Stationarity in moment closure and quasi-stationarity of the SIS model

Previous epidemiological studies on SIS model have only considered the dynamic evolution of the mean value and the variance of the infected individuals. In this paper, through cumulant neglection, we use the dynamic equations of all the moments of infected individuals to develop a recursive method to compute the equilibria manifold of the moment closure ODE's. Specifically, we use the stable equilibria of the moment closure ODE's to obtain good approximations of the quasi-stationary states of the SIS model. This is a crucial step when the quasi-stationary distribution is highly skewed.

► The quasi-stationary distribution of the SIS model does not have explicit expression. ► We compute the equilibria manifold of the moment closure ODE's in cumulant truncation. ► The state equilibria approach the SIS quasi-stationary states. ► The approximations for highly skewed quasi-stationary distributions are improved.