Epidemic Threshold Analysis of an SEIMQR Model Incorporating Healthcare Resource Constraints

Abstract

Introduction Epidemic models commonly assume unlimited healthcare resources and overlook a critical operational reality: healthcare system overload reduces recovery rates and amplifies outbreak severity. We propose an enhanced susceptible-exposed-infected-mutant-quarantined-recovered (SEIMQR) model that explicitly links the recovery process to time-varying hospital-bed availability, and thereby better reflects practical healthcare constraints. Methods The model integrates a saturating, resource-dependent recovery function and uses the quarantine rate as the primary control parameter. We performed a systematic dynamic analysis using bifurcation theory and validated the model through numerical simulations and empirical coronavirus disease 2019 (COVID-19) surveillance data from the United Kingdom. These data covered distinct phases of the pandemic. Results Our analysis identified a precise quarantine threshold (\begin{document}$ \delta =0.573595 $\end{document}) that distinguishes disease elimination from endemic persistence. Simulation results show that strengthening quarantine measures effectively suppresses the epidemic scale. Furthermore, the model fit the reported cumulative case data with high accuracy across different variant-dominant periods and policy regimes, which demonstrates its adaptability. Conclusion These findings quantify a critical intervention threshold and illustrate the synergistic relationship between medical capacity and quarantine intensity. This study provides a theoretically grounded, resource-aware framework for guiding integrated public health strategies when healthcare resources are finite. Therefore, it supports more realistic epidemic preparedness and response planning.