A Mean-Field Approximation of SIR Epidemics on an Erdös-Rényi Network Model.

The stochastic nature of epidemic dynamics on a network makes their direct study very challenging. One avenue to reduce the complexity is a mean-field approximation (or mean-field equation) of the dynamics; however, the classic mean-field equation has been shown to perform sub-optimally in many applications. Here, we adapt a recently developed mean-field equation for SIR epidemics on a network in continuous time to the discrete time case. With this new discrete mean-field approximation, this proof-of-concept study shows that, given the density of the network, there is a strong correspondence between the epidemics on an Erdös-Rényi network and a system of discrete equations. Through this connection, we developed a parameter fitting procedure that allowed us to use synthetic daily SIR data to approximate the underlying SIR epidemic parameters on the network. This procedure has improved accuracy in the estimation of the network epidemic parameters as the network density increases, and is extremely cheap computationally.