Exploring the impact of healthcare capacity and time delays in SIR epidemic model

In this paper, we analyze a compartmental model for the spread of COVID-19 that incorporates the capacity of the healthcare system. The model is governed by a set of delayed differential equations, with a focus on a healthcare capacity function inversely proportional to the size of the infectious compartment. While the properties of the model with constant healthcare capacity have been studied before in Krawczyk et al., (2022), we extend this analysis to the dynamic case. We establish conditions for the global asymptotic stability of the disease-free equilibrium using a Lyapunov functional and investigate how the system’s trajectories depend on various time delay values. Additionally, we fit the model’s infectious compartment dynamics to Polish governmental data from autumn 2021.