Global stability of fractional SIR epidemic model

Santos, José Paulo Carvalho dos; Monteiro, Evandro; Vieira, Gustavo Borges

doi:10.5540/03.2017.005.01.0019

Cited by 13 publications

(8 citation statements)

References 7 publications

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“…This section reviews the fundamental definitions, theorems, concepts, and results that we will use throughout the remainder of this paper. For more details, we refer the reader to [28][29][30][31].…”

Section: Preliminaries Of Fractional-order Derivativementioning

confidence: 99%

Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2

Dehingia¹,

Mohsen

Alharbi

et al. 2022

Mathematics

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The prime objective of the current study is to propose a novel mathematical framework under the fractional-order derivative, which describes the complex within-host behavior of SARS-CoV-2 by taking into account the effects of memory and carrier. To do this, we formulate a mathematical model of SARS-CoV-2 under the Caputo fractional-order derivative. We derived the conditions for the existence of equilibria of the model and computed the basic reproduction number R0. We used mathematical analysis to establish the proposed model’s local and global stability results. Some numerical resolutions of our theoretical results are presented. The main result of this study is that as the fractional derivative order increases, the approach of the solution to the equilibrium points becomes faster. It is also observed that the value of R0 increases as the value of β and πv increases.

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Section: Preliminaries Of Fractional-order Derivativementioning

confidence: 99%

Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2

Dehingia¹,

Mohsen

Alharbi

et al. 2022

Mathematics

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“…The Lasalle invariance principle (see [55], [19]) gives conclusion that P * is globally asymptotically stable.…”

Section: The Stability Of Endemic-equilibrium Pointmentioning

confidence: 99%

“…Recent high-profile outbreaks, like those caused by Ebola, Zika, Pandemic influenza, Middle East Respiratory Syndrome (MERS), and COVID-19, have highlighted the global importance of infectious diseases and the need for coordinated efforts to prevent outbreaks. Fractional order models for influenza, dengue fever, malaria, and tuberculosis, for example [19]- [29]. The COVID-19 pandemic has already spread throughout the world and the people are aware of the disease and they are using precautions against the pandemic.…”

Section: Introductionmentioning

confidence: 99%

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A Fractional Order SITR Model for Forecasting of Transmission of COVID-19: Sensitivity Statistical Analysis

Al‐Zahrani¹,

Elsmih²,

Al-Zahrani³

et al. 2022

MJMS

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In this work, we investigate the effects of the contact rate between people on the covid-19 virus transmission through a susceptible-infected-treatment-recovered (SITR) fractional mathematical model. Several strategies are introduced, and the development methodology is constructed up in various cases based on the rate of individual contact, due to confinement and social distancing rules, which can be useful in reducing infection. The existence and uniqueness of the proposed model solution are established, as well as the basic reproduction number. The basic reproduction number has been used to control the dynamics of the fractional SITR model completely, which determines whether or not the infection is extinguished. The global stability of the infection-free balance and endemic equilibrium point of the proposed model has been fully established using the Lyapunov-LaSalle type theorem. Furthermore, a sensitivity analysis is carried out to find out which parameter is the most dominant to affect the disease's endemicity and to see how changes in parameters affect Covid-19's beginning disease transmission. The fractional Adams-Bashforth method is used to compute an iterative solution to the model. Finally, using the model parameter values to explain the importance of the arbitrary fractional-order derivative, the numerical results using MATLAB are presented.

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“…In epidemiology, many works involving fractional order derivative have been done, and most of them are mainly concerned with SIR-type models with linear incidence rate [9][10][11][12]. In [13], Saeedian et al studied the memory effect of an SIR epidemic model using the Caputo fractional derivative.…”

Section: Introductionmentioning

confidence: 99%