Analytical computation of the epidemic prevalence and threshold for the discrete-time susceptible–infected–susceptible dynamics on static networks

Abstract

By introducing these probabilities of reaching an arbitrary infected individual from individuals of different degrees and states, we derive the explicit analytical solutions of the epidemic prevalence and the threshold for the discrete-time susceptible–infected–susceptible epidemic dynamics on networks. The analytical computation of the epidemic prevalence is not constrained by the network size as the previous master equation methods and the epidemic threshold depends on the infection probability and recovery probability, not their ratio. We compare the results forecasted by our theory with those by Monte Carlo simulations and find good agreement between the results obtained by the two methods. Moreover, for the case of both large infection probability and epidemic prevalence, we find that the susceptible individuals are surrounded by more infected neighbors than infected individuals. This has not been seen in continuous-time susceptible–infected–susceptible epidemic dynamics.