Modelling disease dynamics with realistic population mixing patterns

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Classical mathematical epidemic models assume that individuals randomly contact each other. However, for many diseases, pathogens are transmitted through close contacts, which do not occur randomly. For such diseases, population contacts can be modeled by contact networks, which are graphs with nodes representing individuals and edges representing contacts. They are suitable to model long term heterogeneous contacts, and are indispensable in the study of disease intervention strategies that target this heterogeneity, such as contact tracing and target vaccination. I propose to investigate the following three problems on contact networks to make this modelling approach more applicable. 1) Model recurrent epidemics on a network, and use the model to study the dynamics and evolution of seasonal influenza. In addition, this model will help identify individuals with high risk in infection and transmission. The knowledge on the features determining recurrent epidemics will be used to model the diseases that do not induce immunity after vaccination, and their spread through close contacts. 2) Identify the features of network-based transmissions, such as close contacts, and study observed epidemic curves of diseases (e.g., Ebola and influenza) to determine if contact network is an important mode of transmission for these diseases. I will also study how to correct classical models so that they can more precisely applied to diseases transmitted by close contacts. 3) Model disease dynamics on a nonrandom contact network which contacts are fully known. Individuals in a small community, or inter-connected communities (such as cities or farms) can be represented such networks. However, there is a discrepancy of the condition governing when an epidemic can take off between the network models and the classical models. I propose to develop a mathematical model for disease dynamics on a fully specified contact network, and investigate the cause of this discrepancy. This study will also reveal if such discrepancy exists in classical disease models that consider or neglect within-host pathogen dynamics. Through the proposed research projects, we will gain deeper understandings of the mechanisms of disease spread on networks, and make this modeling approach more applicable to real diseases. We will have a tool more powerful than classical disease models to study disease intervention strategies that target the contact patterns of a population.