Speaker
Description
We analyse an infection-age structured epidemic model where both infectivity and immunity loss depend on time since infection \cite{Scarabel2026}. The model can be formulated as a nonlinear renewal equation for the incidence or as a PDE for the infected population. Using ODE approximations and numerical bifurcation analysis, we study gamma-distributed infection durations and show that distribution shape critically affects endemic equilibrium stability, even when $R_0$ and the mean infectious period are fixed. We identify regions of bistability, where a stable endemic state coexists with a stable periodic orbit—providing, to our knowledge, the first example of such behaviour in models with waning immunity alone. Our analysis also shows how standard compartmental models, which impose implicit assumptions on infection duration, may yield to spurious dynamical outcomes.
Bibliography
@article{Scarabel2026,
title = {Genuine and spurious bistability in a simple epidemic model with waning immunity},
author = {F. Scarabel and H. Coldwell and T. Cassidy},
journal = {Mathematical Biosciences},
volume = {396},
pages = {109671},
year = {2026},
issn = {0025-5564},
doi = {https://doi.org/10.1016/j.mbs.2026.109671},
url = {https://www.sciencedirect.com/science/article/pii/S0025556426000611}
}
