Modelling alcohol problems: total recovery

Abstract

. (2013) 'Modelling alcohol problems : total recovery.', Ricerche di matematica., 62 (1). pp. 33-53. Further information on publisher's website:http://dx.doi.org/10.1007/s11587-012-0138-0Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s11587-012-0138-0.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 1We find that the model has two equilibrium points: one without alcohol problems and one where alcohol problems are endemic in the population. We compare our results with those of an existing model that does not allow for total recovery. We show that without total recovery, the threshold for alcohol problems to become endemic in the population is lowered. The endemic equilibrium solution is also affected, with an increased proportion of the population in the treatment class and a decreased proportion in the susceptible class.Including totally recovery does not determine whether the proportion of individuals with alcohol problems increases or decreases, however it does effect the size of the change. Parameter estimates are made from information regarding binge drinking where we find an increase in the recovery rate decreases the proportion of binge drinkers in the population.

Modelling drinking with information

“…Drinking we believe has been investigated using the techniques of epidemical models, and such approach has proven to accurately predict the percentages of binge and moderate drinkers [7][8][9][10][11][12][13][14].…”

“…Binge drinking can affect well over 25 per cent of the population as may be seen from specific data for Durham City [4] and Stockton-on-Tees [5] in North East England, with some areas being as high as 28.93%, in, for example, Newcastle-upon-Tyne, [4,5]. In addition, the death rate due to drinking alcohol has risen dramatically in the UK with, for example, Glasgow recording a death rate of 83.7 per 100,000 for both men and women during 1988-2004 [6].Drinking we believe has been investigated using the techniques of epidemical models, and such approach has proven to accurately predict the percentages of binge and moderate drinkers [7][8][9][10][11][12][13][14].What has never been modelled in such a field is the influence of external variables that favour or discourage such habits. This external influence can be modelled introducing the concept of an information variable.…”

A mathematical model of anorexia and bulimia

“…Mathematical epidemiology has grown exponentially starting in the middle of the 20th century, and a great variety of models have been formulated, mathematically analyzed, and applied to infectious diseases. In the recent years, models have been formulated to control the 2002-2003 epidemics of SARS [38,39], the H1N1 influenza of 2009 [40][41][42][43], and to predict negative habits and social behaviors [44][45][46][47][48][49].…”

Analysis of a drinking epidemic model

“…As drinking is a chronic relapsing disease, the relapse of drinkers from treatment should be considered to make the work more realistic, which is missing in [23]. There are also some recent research works on this field [28][29][30][31].…”