A higher-order interaction model of susceptible-infected-susceptible epidemics on networks with nonlinear microscopic incidence rate

This work studies spreading of susceptible-infected-susceptible models on general networks characterized by microscopic nonlinear incidence rates, where the likelihood of a susceptible node becoming infected is expressed as a nonlinear function of the number of its infected neighbors. When the infection function is a general polynomial, we analytically develop a quenched mean-field model, encompassing two different types of higher-order interaction terms. Notably, these higher-order terms exhibit strong similarities to the established simplicial spreading model and the general higher-order spreading model, with the primary distinction lying in the varying coefficients of the involved variables. Specifically, when the infection function is formulated as a quadratic polynomial, the theoretical model well approximates results obtained from continuous-time stochastic simulations conducted on scale-free networks. These simulations confirm the existence of discontinuous phase transitions in such systems.