We study a model of disease transmission with continuous age-structure for latently
infected individuals and for infectious individuals. The model is very appropriate for
tuberculosis. Key theorems, including asymptotic smoothness and uniform persistence,
are proven by reformulating the system as a system of Volterra integral equations. The
basic reproduction number $\mathcal{R}_{0}$ is calculated. For $\mathcal{R}_{0}<1$, the disease-free
equilibrium is globally asymptotically stable. For $\mathcal{R}_{0}>1$, a Lyapunov functional
is used to show that the endemic equilibrium is globally stable amongst solutions for
which the disease is present. Finally, some special cases are considered.
Citation: C. Connell McCluskey. Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes[J]. Mathematical Biosciences and Engineering, 2012, 9(4): 819-841. doi: 10.3934/mbe.2012.9.819
Abstract
We study a model of disease transmission with continuous age-structure for latently
infected individuals and for infectious individuals. The model is very appropriate for
tuberculosis. Key theorems, including asymptotic smoothness and uniform persistence,
are proven by reformulating the system as a system of Volterra integral equations. The
basic reproduction number $\mathcal{R}_{0}$ is calculated. For $\mathcal{R}_{0}<1$, the disease-free
equilibrium is globally asymptotically stable. For $\mathcal{R}_{0}>1$, a Lyapunov functional
is used to show that the endemic equilibrium is globally stable amongst solutions for
which the disease is present. Finally, some special cases are considered.
References
DownLoad: