New global dynamical results and application of several SVEIS epidemic models with temporary immunity

Lianwen Wang; Zhijun Liu; Caihong Guo; Yong Li; Xinan Zhang

doi:10.1016/j.amc.2020.125648

New global dynamical results and application of several SVEIS epidemic models with temporary immunity

Appl Math Comput. 2021 Feb 1:390:125648. doi: 10.1016/j.amc.2020.125648. Epub 2020 Sep 10.

Authors

Lianwen Wang¹, Zhijun Liu¹, Caihong Guo², Yong Li³, Xinan Zhang⁴

Affiliations

¹ Department of Mathematics, Hubei Minzu University, Enshi 445000, P.R.China.
² Enshi Special Care Hospital, Enshi 445000, P.R.China.
³ School of Information and Mathematics, Yangtze University, Jingzhou 434023, P.R.China.
⁴ School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P.R.China.

Abstract

This work applies a novel geometric criterion for global stability of nonlinear autonomous differential equations generalized by Lu and Lu (2017) to establish global threshold dynamics for several SVEIS epidemic models with temporary immunity, incorporating saturated incidence and nonmonotone incidence with psychological effect, and an SVEIS model with saturated incidence and partial temporary immunity. Incidentally, global stability for the SVEIS models with saturated incidence in Cai and Li (2009), Sahu and Dhar (2012) is completely solved. Furthermore, employing the DEDiscover simulation tool, the parameters in Sahu and Dhar'model are estimated with the 2009-2010 pandemic H1N1 case data in Hong Kong China, and it is validated that the vaccination programme indeed avoided subsequent potential outbreak waves of the pandemic. Finally, global sensitivity analysis reveals that multiple control measures should be utilized jointly to cut down the peak of the waves dramatically and delay the arrival of the second wave, thereinto timely vaccination is particularly effective.

Keywords: Global stability; Li-Muldowney geometric criterion; Nonlinear incidence; Parameter estimation; Temporary immunity; Vaccination.