Winfried Just

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  Dynamics of Disease Transmission Networks
  Winfried Just

  The most basic models of transmission of infectious diseases assume a partition of the host population into a small number of compartments such as S (susceptible), I (infectious), and R (removed) and conceptualize the number or proportion of individuals in each compartment as variables in an ODE system. But disease transmission is inherently a stochastic event that may occur during a contact between a susceptible and an infectious individual. In real population, this probability will be different for different pairs of individuals. While classical compartment-based ODE models have only a limited capacity for dealing with these heterogeneities, it is, at least in principle, possible to build models of disease transmission based on the underlying contact networks.

  This contribution will introduce models of disease transmission dynamics on a given contact network and the problem of comparing the predictions of such models with coarser, compartment-based ODE models. In other words, we want to know which network properties most significantly influence the course of an epidemic. These questions are currently gaining prominence in research on disease dynamics. Meaningful numerical explorations are feasible at a level suitable for undergraduate research and will constitute a large part of the module. The topic is also well suited for exploring how the choice of modeling assumptions influences the model's predictions. Moreover, the model will introduce some strategies for collecting data on contact networks and building models of such networks based on limited and somewhat unreliable data.