Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks

TL;DR

This paper introduces an Equation-Free multiscale computational framework that uses optimization techniques like Simulated Annealing to analyze and predict epidemic dynamics on networks efficiently without explicit macroscopic equations.

Contribution

It presents a novel methodology combining Equation-Free approaches with optimization to analyze complex epidemic models at a systems level.

Findings

Successfully computed equilibrium bifurcation diagrams

Analyzed stability of stationary states

Demonstrated efficiency on a network epidemic model

Abstract

The surveillance, analysis and ultimately the efficient long-term prediction and control of epidemic dynamics appear to be one of the major challenges nowadays. Detailed atomistic mathematical models 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 simulation with coarse-grained, systems-level, analysis. The methodology provides a systematic approach for analyzing the parametric behavior of complex/ multi-scale 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 epidemic model deploying on a random regular connected graph. Using the individual-based microscopic 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 under a pairwise representation perspective.