  We consider an SIR-type (Susceptible $\to$ Infected $\to$ Recovered)
stochastic epidemic process with multiple modes of transmission on a contact
network. The network is given by a random graph following a multilayer
configuration model where edges in different layers correspond to potentially
infectious contacts of different types. We assume that the graph structure
evolves in response to the epidemic via activation or deactivation of edges. We
derive a large graph limit theorem that gives a system of ordinary differential
equations (ODEs) describing the evolution of quantities of interest, such as
the proportions of infected and susceptible vertices, as the number of nodes
tends to infinity. Analysis of the limiting system elucidates how the coupling
of edge activation and deactivation to infection status affects disease
dynamics, as illustrated by a two-layer network example with edge types
corresponding to community and healthcare contacts. Our theorem extends some
earlier results deriving the deterministic limit of stochastic SIR processes on
static, single-layer configuration model graphs. We also describe precisely the
conditions for equivalence between our limiting ODEs and the systems obtained
via pair approximation, which are widely used in the epidemiological and
ecological literature to approximate disease dynamics on networks. Potential
applications include modeling Ebola dynamics in West Africa, which was the
motivation for this study.
