Modeling disease transmission: Incorporating family cliques in exponential random graphs
Disease transmission is most commonly modeled using compartmental ordinary differential equations or agent based models, both of which have notable drawbacks. Compartmental models permit theoretical results, but they rely on the false assumption that populations mix homogeneously. Agent based models account for the fact that populations are not homogeneously mixed, but are computational models and do not lend themselves to the derivation of theoretical results. A third, more recent approach in which equations governing disease transmission are imposed over a social network attempts to combine the strengths of both model types. The social network utilized represents individuals as nodes and contact between those individuals as edges. This technique accounts for the complexities of social structure while permitting the derivation of theoretical results. Many network models exist which approximate the properties of real-world social networks, but these widely ignore important local network structures such as family units. Therefore, their use in the modeling of disease transmission ignores important mechanisms of disease propagation. A new class of networks which more closely represents real-world social structures would be useful in modeling disease transmission through populations. This project aims to adapt exponential random graph models, a general class of network model which accounts for certain local structures, to specify the existence of family cliques of all sizes. An important characteristic of real world social networks is that each individual belongs to some family clique. We expect the inclusion of this property to change the dynamics of epidemic spread on a network and potentially to allow for more accurate modeling of epidemics.