Hopf and forward bifurcation of an integer and fractional-order SIR epidemic model with logistic growth of the susceptible individuals

2020 ◽  
Vol 64 (1-2) ◽  
pp. 615-633
Author(s):  
M. H. Akrami ◽  
A. Atabaigi
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Logistic Growth ◽  
Sir Epidemic Model ◽  
Sir Epidemic

scholarly journals Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yakui Xue ◽  
Tiantian Li
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic

We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease. First of all, for anyτ, we show that the disease-free equilibrium is globally asymptotically stable; whenR0<1, the disease will die out. Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for anyτ=0; whenR0>1, the disease will persist. However, for anyτ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained. Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate. At last, numerical simulations are performed to illustrate and verify the conclusions.

scholarly journals Solutions of Conformable Fractional-Order SIR Epidemic Model

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Atimad Harir ◽  
Said Malliani ◽  
Lalla Saadia Chandli
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Analytic Solution ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Transformation Method ◽  
Conformable Fractional Derivative ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Fractional Differential

In this paper, the conformable fractional-order SIR epidemic model are solved by means of an analytic technique for nonlinear problems, namely, the conformable fractional differential transformation method (CFDTM) and variational iteration method (VIM). These models are nonlinear system of conformable fractional differential equation (CFDE) that has no analytic solution. The VIM is based on conformable fractional derivative and proved. The result revealed that both methods are in agreement and are accurate and efficient for solving systems of OFDE.

scholarly journals Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease

2020 ◽  
Vol 10 (23) ◽  
pp. 8316
Author(s):  
Kamil Kozioł ◽  
Rafał Stanisławski ◽  
Grzegorz Bialic
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Dynamic Properties ◽  
Sir Model ◽  
Domain Model ◽  
Sir Epidemic Model ◽  
Step Method ◽  
Order Difference ◽  
Sir Epidemic ◽  
The Time Domain

In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth

2016 ◽  
Vol 462 ◽  
pp. 816-826 ◽  
Author(s):  
Qun Liu ◽  
Daqing Jiang ◽  
Ningzhong Shi ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Periodic Solution ◽  
Epidemic Model ◽  
Logistic Growth ◽  
Sir Epidemic Model ◽  
Sir Epidemic

Global dynamics of a fractional-order SIR epidemic model with memory

2020 ◽  
pp. 2050071 ◽  
Author(s):  
Parvaiz Ahmad Naik
Keyword(s):  
Fractional Derivative ◽  
Memory Effect ◽  
Fractional Order ◽  
Epidemic Model ◽  
Memory Trace ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic

In this paper, an investigation and analysis of a nonlinear fractional-order SIR epidemic model with Crowley–Martin type functional response and Holling type-II treatment rate are established along the memory. The existence and stability of the equilibrium points are investigated. The sufficient conditions for the persistence of the disease are provided. First, a threshold value, [Formula: see text], is obtained which determines the stability of equilibria, then model equilibria are determined and their stability analysis is considered by using fractional Routh-Hurwitz stability criterion and fractional La-Salle invariant principle. The fractional derivative is taken in Caputo sense and the numerical solution of the model is obtained by L1 scheme which involves the memory trace that can capture and integrate all past activity. Meanwhile, by using Lyapunov functional approach, the global dynamics of the endemic equilibrium point is discussed. Further, some numerical simulations are performed to illustrate the effectiveness of the theoretical results obtained. The outcome of the study reveals that the applied L1 scheme is computationally very strong and effective to analyze fractional-order differential equations arising in disease dynamics. The results show that order of the fractional derivative has a significant effect on the dynamic process. Also, from the results, it is obvious that the memory effect is zero for [Formula: see text]. When the fractional-order [Formula: see text] is decreased from [Formula: see text] the memory trace nonlinearly increases from [Formula: see text], and its dynamics strongly depends on time. The memory effect points out the difference between the derivatives of the fractional-order and integer order.

Impact of media coverage on a fractional-order SIR epidemic model

2021 ◽  
Author(s):  
Chandan Maji
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Media Coverage ◽  
Lambert W Function ◽  
Order System ◽  
Media Effect ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic ◽  
Number Formula

In this work, we formulated and analyzed a fractional-order epidemic model of infectious disease (such as SARS, 2019-nCoV and COVID-19) concerning media effect. The model is based on classical susceptible-infected-recovered (SIR) model. Basic properties regarding positivity, boundedness and non-negative solutions are discussed. Basic reproduction number [Formula: see text] of the system has been calculated using next-generation matrix method and it is seen that the disease-free equilibrium is locally as well as globally asymptotically stable if [Formula: see text], otherwise unstable. The existence of endemic equilibrium point is established using the Lambert W function. The condition for global stability has been derived. Numerical simulation suggests that fractional order and media have a large effect on our system dynamics. When media impact is stronger enough, our fractional-order system stabilizes the oscillation.

Bifurcation and stability analysis of a discrete SIR epidemic model of fractional order

2022 ◽  
Author(s):  
A. George Maria Selvam ◽  
D. Abraham Vianny ◽  
S. Britto Jacob ◽  
D. Vignesh
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Bifurcation And Stability
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