Stability in a fractional order SIR epidemic model of childhood diseases with discretization

Selvam, A. George Maria; Vianny, D. Abraham; Jacintha, Mary

doi:10.1088/1742-6596/1139/1/012009

Cited by 11 publications

(4 citation statements)

References 2 publications

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“…Vaccination can be included in a epidemic model by assuming a proportion of susceptible individuals are vaccinated during each time interval ( [1], [3], [4], [5]). Vaccination operates by reducing the pool of susceptible individuals, and when this is reduced sufficiently, an infectious disease cannot spread within the population.…”

Section: Sir Epidemic Model With Vaccinationmentioning

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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Section: Sir Epidemic Model With Vaccinationmentioning

confidence: 99%

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

Gümüş

Selvam

Vianny

2019

ijaa

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“…Kermack and McKendrick pioneered compartment model to predict the spread of disease. Hence then, various epidemic models are studied to control infectious disease [3], [4], [5], [6], [7], [11], [12], [15].…”

Section: Introductionmentioning

confidence: 99%

Global stability and bifurcation analysis of a discrete time SIR epidemic model

Gümüş¹,

Cui²,

Selvam³

et al. 2022

MMN

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In this paper, we study the complex dynamical behaviors of a discrete-time SIR epidemic model. Analysis of the model demonstrates that the Diseases Free Equilibrium (DFE) point is globally asymptotically stable if the basic reproduction number is less than one while the Endemic Equilibrium (EE) point is globally asymptotically stable if the basic reproduction number is greater than one. The results are further substantiated visually with numerical simulations. Furthermore, numerical results demonstrate that the discrete model has more complex dynamical behaviors including multiple periodic orbits, quasi-periodic orbits and chaotic behaviors. The maximum Lyapunov exponent and chaotic attractors also confirm the chaotic dynamical behaviors of the model.

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“…Srivastava and Gunerhan 31 approximate the solution of the SIR epidemic model by using the conformable fractional differential transform method (CFDTM). The disease‐free equilibrium, endemic equilibrium points, and stability analysis are studied by Selvam et al 32 in this model. Jena et al 27 studied this model with the homotopy perturbation Elzaki transform method (HPETM).…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of SIR childhood diseases model with fractional Adams–Bashforth method

Rahul

Prakash

2022

Math Methods in App Sciences

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This work investigates a fractional Susceptible Infected Recovered (SIR) model to study childhood disease. We analyzed the proposed model by applying Caputo, Caputo-Fabrizio, and Atangana-Baleanu fractional derivatives. Here, we use the fractional Adams-Bashforth method to solve the childhood disease model with nonlocal operator. The proposed numerical technique is developed by combining the fundamental theorem of integral calculus with Lagrange's interpolation. This numerical approach is more efficient than the other existing numerical techniques and is easily computed using Matlab as a programming language. The existence and uniqueness of this fractional model are studied with the fixed-point theorem. These fractional derivatives show different asymptotic behaviors for the distinct values of the fractional order. The numerical results are presented graphically as well as in tabulated form for some value of fractional order.

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Stability in a fractional order SIR epidemic model of childhood diseases with discretization

Cited by 11 publications

References 2 publications

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

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

Global stability and bifurcation analysis of a discrete time SIR epidemic model

Numerical simulation of SIR childhood diseases model with fractional Adams–Bashforth method

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