## Abstract and Applied Analysis

### Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency

#### Abstract

Vaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccine-induced immunity depends on vaccination age and the vaccinated individuals fall back to the susceptible class after losing immunity. The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. The global dynamics of the model is established through construction of appropriate Lyapunov functionals and application of Lasalle’s invariance principle. As a result, the global stability of the infection-free equilibrium and endemic equilibrium is obtained and is fully determined by the basic reproduction number ${\mathfrak{R}}_{\mathrm{0}}$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2018 (2018), Article ID 8479638, 21 pages.

Dates
Revised: 26 June 2018
Accepted: 18 July 2018
First available in Project Euclid: 19 September 2018

https://projecteuclid.org/euclid.aaa/1537322517

Digital Object Identifier
doi:10.1155/2018/8479638

Mathematical Reviews number (MathSciNet)
MR3847504

Zentralblatt MATH identifier
07029296

#### Citation

M’pika Massoukou, Rodrigue Yves; Oukouomi Noutchie, Suares Clovis; Guiem, Richard. Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency. Abstr. Appl. Anal. 2018 (2018), Article ID 8479638, 21 pages. doi:10.1155/2018/8479638. https://projecteuclid.org/euclid.aaa/1537322517

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