The Role of Medical Supply Shortages on an Age-Structured Epidemic Model

A shortage of medical resources can arise when a multitude of patients rapidly emerge during the initial phases of an emerging infectious disease, due to limited availability of healthcare resources. Chronological age plays a pivotal role in both foreseeing and preventing infection patterns. In this investigation, we present an Susceptible-Infected-Recovered (SIR) model that integrates an age-structured and a saturated treatment function, and demonstrate its well-posedness. Our analysis reveals intricate patterns in the system, characterized by a steady-state bifurcation involving a backward bifurcation and a stable bifurcation representing a Hopf bifurcation. Notably, numerical simulations demonstrate that when R-0 < 1, the system exemplifies a novel phenomenon wherein a disease-free equilibrium coexists harmoniously with an enduring Hopf bifurcation. We conduct a real application for model calibration and suggest that enhancing medical facilities and minimizing treatment delays may prove to be of paramount importance in curtailing the spread of the disease.