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Thursday, December 2, 2010

Sensitivity Analysis of Drinking Dynamics: From Deterministic to Stochastic Formulations



The similarities between drinking behavior and contagion are used to explore — under two types of social structure in the population: homogenous and heterogeneous mixing— the role of nonlinear social interactions on the dynamics of alcohol consumption; quantifying how some model parameters influence the latter dynamics. 

A deterministic model, assuming homogeneous mixing, is used to derive relative sensitivity functions which explain how the recovery and relapse rates affect the establishment of problem drinkers. 

A continuos-time Markov chain model is derived from the deterministic model; stochastic simulations are used to quantify how histograms of the number of problem drinkers depend on the recovery and relapse rates, as these rates are gradually incremented. 

The impact of lowering the relapse rate, as a result of successful treatment, at various intervention times, is assessed by stochastic simulations of drinking dynamics among communities with small-world structure; reductions in the average number of problem drinkers are obtained —with some community structures showing more vulnerability to higher levels of prevalence than others. 

We concludefrom sensitivity analyses (of deterministic and stochastic models) that, either: increasing the recovery rate; or lowering the relapse rate, are measures with positive effects
—they tend to reduce the number of problem drinkers.



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