Abstract
In this paper, we focus on the study of the dynamics of a certain age structured epidemic model. Our aim is to investigate the proposed model, which is based on the classical SIR epidemic model, with a general class of nonlinear incidence rate with some other generalization. We are interested to the asymptotic behavior of the system. For this, we have introduced the basic reproduction number R₀ of model and we prove that this threshold shows completely the stability of each steady state. Our approach is the use of general constructed Lyapunov functional with some results on the persistence theory. The conclusion is that the system has a trivial disease-free equilibrium which is globally asymptotically stable for R₀ < 1 and that the system has only a unique positive endemic equilibrium which is globally asymptotically stable whenever R₀ > 1. Several numerical simulations are given to illustrate our results.
Highlights
Mathematical models for the spread of epidemic infectious diseases in populations have been studied for a long time [1]
Has the structure of infection age, and the complete global stability analysis for an infection age-structured SIR epidemic model was recently done by Magal et al, [5]
We proposed and analyzed an infection age-structured SIR epidemic model with a general incidence rate
Summary
Mathematical models for the spread of epidemic infectious diseases in populations have been studied for a long time [1]. Has the structure of infection age (time elapsed since the infection), and the complete global stability analysis for an infection age-structured SIR epidemic model was recently done by Magal et al, [5] That is, they showed that the disease-free equilibrium in their model is globally asymptotically stable if R0 ≤ 1, whereas the endemic equilibrium is so if R0 > 1. In [27], Bentout and Touaoula established an infection age-structured SIR epidemic model with a general incidence rate They proved for their model that if R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable, whereas if R0 > 1, the endemic equilibrium is globally asymptotically stable.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
