A fractional-order infectivity SIR model

Angstmann, Christopher N.; Henry, Bryan R.; McGann, Anna V.

doi:10.1016/j.physa.2016.02.029

Cited by 76 publications

(61 citation statements)

References 26 publications

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“…While the fractional recovery SIR model can be obtained from the general fractional infectivity and fractional recovery SIR model, we are unable to obtain the fractional infectivity SIR model [11]. The fractional infectivity SIR model requires α = 1 and 0 < β < 1; hence β < α violates our non-negativity conditions for ρ(t).…”

Section: Reduction To Classic and Fractional Recovery Sir Modelsmentioning

confidence: 90%

“…Since Kermack and McKendrick, the SIR model has become widely used for modelling a range of diseases and has been extended to allow for re-infection, latent infections and the interaction of species [4,5]. More recently, there has been increased interest in the extension of SIR models through the incorporation of fractional derivatives [6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…For the standard SIR model, these probabilities are related to exponential waiting-time densities. The model can be constructed as a directed continuous-time random walk (CTRW) through the SIR compartments [10,11,13].…”

Section: Introductionmentioning

confidence: 99%

“…The classic SIR model cannot accomodate this; however, the age-structured models of Kermack and McKendrick [2,3] can model such diseases. Fractional time derivatives, which include integrals over the function's history, can also be used to incorporate the system's history [6][7][8][9][10][11]. The generalisation of an integer-order derivative to a fractional derivative is not unique, with typical examples being the Caputo derivative and Riemann-Liouville derivative [15].…”

Section: Introductionmentioning

confidence: 99%

“…Fractional derivatives have recently been included in compartment models in a physically consistent way by modelling the dynamics of transitions between compartments as a stochastic process, a CTRW [10,11,13]. The parameters in the resulting fractional-order equations are well-defined and consistent with the dynamics of the individuals in the population.…”

Section: Introductionmentioning

confidence: 99%

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A Fractional-Order Infectivity and Recovery SIR Model

2017

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Abstract:The introduction of fractional-order derivatives to epidemiological compartment models, such as SIR models, has attracted much attention. When this introduction is done in an ad hoc manner, it is difficult to reconcile parameters in the resulting fractional-order equations with the dynamics of individuals. This issue is circumvented by deriving fractional-order models from an underlying stochastic process. Here, we derive a fractional-order infectivity and recovery Susceptible Infectious Recovered (SIR) model from the stochastic process of a continuous-time random walk (CTRW) that incorporates a time-since-infection dependence on both the infectivity and the recovery of the population. By considering a power-law dependence in the infectivity and recovery, fractional-order derivatives appear in the generalised master equations that govern the evolution of the SIR populations. Under the appropriate limits, this fractional-order infectivity and recovery model reduces to both the standard SIR model and the fractional recovery SIR model.

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Section: Reduction To Classic and Fractional Recovery Sir Modelsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Fractional-Order Infectivity and Recovery SIR Model

2017

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A fractional order HIV/AIDS model based on the effect of screening of unaware infectives

Babaei

Jafari

Ahmadi

2019

Math Methods in App Sciences

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In this paper, a fractional order model for the spread of human immunodeficiency virus (HIV) infection is proposed to study the effect of screening of unaware infected individuals on the spread of the HIV virus. For this purpose, local asymptotic stability analysis of the disease‐free equilibrium is investigated. In addition, the model is studied for different values of the fractional order to show the relation between the variations of the reproduction number and the order of the proposed model. Finally, numerical solutions are simulated by using a predictor‐corrector method to illustrate the dynamics between susceptible individuals and unaware infected individuals.

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Global dynamics and bifurcation analysis of a fractional‐order SEIR epidemic model with saturation incidence rate

Ghori

Naik

et al. 2022

Math Methods in App Sciences

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The present paper studies a fractional‐order SEIR epidemic model for the transmission dynamics of infectious diseases such as HIV and HBV that spreads in the host population. The total host population is considered bounded, and Holling type‐II saturation incidence rate is involved as the infection term. Using the proposed SEIR epidemic model, the threshold quantity, namely, basic reproduction number scriptR0, is obtained that determines the status of the disease, whether it dies out or persists in the whole population. The model's analysis shows that two equilibria exist, namely, disease‐free equilibrium (DFE) and endemic equilibrium (EE). The global stability of the equilibria is determined using a Lyapunov functional approach. The disease status can be verified based on obtained threshold quantity scriptR0. If scriptR0<1, then DFE is globally stable, leading to eradicating the population's disease. If scriptR0>1, a unique EE exists, and that is globally stable under certain conditions in the feasible region. The Caputo type fractional derivative is taken as the fractional operator. The bifurcation and sensitivity analyses are also performed for the proposed model that determines the relative importance of the parameters in disease transmission. The numerical solution of the model is obtained by the generalized Adams–Bashforth–Moulton method. Finally, numerical simulations are performed to illustrate and verify the analytical results. From the obtained results, it is concluded that the order of the fractional derivative plays a significant role in the dynamic process. Also, from the sensitivity analysis results, it is seen that the parameter δ ( infection rate) is positively correlated to scriptR0, while the parameter μ (inhibition rate) is negatively correlated to scriptR0, which means these parameters are more sensitive than others in disease dynamics.

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A fractional-order infectivity SIR model

Cited by 76 publications

References 26 publications

A Fractional-Order Infectivity and Recovery SIR Model

A Fractional-Order Infectivity and Recovery SIR Model

A fractional order HIV/AIDS model based on the effect of screening of unaware infectives

Global dynamics and bifurcation analysis of a fractional‐order SEIR epidemic model with saturation incidence rate

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