@article{Mozokhina2025, 
author = {Anastasia Mozokhina and Ivan Popravka and Masoud Saade and Vitaly Volpert},
title = {Epidemic model with time delays and fertility/mortality rates},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {25849-25878},
keywords = {epidemic-model, time delay, fertility, mortality},
url = {https://www.sciopen.com/article/10.3934/math.20251143},
doi = {10.3934/math.20251143},
abstract = {We developed a delayed SIR (Susceptible-Infected-Recovered) model incorporating infectious/immune periods and demographics (fertility and mortality rates), proving the existence, nonnegativity, and uniqueness of solutions for the system under demographic equilibrium. Analysis confirmed a threshold at              R        0    =  1, with an endemic equilibrium emerging when              R        0    >  1. Crucially, the stability of this endemic state was governed by a critical mortality rate (       μ    c  ). High-mortality populations (   μ  >      μ    c  ) exhibited a stable endemic state, whereas low-mortality populations (   μ  <        μ    c  ) experienced instability and sustained oscillations. For these low-mortality populations, critical thresholds for the transmission rate (       β    c  ) and disease duration (       τ          1      c      ) were identified, beyond which destabilization occurred. This demonstrated a fundamental dual dependence of long-term disease dynamics on both demographic (e.g., life expectancy) and epidemiological (e.g., transmission rate, disease duration) parameters. Consequently, public health strategies (like vaccination targets) may need adjustment based on a population's demographic structure, not just its immediate epidemiological characteristics.}
}