TY - JOUR
T1 - Stability and Persistence of an Age Structured Epidemic Model with Mutation and Vaccination
AU - Duan , Xi-Chao
AU - Li , Xi-Na
AU - Li , Xue-Zhi
AU - Martcheva , Maia
JO - CSIAM Transactions  on Life Sciences
VL - 3
SP - 438
EP - 465
PY - 2025
DA - 2025/10
SN - 1
DO - http://doi.org/10.4208/csiam-ls.SO-2024-0010
UR - https://global-sci.org/intro/article_detail/csiam-ls/24510.html
KW - Age structured epidemic model, mutation, vaccination, basic reproduction number,
local stability, uniform persistence.
AB - <p style="text-align: justify;">In this paper, we propose an age-structured epidemic model with strain mutation and age-based vaccination. We define the reproduction numbers of both the original and mutant strains ($R_{0}^{1}$ and $R_{0}^{2}$). If the reproduction number $R_{0} &lt; 1$, the disease-free steady state is locally asymptotically stable. If the reproduction number $R_{0}^{2} &gt; 1$, there exists a dominant steady state of the mutant strain. Conditions for local stability of this dominant steady state are also obtained. If both reproduction numbers $R_{0}^{1}$ and $R_{0}^{2}$ are greater than 1, a coexistence steady state may occur. Finally, the uniform persistence of the disease described by our age-structured model is strictly proved when the reproduction number $R_{0}^{1} &gt; 1.$ By using the data of the COVID-19 epidemic in Wuhan and the theoretical results obtained in this paper, some numerical calculations are carried out to demonstrate the effect of the age-based vaccination strategy.</p>