A Kind of Time-Delayed COVID-19 Dynamical Model with Vaccination  

作　　者：Cheng’ao Li Junliang Lu Cheng’ao Li;Junliang Lu(School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, China)

机构地区：[1]School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, China

出　　处：《Applied Mathematics》2022年第4期356-375,共20页应用数学（英文）

摘　　要：In the paper, we study a kind of time-delayed novel coronavirus pneumonia dynamical model with vaccination. This model considers that people are vaccinated, and the human immune system has a series of processes, which need a certain time. We first obtain the disease-free equilibrium and the basic reproduction number R₀, and the system has a unique endemic equilibrium when R₀ > 1. Then we discuss the stability of the disease-free equilibrium and the endemic equilibrium with different delays τ. For τ = 0, using the Lyapunov function approach, we obtained the stability of disease-free equilibrium and the endemic equilibrium, respectively. For any delay τ ≠ 0, using the Routh-Hurwitz Criteria, we obtained that the disease-free equilibrium is locally asymptotically stable. We also find the critical value τ₀ at the endemic equilibrium, and obtain the condition that the system has a Hopf bifurcation at the endemic equilibrium. Finally, with the suitable choices of the parameters, some numerical simulations are presented in order to verify the effectiveness of the obtained theoretical results.In the paper, we study a kind of time-delayed novel coronavirus pneumonia dynamical model with vaccination. This model considers that people are vaccinated, and the human immune system has a series of processes, which need a certain time. We first obtain the disease-free equilibrium and the basic reproduction number R₀, and the system has a unique endemic equilibrium when R₀ > 1. Then we discuss the stability of the disease-free equilibrium and the endemic equilibrium with different delays τ. For τ = 0, using the Lyapunov function approach, we obtained the stability of disease-free equilibrium and the endemic equilibrium, respectively. For any delay τ ≠ 0, using the Routh-Hurwitz Criteria, we obtained that the disease-free equilibrium is locally asymptotically stable. We also find the critical value τ₀ at the endemic equilibrium, and obtain the condition that the system has a Hopf bifurcation at the endemic equilibrium. Finally, with the suitable choices of the parameters, some numerical simulations are presented in order to verify the effectiveness of the obtained theoretical results.

关 键 词：SVIQR Epidemic Model the Time-Delayed COVID-19 Dynamical Model Lyapunov Functional Hopf Bifurcation STABILITY 

分 类 号：O175[理学—数学]