  We study the influence of heterogeneous mobility patterns in a population on
the SIS epidemic model. In particular, we consider a patchy environment in
which each patch comprises individuals belonging the different classes, e.g.,
individuals in different socio-economic strata. We model the mobility of
individuals of each class across different patches through an associated
Continuous Time Markov Chain (CTMC). The topology of these multiple CTMCs
constitute the multi-layer network of mobility. At each time, individuals move
in the multi-layer network of spatially-distributed patches according to their
CTMC and subsequently interact with the local individuals in the patch
according to an SIS epidemic model. We derive a deterministic continuum limit
model describing these mobility-epidemic interactions. We establish the
existence of a Disease-Free Equilibrium (DFE) and an Endemic Equilibrium (EE)
under different parameter regimes and establish their (almost) global
asymptotic stability using Lyapunov techniques. We derive simple sufficient
conditions that highlight the influence of the multi-layer network on the
stability of DFE. Finally, we numerically illustrate that the derived model
provides a good approximation to the stochastic model with a finite population
and also demonstrate the influence of the multi-layer network structure on the
transient performance.
