Exact epidemic analysis for the star topology

A methodology is formulated for studying the effects of network structure on the dynamics and spread of an epidemic. We study the well known SIS (susceptible-infected-susceptible) epidemic model and introduce exact moment equations relevant for any network connections. The equations take into account all possible 2N states of the network and the specific topology of the network at hand. For the star topology we are able to calculate the threshold value analytically, and also the proportion of infected individuals at steady state for any parameters. Our analytical results are verified with computer simulations. This study of epidemic dynamics on the star network evaluates both the threshold as well as the stability properties of the model's steady state.