On an Sir Epidemic Model for the COVID-19 Pandemic and the Logistic Equation

Sen, Manuel De la; Ibeas, Asier

doi:10.1155/2020/1382870

Cited by 19 publications

(29 citation statements)

References 52 publications

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“…follow under the same condition using similar arguments to those of the second part of the proof of Theorem 2 on the uniqueness of the disease-free equilibrium point, the lack of complex eigenvalues in the dynamics of a formally similar auxiliary system to (32) by replacing for all samples ∆E i → E i , ∆I i → I i and the convergence to a limit of its forcing term as a result of the convergence to zero of the infective subpopulations.…”

Section: Stability Around the Disease-free Equilibrium Pointmentioning

confidence: 94%

“…Figure 15 displays the dynamics of the model along with the number of real cases reported in Italy from 26 February 2020 (which corresponds to the first day of simulation) for 145 consecutive days. This example for the COVID-19 pandemic has been considered previously in [31,32].…”

Section: Example 2 Application To the Covid-19 Pandemicmentioning

confidence: 99%

“…There is no vaccination nor loss of immunity. Figure 15 displays th namics of the model along with the number of real cases reported in Italy from 26 ruary 2020(which corresponds to the first day of simulation) for 145 consecutive This example for the COVID-19 pandemic has been considered previously in [31,32] In the absence of loss of immunity, all the population becomes immune asym cally. The following cases discuss the effects of loss of immunity and vaccination o COVID-19 dynamics.…”

Section: Example 2 Application To the Covid-19 Pandemicmentioning

confidence: 99%

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On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility

2021

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A new discrete Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is proposed, and its properties of non-negativity and (both local and global) asymptotic stability of the solution sequence vector on the first orthant of the state-space are discussed. The calculation of the disease-free and the endemic equilibrium points is also performed. The model has the following main characteristics: (a) the exposed subpopulation is infective, as it is the infectious one, but their respective transmission rates may be distinct; (b) a feedback vaccination control law on the Susceptible is incorporated; and (c) the model is subject to delayed partial re-susceptibility in the sense that a partial immunity loss in the recovered individuals happens after a certain delay. In this way, a portion of formerly recovered individuals along a range of previous samples is incorporated again to the susceptible subpopulation. The rate of loss of partial immunity of the considered range of previous samples may be, in general, distinct for the various samples. It is found that the endemic equilibrium point is not reachable in the transmission rate range of values, which makes the disease-free one to be globally asymptotically stable. The critical transmission rate which confers to only one of the equilibrium points the property of being asymptotically stable (respectively below or beyond its value) is linked to the unity basic reproduction number and makes both equilibrium points to be coincident. In parallel, the endemic equilibrium point is reachable and globally asymptotically stable in the range for which the disease-free equilibrium point is unstable. It is also discussed the relevance of both the vaccination effort and the re-susceptibility level in the modification of the disease-free equilibrium point compared to its reached component values in their absence. The influences of the limit control gain and equilibrium re-susceptibility level in the reached endemic state are also explicitly made viewable for their interpretation from the endemic equilibrium components. Some simulation examples are tested and discussed by using disease parameterizations of COVID-19.

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Section: Stability Around the Disease-free Equilibrium Pointmentioning

confidence: 94%

Section: Example 2 Application To the Covid-19 Pandemicmentioning

confidence: 99%

Section: Example 2 Application To the Covid-19 Pandemicmentioning

confidence: 99%

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On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility

2021

Self Cite

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“…In the last century several compartmental models in epidemiology are derivatives of the type Susceptible, Infected, and Recovered individuals (SIR), see for example [1,2] for further details and recent modeling contributions with more references therein [3][4][5][6][7]. The most widely used models, and among the simplest ones, proved to be those proposed by .…”

Section: Introductionmentioning

confidence: 99%

A mathematical model for the spread of COVID-19 and control mechanisms in Saudi Arabia

Bachar

Khamsi²,

Bounkhel

2021

Adv Differ Equ

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In this work, we develop and analyze a nonautonomous mathematical model for the spread of the new corona-virus disease (COVID-19) in Saudi Arabia. The model includes eight time-dependent compartments: the dynamics of low-risk $S_{L}$ S L and high-risk $S_{M}$ S M susceptible individuals; the compartment of exposed individuals E; the compartment of infected individuals (divided into two compartments, namely those of infected undiagnosed individuals $I_{U}$ I U and the one consisting of infected diagnosed individuals $I_{D}$ I D ); the compartment of recovered undiagnosed individuals $R_{U}$ R U , that of recovered diagnosed $R_{D}$ R D individuals, and the compartment of extinct Ex individuals. We investigate the persistence and the local stability including the reproduction number of the model, taking into account the control measures imposed by the authorities. We perform a parameter estimation over a short period of the total duration of the pandemic based on the COVID-19 epidemiological data, including the number of infected, recovered, and extinct individuals, in different time episodes of the COVID-19 spread.

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“…Based on heart rate and sleep data collected from wearables, Zhu et al [15] proposed a framework to predict the prevalence of COVID-19 in different countries and cities. In [16], the Susceptible-Infectious-Recovered (SIR) epidemic model was proposed and explained by logistic equation. Msmali et al [17] used a mathematical model to study the role of behavior change in slowing the spread of COVID-19 in Saudi Arabia.…”

Section: Introductionmentioning

confidence: 99%

Generalized SEIR Epidemic Model for COVID-19 in a Multipatch Environment

Meng

Zhu

2021

Discrete Dynamics in Nature and Society

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In this paper, an n -patch SEIR epidemic model for the coronavirus disease 2019 (COVID-19) is presented. It is shown that there is unique disease-free equilibrium for this model. Then, the dynamic behavior is studied by the basic reproduction number. The transmission of COVID-19 is fitted based on actual data. The influence of quarantined rate and population migration rate on the spread of COVID-19 is also discussed by simulation.

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On an Sir Epidemic Model for the COVID-19 Pandemic and the Logistic Equation

Cited by 19 publications

References 52 publications

On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility

On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility

A mathematical model for the spread of COVID-19 and control mechanisms in Saudi Arabia

Generalized SEIR Epidemic Model for COVID-19 in a Multipatch Environment

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