Modeling and analysis of epidemic dynamics on an adaptive network

Using the semi-tensor product method, this paper investigates the epidemic dynamics on an adaptive network, and presents several new results. First, a formal susceptible-infected-susceptible epidemic dynamic model on an adaptive network is given. Second, the dynamics of individual states and the dynamics of network topologies are converted into algebraic forms via the semi-tensor product of matrices, respectively. Third, with the help of the algebraic formulation, all possible final spreading equilibria are obtained for any given initial epidemic state and network topology. The study of an illustrative example shows that the new results obtained are effective.