| Abstract: |
| Epidemics have profoundly affected humanity throughout history, causing not only severe human losses but also major social and economic disruptions. Many infectious diseases that have produced large outbreaks in the past still persist today, while new ones continue to emerge. For this reason, mathematical models play a crucial role in understanding disease dynamics and in designing strategies to control their spread.
One of the fundamental models in mathematical epidemiology is the classical SIR model introduced by Kermack and McKendrick in 1927. This compartmental model divides the population into three groups: susceptible, infected, and recovered individuals. Despite its importance, the classical SIR framework relies on several simplifying assumptions, such as constant population size, deterministic transmission, and the absence of vaccination, which limit its applicability to real epidemic scenarios.
In this talk, we study more realistic epidemic models obtained by extending the classical SIR framework. In particular, we incorporate demographic effects and time-dependent vaccination, and we also introduce randomness in key parameters, such as the transmission rate, to capture the inherent variability observed in real epidemics.
Using systems of differential equations, we analyze the resulting models and investigate the conditions under which the disease either dies out or persists in the population. Finally, we complement the theoretical results with numerical simulations and discuss their epidemiological interpretation. |
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