Convergence Analysis of Epidemic Models over Contact and Migration Graphs

In this paper, we study the susceptible-infected-susceptible (SIS) epidemic spreading model under population migration on multilayer networks. Specifically, we consider two-layer contact-migration networks, in which one layer of the multilayer networks describes the contact patterns between different populations and the other one captures the possible migration paths between any two sites. By using Lyapunov methods as well as Markov chain theory, we study convergence properties of the SIS epidemic dynamics on the two-layer contact-migration networks either by establishing the structural conditions under which the multilayer networked system always evolves into the disease-free equilibrium or by deriving the algebraic conditions below which the system converges to the disease-free equilibrium. Finally, two simulation examples are given to verify our theoretical results.