Qualitative behavior of a discrete SIR epidemic model

Din, Qamar

doi:10.1142/s1793524516500923

Cited by 15 publications

(8 citation statements)

References 17 publications

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“…Kwon and Jung [23] employed a discrete version of SEIR model to characterize the spread of coronavirus MERS in Korea, showing that an effective quarentine plan would reduce the maximum number of infected population by about 69% and MERS fade-out period may be shortened by about 30%. Din [24] analyzed the global stability analysis of the equilibrium points in the discrete-time form of SIR model. Enatsu et al [22] used a backward differential scheme to discretize a class of SIR differential models showing that the effect of discretization is harmless to the global stability of the epidemic equilibrium.…”

Section: Introductionmentioning

confidence: 99%

A Dynamical Map to Describe COVID-19 Epidemics

Reis¹,

Savi²

2021

Preprint

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This paper proposes a dynamical map to describe COVID-19 epidemics based on the classical susceptible-exposed-infected-recovered (SEIR) model. The novel map represents Covid-19 discrete-time dynamics standing for the infected, cumulative infected and vaccinated populations. The simplicity of the discrete description allows the analytical calculation of useful information to evaluate the epidemic stage and to support decision making. In this regard, it should be pointed out the estimation of the number death cases and the herd immunization point. Numerical simulations show the model capacity to describe Covid-19 dynamics properly representing real data and describing different scenario patterns. Real data of Germany, Italy and Brazil are of concern to verify the model ability to describe Covid-19 dynamics. The model showed to be useful to describe the epidemic evolution and the effect of vaccination, being able to predict different pandemic scenarios.

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Section: Introductionmentioning

confidence: 99%

A Dynamical Map to Describe COVID-19 Epidemics

Reis¹,

Savi²

2021

Preprint

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“…In this paper, we consider an discrete time SIR epidemic model with vaccination and obtained the conditions for the existence of the equilibrium points and discussed the stability of the system at DFE and Estimates on R 0 have been obtained to determine the emergence of diseases such as measles, chickenpox and smallpox [24]. We present the dynamics of the model with the effect of vaccine ( [1], [2]). In Example 4.1-(a) and in Example 4.2-(a), we observe that the diseases free equilibrium is local asymptotic stable since R 0 < 1 (see Figure-1) and the endemic equilibrium point is local asymptotic stable since R 0 > 1 (see Figure-3) by taking p = 0.0005 and N = 100.…”

Section: Resultsmentioning

confidence: 99%

“…In this paper, we focus on the dynamics of a SIR epidemic model by including vaccination to the model as presented in [2]. The general SIR epidemic model is of the following form [1]:…”

Section: The Discrete Time Systemmentioning

confidence: 99%

Bifurcation and Stability Analysis of a Discrete Time Sir Epidemic Model with Vaccination

Gümüş

Selvam

Vianny

2019

ijaa

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In this paper, we study the qualitative behavior of a discrete-time epidemic model with vaccination. Analysis of the model shows forth that the Disease Free Equilibrium (DFE) point is asymptotically stable if the basic reproduction number R 0 is less than one, while the Endemic Equilibrium (EE) point is asymptotically stable if the basic reproduction number R 0 is greater than one. The results are reinforced with numerical simulations and enhanced with graphical representations like time trajectories, phase portraits and bifurcation diagrams for different sets of parameter values.

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“…Kwon and Jung [25] employed a discrete version of the SEIR model to characterize the spread of coronavirus MERS in Korea, showing that an effective quarentine plan would reduce the infected population maximum number of 69% and MERS fade-out period may be shortened of 30%. Din [26] analyzed the global stability of the equilibrium points of a discrete-time form of SIR model. Enatsu et al [24] used a backward differential scheme to discretize a class of SIR differential model, analyzing the global stability of the epidemic equilibrium.…”

Section: Introductionmentioning

confidence: 99%

A dynamical map to describe COVID-19 epidemics

Reis

Savi

2021

Eur. Phys. J. Spec. Top.

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Nonlinear dynamics perspective is an interesting approach to describe COVID-19 epidemics, providing information to support strategic decisions. This paper proposes a dynamical map to describe COVID-19 epidemics based on the classical susceptible-exposed-infected-recovered (SEIR) differential model, incorporating vaccinated population. On this basis, the novel map represents COVID-19 discretetime dynamics by adopting three populations: infected, cumulative infected and vaccinated. The map promotes a dynamical description based on algebraic equations with a reduced number of variables and, due to its simplicity, it is easier to perform parameter adjustments. In addition, the map description allows analytical calculations of useful information to evaluate the epidemic scenario, being important to support strategic decisions. In this regard, it should be pointed out the estimation of the number deaths, infection rate and the herd immunization point. Numerical simulations show the model capability to describe COVID-19 dynamics, capturing the main features of the epidemic evolution. Reported data from Germany, Italy and Brazil are of concern showing the map ability to describe different scenario patterns that include multi-wave pattern with bell shape and plateaus characteristics. The effect of vaccination is analyzed considering different campaign strategies, showing its importance to control the epidemics.

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Qualitative behavior of a discrete SIR epidemic model

Cited by 15 publications

References 17 publications

A Dynamical Map to Describe COVID-19 Epidemics

A Dynamical Map to Describe COVID-19 Epidemics

Bifurcation and Stability Analysis of a Discrete Time Sir Epidemic Model with Vaccination

A dynamical map to describe COVID-19 epidemics

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