Stability analysis of a novel epidemics model with vaccination and nonlinear infectious rate

Defang Liu; Bochu Wang; Songtao Guo

doi:10.1016/j.amc.2013.07.016

Stability analysis of a novel epidemics model with vaccination and nonlinear infectious rate

Appl Math Comput. 2013 Sep 15:221:786-801. doi: 10.1016/j.amc.2013.07.016. Epub 2013 Aug 2.

Authors

Defang Liu^{1

2}, Bochu Wang^{1

2}, Songtao Guo³

Affiliations

¹ College of Bioengineering, Chongqing University, Chongqing 400044, China.
² Key Laboratory of Biorheological Science and Technology (Chongqing University), Ministry of Education, Bioengineering College, Chongqing University, Chongqing 400044, China.
³ College of Computer Science, Chongqing University, Chongqing 400044, China.

Abstract

In this paper, by considering pathogen evolution and human interventions behaviors with vaccines or drugs, we build up a novel SEIRW model with the vaccination to the newborn children. The stability of the SEIRW model with time-varying perturbation to predict the evolution tendency of the disease is analyzed. Furthermore, we introduce a time-varying delay into the susceptible and infective stages in the model and give some global exponential stability criteria for the time-varying delay system. Finally, numerical simulations are presented to verify the results.

Keywords: Epidemic model; Growth behavior; Growth rate of viruses; Stability analysis; Vaccination.