A novel analysis approach of uniform persistence for a COVID-19 model with quarantine and standard incidence rate

Guo, Shuaiqi; Yang, Xue; Li, Xiliang; Zhang, Zheng

doi:10.48550/arxiv.2205.15560

Cited by 2 publications

(10 citation statements)

References 22 publications

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“…Then x t is the solution of system (1) through ϕ. Motivated by the persistence approach in [8], we have the following results.…”

Section: Weak Persistencementioning

confidence: 98%

Global stability of a time-delayed malaria model with standard incidence rate

Guo¹,

He²,

Cui³

2022

Preprint

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A four-dimensional delay differential equations (DDEs) model of malaria with standard incidence rate is proposed. By utilizing the limiting system of the model and Lyapunov direct method, the global stability of equilibria of the model is obtained with respect to the basic reproduction number R 0 . Specifically, it shows that the disease-free equilibrium E 0 is globally asymptotically stable (GAS) for R 0 < 1, and globally attractive (GA) for R 0 = 1, while the endemic equilibrium E * is GAS and E 0 is unstable for R 0 > 1. Especially, to obtain the global stability of the equilibrium E * for R 0 > 1, the weak persistence of the model is proved by some analysis techniques.

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“…Then x t is the solution of system (1) through ϕ. Motivated by the persistence approach in [8], we have the following results.…”

Section: Weak Persistencementioning

confidence: 98%

Global stability of a time-delayed malaria model with standard incidence rate

Guo¹,

He²,

Cui³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…From [16,Theorem 4.1], it follows that the COVID-19-free equilibrium V 0 is locally asymptotically stable if the control reproduction number R c < 1 and unstable if R c > 1. It is difficult to prove the local stability of the COVID-19 equilibrium V * by using the Routh-Hurwitz criterion.…”

Section: Local Stability Of the Covid-19 Equilibriummentioning

confidence: 99%

“…In this section, we will study the weak persistence of model (1) based on some analysis techniques in [14,16].…”

Section: Weak Persistencementioning

confidence: 99%

“…In particular, they proposed a novel analysis approach of uniform persistence of model (1) different from the traditional persistence methods. It is not difficult to obtain that model ( 1) is well-posed and dissipative in D = ϕ = (ϕ 1 , ϕ 2 , ϕ 3 , ϕ 4 , ϕ 5 , ϕ 6 ) T ∈ R 6 + : ∑ 6 i=1 ϕ i > 0 with R + = [0, ∞) (see [16]). Guo et al [16] remarked that the global stability problems of V 0 and V * were very practical and challenging, and they would settle these problems in future work.…”

Section: Introductionmentioning

confidence: 99%

“…It is not difficult to obtain that model ( 1) is well-posed and dissipative in D = ϕ = (ϕ 1 , ϕ 2 , ϕ 3 , ϕ 4 , ϕ 5 , ϕ 6 ) T ∈ R 6 + : ∑ 6 i=1 ϕ i > 0 with R + = [0, ∞) (see [16]). Guo et al [16] remarked that the global stability problems of V 0 and V * were very practical and challenging, and they would settle these problems in future work. The purpose of the current research is to solve those problems.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of COVID-19 models with asymptomatic infections and quarantine measures

Guo

Yang

et al. 2022

Preprint

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Considering the propagation characteristics of COVID-19 in different regions, the dynamics analysis and numerical demonstration of long-term and short-term models of COVID-19 are carried out, respectively. The long-term model is devoted to investigate the global stability of COVID-19 model with asymptomatic infections and quarantine measures. By using the limit system of the model and Lyapunov function method, it is shown that the COVID-19-free equilibrium V 0 is globally asymptotically stable if the control reproduction number Rc < 1 and globally attractive if Rc = 1, which means that COVID-19 will die out; the COVID-19 equilibrium V∗ is globally asymptotically stable if Rc > 1, which means that COVID-19 will be persistent. In particular, to obtain the local stability of V∗ , we use proof by contradiction and the properties of complex modulus with some novel details, and we prove the weak persistence of the system to obtain the global attractivity of V∗ . Moreover, the final size of the corresponding short-term model is calculated and the stability of its multiple equilibria is analyzed. Numerical simulations of COVID-19 cases show that quarantine measures and asymptomatic infections have a non-negligible impact on the transmission of COVID-19 2020 MSC: 34D23, 37N25, 92D30

show abstract

A novel analysis approach of uniform persistence for a COVID-19 model with quarantine and standard incidence rate

Cited by 2 publications

References 22 publications

Global stability of a time-delayed malaria model with standard incidence rate

Global stability of a time-delayed malaria model with standard incidence rate

Dynamics of COVID-19 models with asymptomatic infections and quarantine measures

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