Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence

Lianwen Wang, Zhijun Liu and Xingan Zhang

Applied Mathematics and Computation, 2016, vol. 284, issue C, 47-65

Abstract: An SVEIR epidemic model with imperfect vaccination and nonlinear incidence, and a general latent distribution is formulated. By constructing Lyapunov functionals, it is shown that the disease will die out if the vaccination reproduction number Rvac≤1 and the disease becomes endemic if Rvac>1. Furthermore, vaccination effects are analyzed. Two special forms the probability of remaining in latent class are discussed. When the probability is negatively exponentially distributed, we present an efficient approach of proving global stability of the endemic equilibrium of the SVEIR system of ordinary differential equations (ODEs), which may improve some known approaches. When the probability is a step-function, the delay differential equation (DDE) system derived is used to study the impacts of vaccination and saturated incidence on the mumps transmission.

Keywords: SVEIR model; Vaccination; Nonlinear incidence; Infinite distributed delay; Global stability; Lyapunov functional (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300316301771
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:284:y:2016:i:c:p:47-65

DOI: 10.1016/j.amc.2016.02.058

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().