MATHEMATICAL ANALYSIS OF AN AGE-STRUCTURED QUARANTINE/ISOLATION MODEL

Abstract

A new age-structured model for disease transmission, subject to the use of quarantine (of asymptomatic cases) and isolation (of individuals with disease symptoms) is presented and rigorously analyzed.  The model is, first of all, shown to be properly-posed mathematically by formulating it as an abstract Cauchy problem.  For the case where the contact rate is separable (i.e., β(a, b) = β₁(a)β₂(b)), rigorous analysis of the model reveals that it has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity.  The model has a unique endemic equilibrium when the threshold quantity exceeds unity.  The endemic equilibrium is shown to be locally stable whenever its associated reproduction number exceeds unity.  Furthermore, it is shown that adding age-factor to the basic quarantine-isolation model in M. A. Safi and A. B. Gumel (Discrete Contin. Dyn. Syst. Ser. B. : 209-231, 2010) does not alter the qualitative dynamics of the autonomous system (with respect to the elimination or persistence of the disease).  Numerical simulations show disease elimination whenever its associated reproduction number is less than unity and the disease will persist in this case whenever its associated reproduction number exceeds unity.