# Modeling Heterogeneity in Susceptibility and Infectivity for HIV Infection

## Abstract

Models of the spread of human immunodeficiency virus (HIV) infection must deal with substantial heterogeneity in the populations at risk. The virus is spread by behaviors that are far from uniformly distributed in the population, and substantial variations in biological aspects of susceptibility and infectivity are also likely. How adequately a model represents this heterogeneity will substantially determine its accuracy and usefulness for capturing the dynamics of the epidemic, for making forecasts of future spread, and for answering questions of policy interest.

There are two main ways in which a model may handle heterogeneity: by partitioning the population into discrete risk groups that are in some respect homogeneous within group but heterogeneous between groups, and by introducing model parameters to capture the effects of heterogeneity in a group or in the population as a whole. This paper discusses the dynamics of heterogeneity in HIV spread and develops a theory of heterogeneity in susceptibility and infectivity within a population that allows a simple representation of key phenomena within an epidemic model. It is suggested that the effects of heterogeneity-related phenomena can be captured by letting two key parameters, the mean susceptibility over time of the uninfected and the mean infectivity of the infected, depend upon X/P, the proportion of the population that is uninfected. (The mean infectivity may also depend on the cumulative proportion of the population that is removed through death or other causes). Because X/P, aswe define it, is monotonic over time, this approach is general, and it allows considerable flexibility in the choice of functional form to fit available data.

### Keywords

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