Modelling alcohol problems: total recovery
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Modelling alcohol problems: total recovery Caroline Elizabeth Walters · Brian Straughan · Jeremy R. Kendal
Received: 18 October 2012 / Revised: 18 November 2012 / Published online: 13 December 2012 © Università degli Studi di Napoli "Federico II" 2012
Abstract Binge drinking in the UK is an increasing problem, resulting in negative health, social and economic effects. Mathematical modelling allows for future predictions to be made and may provide valuable information regarding how to approach solving the problem of binge drinking in the UK. We develop a 3-equation model for alcohol problems, specifically binge drinking, which allows for total recovery. Individuals are split into those that are susceptible to developing an alcohol problem, those with an alcohol problem and those in treatment. We 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.
Communicated by editor in chief. C. E. Walters (B) · B. Straughan Department of Mathematics and the Centre for the Coevolution of Biology and Culture, University of Durham, Durham DH1 3LE, UK e-mail: [email protected] C. E. Walters · J. R. Kendal Department of Anthropology and the Centre for the Coevolution of Biology and Culture, University of Durham, Durham DH1 3LE, UK
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Keywords
C. E. Walters et al.
Epidemics · ODE model · Stability · Equilibria · Binge drinking
1 Introduction Smith and Foxcroft [39] report that between 1998 to 2006 there was an overall increase in the proportion of individuals in Great Britain who exceed the recommended alcohol consumption limits, including a doubling of the proportion of women who binge drink. Excessive alcohol consumption can lead to a range of negative health and social effects [16] and it is estimated that alcohol misuse costs the NHS £2.7 billion per year with alcohol related hospital admissions having increased by 100 % from 2002/03 to 2009/10 [2]. These figures suggest that there is an increasing trend of alcohol misuse, which is resulting in costs to health and the economy. Here we devise a predictive mathematical model which may offer an insight into the best strategy for tackling problems with alcohol, in particular binge drinking. Mathematical models for behaviours such as alcoholism have
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