snyder, L. B., Health communication campaigns and their impact on behavior, Journal of Nutrition Education and Behavior, 39, 2, S32-S40, (2007)
[29] Clark, D. B.; Bukstein, O.; Cornelius, J., Alcohol use disorders in adolescents: epidemiology, diagnosis, psychosocial interventions, and pharmacological treatment, Pediatric Drugs, 4, 8, 493-502, (2002)
[30] WebMD Report of Alcohol Abuse Health Center
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