This paper studies a discrete-time time-varying multi-layer networked SIWS (susceptible-infected-water-susceptible) model with multiple resources under both single-virus and competing multi-virus settings. Besides the human-to-human interaction, we also consider that the disease can diffuse on different types of medium. We use \emph{resources} to refer to any media that the pathogen of a virus can spread through, and do not restrict the resource only to be water. In the single-virus case, we give a full analysis of the system's behaviour related to its healthy state and endemic equilibrium. In the multi-virus case, we show analytically that different equilibria appear driven by the competition among all viruses. We also show that some analytical results of the time-invariant system can be expanded into time-varying cases. Finally, we illustrate the results through some simulations.
@article{arxiv.2206.07425,
title = {Discrete-time Layered-network Epidemics Model with Time-varying Transition Rates and Multiple Resources},
author = {Shaoxuan Cui and Fangzhou Liu and Hildeberto Jardón-Kojakhmetov and Ming Cao},
journal= {arXiv preprint arXiv:2206.07425},
year = {2023}
}