Epidemic extinction in a generalized susceptible-infected-susceptible model

Abstract We study the extinction of epidemics in a generalized contact process, where a susceptible individual becomes infected with the rate λ when contacting m infective individual(s) simultaneously, and an infected individual spontaneously recovers with the rate μ. By employing WKB approximation for the master equation, the problem is reduced to finding the zero-energy trajectories in an effective Hamiltonian system, and the mean extinction time 〈T 〉 depend exponentially on the associated action S and the size of the population N , 〈T 〉 ∼ exp(NS). Because of qualitatively different bifurcation features for m = 1 and m ≥ 2, we derive independently the expressions of S as a function of the rescaled infection rate λ/μ. For the weak infection, S scales to the distance to the bifurcation with an exponent 2 for m = 1 and 3/2 for m ≥ 2. Finally, a rare-event simulation method is used to validate the theory.