SIS Epidemic Modelling on Homogeneous Networked System: General Recovering Process and Mean-Field Perspective

Abstract: Although we have made progress in understanding disease spread in complex systems with non-Poissonian activity patterns, current models still fail to capture the full range of recovery time distributions. In this paper, we propose an extension of the classic susceptible-infected-susceptible (SIS) model, called the general recovering process SIS (grp-SIS) model. This model incorporates arbitrary recovery time distributions for infected nodes within the system. We derive the mean-field equations assuming a homogeneous network, provide solutions for specific recovery time distributions, and investigate the probability density function (PDF) for infection times in the system's steady state. Our findings show that recovery time distributions significantly affect disease dynamics, and we suggest several future research directions, including extending the model to arbitrary infection processes and using the quasistationary method to address deviations in numerical results.