On global dynamics of COVID-19 by using SQIR type model under non-linear saturated incidence rate

Algehyne, Ebrahem A.; Din, Rahim Ud

doi:10.1016/j.aej.2020.08.040

Cited by 20 publications

(18 citation statements)

References 24 publications

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“…Novel coronavirus pneumonia transmission model (1) has a disease-free equilibrium E 0 (x) = (S 0 (x), 0, 0, 0, 0, 0, 0) . In order to further study the long-term dynamic behavior of the delayed diffusive self-limiting epidemics model in temporal-spatial heterogeneous environment, we demand to prove the existence of principal eigenvalues of novel coronavirus pneumonia transmission model (1). If τ is equal to 0, linearizing the second, the third, the forth, the fifth and the sixth equations of novel coronavirus pneumonia transmission model (1) at disease-free equilibrium, we get Let E = e λt (x), L = e λt (x), I 1 = e λt (x), I 2 = e λt (x), R = e λt (x), Q = e λt (x) , eq.…”

Section: Resultsmentioning

confidence: 99%

“…However, from the current research results, most of the researches are still based on ordinary differential equations. In Algehyne’s study [ 1 ], a new mathematical SQIR model for COVID-19 formed by taking into account the impact of quarantine has been examined. Although authors performed a detailed analysis of the local and global stability of the model, but they ignored the huge impact of the exposed population on the infection of the COVID-19 epidemic.…”

Section: Introductionmentioning

confidence: 99%

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The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

Zhu

Jiang

2021

BMC Infect Dis

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Background The global spread of the novel coronavirus pneumonia is still continuing, and a new round of more serious outbreaks has even begun in some countries. In this context, this paper studies the dynamics of a type of delayed reaction-diffusion novel coronavirus pneumonia model with relapse and self-limiting treatment in a temporal-spatial heterogeneous environment. Methods First, focus on the self-limiting characteristics of COVID-19, incorporate the relapse and self-limiting treatment factors into the diffusion model, and study the influence of self-limiting treatment on the diffusion of the epidemic. Second, because the traditional Lyapunov stability method is difficult to determine the spread of the epidemic with relapse and self-limiting treatment, we introduce a completely different method, relying on the existence conditions of the exponential attractor of our newly established in the infinite-dimensional dynamic system to determine the diffusion of novel coronavirus pneumonia. Third, relapse and self-limiting treatment have led to a change in the structure of the delayed diffusion COVID-19 model, and the traditional basic reproduction number $$R_0$$ R 0 no longer has threshold characteristics. With the help of the Krein-Rutman theorem and the eigenvalue method, we studied the threshold characteristics of the principal eigenvalue and found that it can be used as a new threshold to describe the diffusion of the epidemic. Results Our results prove that the principal eigenvalue $$\uplambda ^{*}$$ λ ∗ of the delayed reaction-diffusion COVID-19 system with relapse and self-limiting treatment can replace the basic reproduction number $$R_0$$ R 0 to describe the threshold effect of disease transmission. Combine with the latest official data and the prevention and control strategies, some numerical simulations on the stability and global exponential attractiveness of the diffusion of the COVID-19 epidemic in China and the USA are given. Conclusions Through the comparison of numerical simulations, we find that self-limiting treatment can significantly promote the prevention and control of the epidemic. And if the free activities of asymptomatic infected persons are not restricted, it will seriously hinder the progress of epidemic prevention and control.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

Zhu

Jiang

2021

BMC Infect Dis

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“…SIQRtype models have been applied to COVID-19 (Abdullah et al, 2021;Bhadauria et al, 2021;Mandal et al, 2020;Zeb et al, 2020). On the other hand, SQIR-type models have also been studied to consider the quarantine of susceptible individuals (Safi & Gumel, 2013;Algehyne & Din, 2021). SQIR-type models seem to correspond to the SVIR-type models, where V denotes the vaccinated population (Kribs-Zaleta & Velasco-Hernández, 2000;Liu et al, 2008).…”

Section: Addition Of Treatment Classesmentioning

confidence: 99%

Structure of epidemic models: toward further applications in economics

Kuniya¹

2021

JER

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In this paper, we review the structure of various epidemic models in mathematical epidemiology for the future applications in economics. The heterogeneity of population and the generalization of nonlinear terms play important roles in making more elaborate and realistic models. The basic, effective, control and type reproduction numbers have been used to estimate the intensity of epidemic, to evaluate the effectiveness of interventions and to design appropriate interventions. The advanced epidemic models includes the age structure, seasonality, spatial diffusion, mutation and reinfection, and the theory of reproduction numbers has been generalized to them. In particular, the existence of sustained periodic solutions has attracted much interest because they can explain the recurrent waves of epidemic. Although the theory of epidemic models has been developed in decades and the development has been accelerated through COVID-19, it is still difficult to completely answer the uncertainty problem of epidemic models. We would have to mind that there is no single model that can solve all questions and build a scientific attitude to comprehensively understand the results obtained by various researchers from different backgrounds.

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“…Always when a new virus appears, researchers look for effective solutions and methods to control the new virus, including vaccination, isolation, and quarantine. In the absence of the vaccine, the isolation and quarantine strategies remain effective to mitigate and eliminate the impact of the virus (see [26,27,28,29,30,31,32,33]).…”

Section: Introductionmentioning

confidence: 99%

On dynamics of fractional incommensurate model of Covid-19 with nonlinear saturated incidence rate

Hamou¹,

Azroul²,

Hammouch

et al. 2021

Preprint

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In December 2019, a new virus belonging to the coronavirus strain has been discovered in Wuhan, China, this virus has attracted world-wide attention and it spread rapidly in the world, reaching nearly 216 countries in the world in November 2020. In this chapter, we study the fractional incommensurate SIQR (susceptible, infections, quarantined and removed) COVID-19 model with nonlinear saturated incidence rate using Atangana-Baleanu fractional derivatives. The existence and uniqueness of the solutions for the fractional model is proved using fixed point theorem, the model are shown to have two equilibrium point (disease free and an endemic equilibrium). Some numerical simulations using Euler method are also carried out to support our theoretical results. We estimated the value of the fractional orders and the parameters of the proposed model using the least squares method. Further, the sensitivity analysis of the parameter is performed as a result, our incommensurate model gives a good approximation to real data of COVID-19.

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On global dynamics of COVID-19 by using SQIR type model under non-linear saturated incidence rate

Cited by 20 publications

References 24 publications

The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

Structure of epidemic models: toward further applications in economics

On dynamics of fractional incommensurate model of Covid-19 with nonlinear saturated incidence rate

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