Theoretical and numerical results for an age-structured SIVS model with a general nonlinear incidence rate

• Main Authors: Junyuan Yang, Yuming Chen
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2018-01-01
• Series: Journal of Biological Dynamics
• Subjects: infection age; vaccination age; nonlinear incidence; persistence; lyapunov functional
• Online Access: http://dx.doi.org/10.1080/17513758.2018.1528393

In this paper, we propose an SIVS epidemic model with continuous age structures in both infected and vaccinated classes and with a general nonlinear incidence. Firstly, we provide some basic properties of the system including the existence, uniqueness and positivity of solutions. Furthermore, we show that the solution semiflow is asymptotic smooth. Secondly, we calculate the basic reproduction number $ \mathcal {R}_0 $ by employing the classical renewal process, which determines whether the disease persists or not. In the main part, we investigate the global stability of the equilibria by the approach of Lyanpunov functionals. Some numerical simulations are conducted to illustrate the theoretical results and to show the effect of the transmission rate and immunity waning rate on the disease prevalence.