Modeling the spread of infectious diseases on contact networks

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The proposed research program aims to develop realistic mathematical models to study diseases such as HIV and influenza and their intervention strategies. For intervention strategies that explore the heterogeneity in human contacts (e.g. prioritized vaccination and contact tracing), classical epidemic models are difficult to apply because they unrealistically assume that every pair of individuals in a community can make contacts and transmit diseases with the same probability. On the other hand, realistic human contacts can be represented by networks where nodes represent individuals and edges represent contacts. However, current mathematical models for disease dynamics on such contact networks are limited to static networks, and neglect loss of immunity. Thus they are not suitable for diseases like influenza (with loss of immunity) and HIV (with births, deaths and migration), and their intervention strategies (altering contact networks by isolating individuals and removing contacts). I will develop mathematical models for disease spread on contact networks, incorporating births, deaths, migration, and loss of immunity. The conditions that determine whether a disease can emerge in a population will be derived. These conditions are crucial to designing optimal intervention strategies. The proposed models will be applied to answer such questions as how pandemic influenza strains become seasonal; whom we should target for antiviral treatment; and whom we should first vaccinate.