Abid Ali Lashari: Modeling the spread of two successive SIR epidemics on a configuration model network

Abstract: We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one. The first epidemic is analysed through a bond percolation model, while the second epidemic is approximated by a three-type branching process in which the types of individuals depend on their position in the percolation clusters used for the first epidemic. This branching process approximation enables us to calculate a threshold parameter and the probability of a large outbreak for the second epidemic. The impact of two types of immunity is also incorporated.