Age-Structured Modeling of COVID-19 Transmission and Vaccine Response

Abstract

This research presents an age-structured Susceptible-Vaccinated-Exposed-AsymptomaticSymptomatic-Hospitalized (SVEASH) model for COVID-19 transmission, which incorporates agedependent recruitment rates, transmission dynamics, contact patterns, and various infection forces. It assumes perfect vaccination, ensuring permanent immunity. The study investigates the mathematical properties of  the model, including the existence of equilibrium states and the local stability of the disease-free equilibrium (E^0). The basic  reproduction number (R0), a critical threshold for stability, is derived as a weighted average across both asymptomatic and symptomatic  infection classes. The model is solved analytically using the Laplace transform, and simulations demonstrate that vaccinating up to 85% of  the global population between the ages of 0 and 80 can significantly reduce the peak of the disease and shorten the duration of the  epidemic. Additionally, the research emphasizes the importance of vaccinating not only susceptible and hospitalized individuals but also  those who have recovered, further aiding in the control of the outbreak.