Dynamics of an fractional SEIR epidemic model with infectivity in latent period and general nonlinear incidence rate

Naim, Mouhcine; Lahmidi, Fouad; Namir, Abdelwahed; Kouidere, Abdelfatah

doi:10.1016/j.chaos.2021.111456

Cited by 14 publications

(4 citation statements)

References 42 publications

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“…Applications of SEIR model in epidemics can be found in [10,51,52]. In [53][54][55][56][57][58], fractional extensions of SEIR model with Caputo-type derivative were presented and studied.…”

Section: Generalized Mathematical Modelmentioning

confidence: 99%

Numerical solutions of fractional epidemic models with generalized Caputo-type derivatives

Hajaj

Odibat²

2023

Phys. Scr.

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Recently, a general framework of fractional operators, that includes the Caputo model as a particular case, has been introduced and some applications in the area of fractional calculus have been presented. In this paper, novel fractional epidemic models with generalized Caputo-type derivatives were proposed. The universal predictor-corrector method was modified here to deal with the considered epidemic models for the purposes of simulation. The behavior and complex dynamic of these hybrid fractional epidemic models were studied using the modified method. The dynamics of the generalized Caputo-type fractional SIR, HIV and SEIR models were investigated by numerical simulation. Basically, the effect of generalized Caputo-type fractional derivative operator parameters on the dynamic behavior of the proposed epidemic models was discussed.

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Section: Generalized Mathematical Modelmentioning

confidence: 99%

Numerical solutions of fractional epidemic models with generalized Caputo-type derivatives

Hajaj

Odibat²

2023

Phys. Scr.

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“…Naim. et al [14] discussed the global existence and uniqueness, non-negativity, and finiteness of solutions pertaining to an SEIR model characterized by a nonlinear incidence rate given by the function f (S, I)I + g(S, E)E. The study demonstrated that the model features two primary equilibria: the disease-free equilibrium and the endemic equilibrium. Utilizing Lyapunov functionals in conjunction with LaSalle's invariance principle, the authors have established the global asymptotic stability of these equilibria.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Semi-Parametric SEIR Model with Infectivity in an Incubation Period

Zhang,

Jin

2024

Mathematics

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This paper introduces stochastic disturbances into a semi-parametric SEIR model with infectivity in an incubation period. The model combines the randomness of disease transmission and the nonlinearity of transmission rate, providing a flexible framework for more accurate description of the process of infectious disease transmission. On the basis of the discussion of the deterministic model, the stochastic semi-parametric SEIR model is studied. Firstly, we use Lyapunov analysis to prove the existence and uniqueness of global positive solutions for the model. Secondly, the conditions for disease extinction are established, and appropriate stochastic Lyapunov functions are constructed to discuss the asymptotic behavior of the model’s solution at the disease-free equilibrium point of the deterministic model. Finally, the specific transmission functions are enumerated, and the accuracy of the results are demonstrated through numerical simulations.

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“…Memory effect is an essential characteristic of fractional-order derivatives which made fractional calculus and its applications widely used in many fields of science and engineering [11,12,13,14,15,16,17]. Obviously, this feature is very relevant for modeling the spread of infections [18,19,20,21,22,23,24]. For this reason, many researchers have adopted this analytical vision [25,26,27,28,29,30,31].…”

Section: Introductionmentioning

confidence: 99%

Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption

Naim

Sabbar

Zeb

2022

mmnsa

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This article deals with a Caputo fractional-order viral model that incorporates the non-cytolytic immune hypothesis and the mechanism of viral replication inhibition. Firstly, we establish the existence, uniqueness, non-negativity, and boundedness of the solutions of the proposed viral model. Then, we point out that our model has the following three equilibrium points: equilibrium point without virus, equilibrium state without immune system, and equilibrium point activated by immunity with humoral feedback. By presenting two critical quantities, the asymptotic stability of all said steady points is examined. Finally, we examine the finesse of our results by highlighting the impact of fractional derivatives on the stability of the corresponding steady points.

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Dynamics of an fractional SEIR epidemic model with infectivity in latent period and general nonlinear incidence rate

Cited by 14 publications

References 42 publications

Numerical solutions of fractional epidemic models with generalized Caputo-type derivatives

Numerical solutions of fractional epidemic models with generalized Caputo-type derivatives

A Stochastic Semi-Parametric SEIR Model with Infectivity in an Incubation Period

Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption

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