Modelling Covid-19 Transmissions and Vaccine Response in An Age-Structured Population

This research presents an age-structured Susceptible-Vaccinated-Exposed-AsymptomaticSymptomatic-Hospitalized (SVEASH) COVID-19 model that accounts for age-dependent recruitment and transmission rates, contact ratios, and multiple infection forces. It assumes perfect vaccination that guarantees permanent immunity. The study explores the mathematical properties of the model, determining the existence of equilibrium and the local stability of the disease-free equilibrium (𝐸 0 ). The basic reproduction number R0, a key threshold for stability, is calculated as a weighted average from both asymptomatic and symptomatic infection classes. Using the Laplace transform, the model is solved analytically, and simulations show that vaccinating up to 85% of the global population between ages 0-80 significantly reduces the disease's peak and shortens the epidemic's duration. The research also highlights the importance of vaccinating not only susceptible and hospitalized individuals but also those who have recovered, further aiding in controlling the outbreak.