Modeling of Alcoholism and Policy Effects on a Social Network
Data are available from random surveys of populations regarding alcohol dependence. This information is relatively reliable compared to many types of hard drug abuse. Data are available in relatively small geographic areas such as zip codes. Can these data be used to evaluate the ecology of the population and to help make effective policy decisions? We want to develop epidemiological models  of alcohol dependence on models of social networks [2-5].
The key idea is to integrate the study of alcohol dependence with the study of networks. We would like to begin to answer the question “What is the effect of network topology on the spread and persistence of alcohol dependence and what policy conclusions can be drawn from understanding this effect?” We would like to build on the pioneering work of Watts [3,4] and Newman  who addressed similar questions in the case of infectious disease. Examples of random and small-world networks that may be used in this kind of study are shown in Figure 1. Several functions in Matlab will be available for use to construct networks and to compute properties of those networks such as those shown in Figure 1.
Figure 1. Sample random (left) and small-world (right) networks that could be used in this study.
We can start by studying some very basic models of the evolution of alcohol dependence on random and small-world networks. One strategy is to simulate the evolution of different initial conditions on a set of social network realizations and examine the resulting mean and variance of the final fraction of alcohol dependent people. What are appropriate model equations to compute these states? One particularly promising approach may be to use the idea of thresholds  for becoming alcohol dependent; if conditions exceed a threshold a person is driven toward dependence.
Figure 2. What does a connected caveman have to do with the small-world network on the right in Figure 1?
After understanding the evolution of a basic epidemiological model, the effect of treatment regimes can be studied. What should “treatment” be in the model? The model should show some sensitivity to the fraction of the dependent population that is treated; policy decisions that impact initial or ongoing values of the proportion of treated individuals could be evaluated using such a model. In particular, can we evaluate the effectiveness and cost of policy decsions using the models we develop?
 H.W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42, 599-653 (2002).
 M.E.J. Newman, The Structure and Function of Complex Networks, SIAM Review 45, 167-256 (2003).
 D.J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton University Press, Princeton, 1999.
 D.J. Watts, Networks, Dynamics, and the Small World Phenomenon, Amer. J. Sociology,105, 493-592 (1999).
 M.E.J. Newman, Spread of epidemic disease on networks, Phys. Rev. E, 66, 016128 (2002).
 D.J. Watts, A simple model of global cascades on random networks, Proc. Natl. Acad. Sci., 99, 5766-5771 (2002).
 Originally at MPI 2004 for Dr. Robert Wilson, School of Urban Affairs and Public Policy, University of Delaware.