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We study SIS epidemic spreading models under population dispersal onmulti-layer networks. We consider a patchy environment in which each patchcomprises individuals belonging to different classes. Individuals disperse toother patches on a multi-layer network in which each layer corresponds to aclass. The dispersal on each layer is modeled by a Continuous Time Markov Chain(CTMC). At each time, individuals disperse according to their CTMC andsubsequently interact with the local individuals in the patch according to anSIS model. We establish the existence of various equilibria under differentparameter regimes and establish their (almost) global asymptotic stabilityusing Lyapunov techniques. We also derive simple conditions that highlight theinfluence of the multi-layer network on the stability of these equilibria. Forthis model, we study optimal intervention strategies using a convexoptimization framework. Finally, we numerically illustrate the influence of themulti-layer network structure and the effectiveness of the optimal interventionstrategies.

SIS Epidemic Spreading under Multi-layer Population Dispersal in Patchy Environments