Discrete-time layered-network epidemics model with time-varying transition rates and multiple resources

• DOI: 10.1016/j.automatica.2023.111303
• Publication Date: 2023-10-05T16:44:42Z
• Authors: Shaoxuan Cui; Fangzhou Liu; Hildeberto Jardón...; Ming Cao
• Keywords: 0301 basic medicine; Time-varying transition rates; Epidemic processes; 02 engineering and technology; Systems and Control (eess.SY); Electrical Engineering and Systems Science - Systems and Control; 3. Good health; 03 medical and health sciences; Multi-layer network; Discrete-time systems; 0202 electrical engineering, electronic engineering, information engineering; FOS: Electrical engineering, electronic engineering, information engineering; 93A15 37N25 92F05; Stability

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.