Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination

Abdelaziz, Mahmoud A. M.; Ismail, Ahmad Izani Md.; Abdullah, Farah Aini; Mohd, Mohd Hafiz

doi:10.1016/j.chaos.2020.110104

Cited by 16 publications

(11 citation statements)

References 26 publications

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“…Proposition 4. If P < P u (α, k ) , given in (19) , then the solution of the DTFO system ( 16) is nonnegative.…”

Section: Equilibrium Pointsmentioning

confidence: 99%

“…given by (19) . Note that, if the trajectory of the system ( 16) is in α,k , the system is well defined and represents an epidemiologic process with nonnegative solutions.…”

Section: Equilibrium Pointsmentioning

confidence: 99%

“…Finally, to show that depending on the population size the model can have negative solutions we set the total population to P = 270 , which is a value larger than P u (α, k ) given by (19) , consider α = 0 . 82 and k = 5 and 6.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Most models, follow the process of starting from models represented by equations or systems of differential equations, and substituting the ordinary derivatives by a fractional order ones using, for example, Caputo's definition of fractional derivative, [6] . A discrete model is obtained by applying some of the known discretization processes for this derivative [18][19][20][21][22] . In the last year, a new notion of fractional G-transform using modified Riemann-Liouville derivative with the Mittag-Leffler function as a kernel is introduced to analyze fractional epidemic models, [23] .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The discrete fractional order difference applied to an epidemic model with indirect transmission

Coll

Herrero

Ginestar

et al. 2022

Applied Mathematical Modelling

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“…Proposition 4. If P < P u (α, k ) , given in (19) , then the solution of the DTFO system ( 16) is nonnegative.…”

Section: Equilibrium Pointsmentioning

confidence: 99%

“…given by (19) . Note that, if the trajectory of the system ( 16) is in α,k , the system is well defined and represents an epidemiologic process with nonnegative solutions.…”

Section: Equilibrium Pointsmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The discrete fractional order difference applied to an epidemic model with indirect transmission

Coll

Herrero

Ginestar

et al. 2022

Applied Mathematical Modelling

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“…Recently, a very short number of contributions dedicated to study the dynamics of three dimensional discrete systems [1,5,8,9,11,13,19,27]. For example, discrete-time epidemic models SIR, SEIR and hypertensive or diabetic exposed to COVID-19 discussed in [1,9,13] respectively, in [27] the authors investigated discrete financial system and in [19], the authors studied discrete chaotic system.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Discrete-Time Chaotic Lü System

Rana

Uddin

2022

Pan-Amer. J. Math.

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A discrete-time chaotic Lü system is investigated. Firstly, we give the conditions of local stability of this system around feasible fixed points. Then, we show analytically that discretized Lü system undergoes a flip-Neimark Sacker (NS) bifurcation when one of the system parameter varies near its critical value. We confirm the existence of flip-NS bifurcation via explicit Flip-NS bifurcation criterion and determine the direction of both bifurcations with the help of center manifold theory and bifurcation theory. We carry out numerical simulations to affirm our analytical findings. Furthermore, we present Maximum Lyapunov exponents (MLEs) and Fractal dimension (FD) numerically in order to justify whether chaos exists in the system or not. At the end, we apply hybrid control strategy to eliminate chaotic trajectories of the system.

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Mathematical approach for impact of media awareness on measles disease

Kavya,

Veeresha

2023

Math Methods in App Sciences

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During the recent pandemic caused by COVID‐19, media awareness played a crucial role in educating people about social distancing, wearing masks, quarantine, vaccination, and medication. Media awareness brought individual behavioral changes among the people, which in turn helped reduce the infection rate. Motivated by this, we have formulated a mathematical model introducing a media compartment to mitigate measles disease transmission. In this paper, the SEIR model is used to study measles disease in three cases: one with a delay in vaccination, the second with regular vaccination, and the third with the impact of media awareness on the spreading of measles disease. Further, the dynamical behavior of the models is studied in terms of positivity, boundedness, equilibrium, and basic reproduction number (BRN). The sensitivity analysis of the models is conducted, which verifies the importance of the BRN ( ) to be less than one for disease eradication. The numerical study confirms the impact of media awareness on exposed and infected populations.

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Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination

Cited by 16 publications

References 26 publications

The discrete fractional order difference applied to an epidemic model with indirect transmission

The discrete fractional order difference applied to an epidemic model with indirect transmission

Dynamics of a Discrete-Time Chaotic Lü System

Mathematical approach for impact of media awareness on measles disease

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