**Modeling of Alcoholism and Policy Effects on
a Social Network**[1]

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 [1] 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 ÒWhat 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?Ó We would like to build on the
pioneering work of Watts [3,4] and Newman [5] 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 [6] 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 ÒtreatmentÓ 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?

[1] H.W. Hethcote, *The mathematics of
infectious diseases*, SIAM Review, **42**, 599-653 (2002).

[2] M.E.J. Newman, *The Structure and Function
of Complex Networks*, SIAM Review **45**, 167-256 (2003).

[3] D.J. Watts, *Small Worlds: The Dynamics of Networks
between Order and Randomness*, Princeton University Press, Princeton, 1999.

[4] D.J. Watts, *Networks, Dynamics, and the
Small World Phenomenon*, Amer. J. Sociology,**105**, 493-592 (1999).

[5] M.E.J. Newman, *Spread of epidemic disease
on networks*, Phys. Rev. E, **66**, 016128 (2002).

[6] D.J. Watts, *A simple model of global
cascades on random networks*, Proc. Natl. Acad. Sci., **99**, 5766-5771 (2002).

[1] Originally at MPI 2004 for Dr. Robert Wilson, School of Urban Affairs and Public Policy, University of Delaware.