Epidemic spreading on midscopic multi-layer network with optimal control mechanism

Abstract In this paper, an SIS-based model on heterogeneity, midscopic multi-layer network combining the inter-layer topology with the intra-layer statistical property is proposed. We discuss the global stability of disease-free and endemic equilibrium of the model. Then the dynamic optimization problem of epidemic spreading on multi-layer network is studied considering the heterogeneity of layers. An explicit expression of the optimal solutions is presented in the case where the interaction radius of intra-layer individual is heterogeneous. Numerical simulations are performed to illustrate the obtained theoretical results. It is proved that the optimal control mechanism can effectively minimize specific objective function. Meanwhile, the dynamics of sub-costs is constructed as the cost coefficients varying. Our findings reveal the necessity of studying midscopic networks and demonstrate the underlying interrelationship between individuals behavioral responses and spreading process on multi-layer network.