Efficiency of Protection in the Presence of Immigration Process for an Age-Structured Epidemiological Model.

This paper studies the efficiency of protection in containing an epidemic in the case of immigration using a triple age structured model. For determining this efficiency, we split our study into two different cases, (i) with immigration flow into all model classes, (ii) without infected immigrants flow. For (i), we prove that the investigated model has no threshold dynamics and the infection always persists and the unique endemic equilibrium is globally stable. For (ii), we prove that by stopping the infected immigration flow, we obtain the threshold dynamics again. Therefore, we confirm that the infected immigration flow is responsible for eliminating the threshold dynamics. The global stability results in each case are shown with the help of the Lyapunov method. Some graphical representations are used to confirm the obtained results. [ABSTRACT FROM AUTHOR]