Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes - C. Connell McCluskey (Mathematical Biosciences and Engineering)
We study a model of disease transmission with continuous age-structure for latentlyinfected individuals and for infectious individuals. The model is very appropriate fortuberculosis. Key theorems, including asymptotic smoothness and uniform persistence,are proven by reformulating the system as a system of Volterra integral equations. Thebasic reproduction number $\mathcal{R}_{0}$ is calculated. For $\mathcal{R}_{0}1$, a Lyapunov functionalis used to show that the endemic equilibrium is globally stable amongst solutions forwhich the disease is present. Finally, some special cases are considered.