[SS07] Dynamic system and applications to mathematical biology

[SS07-03] The role of medical supply shortages on an age-structured epidemic model

*Junyuan Yang¹, Miao Zhou¹, Jiaxu Li, Guiquan Sun¹ (1. Shanxi University (China))

Keywords:

backward bifurcation,Hopf bifurcation,limited medical resources,Lyapunov–Schmidt approach

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 talk, 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 R₀< 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.