Equation-Free multiscale computational analysis of individual-based epidemic dynamics on networks

The surveillance, analysis and ultimately the efficient long‐term prediction and control of epidemic dynamics appear to be some of the major challenges nowadays. Detailed individual‐based mathematical models on complex networks play an important role towards this aim. In this work, it is shown how one can exploit the Equation‐Free approach and optimization methods such as Simulated Annealing to bridge detailed individual‐based epidemic models with coarse‐grained, system‐level analysis within a pair‐wise representation perspective. The proposed computational methodology provides a systematic approach for analyzing the parametric behavior of complex/multiscale epidemic simulators much more efficiently than simply simulating forward in time. It is shown how steady state and (if required) time‐dependent computations, stability computations, as well as continuation and numerical bifurcation analysis can be performed in a straightforward manner. The approach is illustrated through a simple individual‐based SIRS epidemic model deploying on a random regular connected graph. Using the individual‐based simulator as a black box coarse‐grained timestepper and with the aid of Simulated Annealing I compute the coarse‐grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level.