Dynamics of a Double Age-Structured SEIRI Epidemic Model

Abstract

The age-structured approach plays a crucial role in epidemiological modelling as it accounts for age-specific variations in susceptibility, transmission and disease progressions, providing a more accurate description of disease dynamics. In this paper, we create an age-structured epidemic model that incorporates age-dependent susceptibility and latency, as well as a relapse phase, with the objective of investigating the global dynamics of this model under the impact of that combination. The very important threshold parameter \(\mathcal{R}_{0}\) was introduced, and it has shown that it completely controls the stability of each equilibrium of the model. Based on the Lyapunov functional approach, we show that the disease-free equilibrium is globally asymptotically stable when \(\mathcal{R}_{0}<1\), while the positive endemic equilibrium is globally asymptotically stable whenever \(\mathcal{R}_{0}>1\). Our results suggest that early diagnostic of latency individuals, reduction in transmission rate and improvements in treatment and heath-care of infected individuals may effectively control the spread of the disease.