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An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model

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Abstract

This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20–43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of Cai and Li (AMM 33:2919–2926, 2009) are effectively solved. The corresponding optimal control system with vaccination, awareness campaigns and treatment is further established and four different control strategies are compared by numerical simulations to contain hepatitis B. It is concluded that joint implementation of these measures can minimize the numbers of exposed and infectious individuals in the shortest time, so it is the most efficient strategy to curb the hepatitis B epidemic. Moreover, vaccination for newborns plays the core role and maintains the high level of population immunity.

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Acknowledgements

The work is supported by Natural Science Foundation of Hubei Province (Nos. 2019CFB241, 2019CFB773) and National Natural Science Foundation of China (Nos. 11871201,11961023).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Minzu University, Enshi, 445000, People’s Republic of China

    Xingyu Wang, Zhijun Liu, Lianwen Wang & Huili Xiang

  2. Enshi Special Care Hospital, Enshi, 445000, People’s Republic of China

    Caihong Guo

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  1. Xingyu Wang
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Correspondence to Lianwen Wang.

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Wang, X., Liu, Z., Wang, L. et al. An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model. J. Appl. Math. Comput. 67, 707–730 (2021). https://doi.org/10.1007/s12190-020-01487-5

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