| Abstract: |
| We present a dynamical system that models the long-term impact of a pandemic on a population structured by age. Our analysis focuses on deriving the basic reproduction number to gain qualitative insight into the stability of the disease-free equilibrium states. This quantity, obtained through the next-generation matrix framework, serves as a key threshold parameter that determines whether an infection can invade and persist within the population. The methodology provides a rigorous mathematical foundation for understanding how age-dependent contact patterns, susceptibility, and demographic processes influence disease dynamics. This approach not only clarifies the role of population structure in shaping epidemic trajectories but also offers a systematic way to evaluate potential intervention strategies. Other aspects, such as the effect of vaccination, can also be incorporated and analyzed within this framework. |
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