Stability of The Equilibrium of Nonlinear Dynamical Systems

Dzhalladova, Irada; Růžičková, Miroslava

doi:10.2478/tmmp-2018-0007

Cited by 3 publications

(3 citation statements)

References 2 publications

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“…There are two equilibrium points for the system (5), namely the disease-free equilibrium point and the endemic equilibrium point. The equilibrium point for the Caputo fractional model occurs when [29]…”

Section: The Equilibrium Point Of Fractional Modelmentioning

confidence: 99%

Fractional Mathematical Model of Hiv and Cd4+ T-Cells Interactions With Haart Treatment

Nisardi,

Kasbawati,

Putra

2023

JFMA

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This study provides the mathematical model of the interaction between the HIV and CD4+ T cells. This research develops other research by formulating a model with the fractional Caputo derivative approach with fractional order α. Based on the model, we obtain the equilibrium point and analyze the stability criterion of the equilibrium point. Furthermore, we perform the Next Generation Matrix method to calculate the basic reproduction number (𝑅 0 ). Then, we apply the Grunwald-Letnikov Explicit method to show the numerical result of the model. The result of this study could assist for future improvement, especially for fractional modelling.

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Section: The Equilibrium Point Of Fractional Modelmentioning

confidence: 99%

Fractional Mathematical Model of Hiv and Cd4+ T-Cells Interactions With Haart Treatment

Nisardi,

Kasbawati,

Putra

2023

JFMA

View full text Add to dashboard Cite

show abstract

“…There are two equilibrium points in a model ( 2), the disease-free equilibrium point and the endemic equilibrium point. The equilibrium point for the Caputo fractional model ( 2) is when [30], [31]…”

Section: The Equilibrium Point Of the Fractional Modelmentioning

confidence: 99%

Fractional Mathematical Model of Covid-19 with Quarantine

Nisardi

Kasbawati

Khaeruddin

et al. 2022

InPrime:Ind.Jour.Pure.Applied.Math

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This study aims to observe the dynamics of the spread of COVID-19 with the SIR-Model by considering the quarantine (Q) scheme. We also involve a fractional order in the model. Then the basic reproduction numbers were calculated using the generation matrix method, analyzed the local stability of the fractional model for each equilibrium point, and observed its relation to the basic reproduction numbers. We perform the sensitivity analysis to see the effect of parameters on changes in the basic reproduction numbers. We applied the Grunwald-Letnikov method for numerical simulations. Estimation for parameters was also carried out on the existing parameters in the model to obtain parameter values that could represent the actual conditions. Furthermore, with a fractional model, we approximated the model to the data of COVID-19 in West Sulawesi, Indonesia, so that we could obtain a fractional order since it could describe the data more accurately.Keywords: SIR-Q Model; COVID-19; basic reproduction number; Fractional Mathematical Model; Grunwald Letnikov Method. AbstrakPenelitian ini bertujuan untuk mengkaji dinamika penyebaran COVID-19 dengan model matematika orde fraksional penyebaran penyakit SIR-Q dengan mempertimbangkan skema karantina (Q) untuk mengendalikan penyebaran COVID-19. Bilangan reproduksi dasar dihitung menggunakan metode matriks generasi. Kemudian, dianalisa kestabilan lokal model fraksional untuk titik kesetimbangan dan lalu dianalisa kaitannya dengan bilangan reproduksi dasar. Analisis sensitivitas dilakukan untuk mengamati pengaruh parameter terhadap perubahan bilangan reproduksi dasar. Simulasi numerik dilakukan dengan menggunakan metode eksplisit Grunwald-Letnikov. Estimasi juga dilakukan terhadap parameter yang ada pada model untuk memperoleh nilai parameter yang merepresentasikan kondisi aktual penyebaran COVID-19 di Sulawesi Barat. Selanjutnya dengan model fraksional dilakukan pendekatan terhadap data kasus aktif COVID-19 di Sulawesi Barat sehingga diperoleh orde fraksional tertentu yang menghasilkan pendekatan nilai kasus aktif COVID-19 yang lebih akurat terhadap real data.Kata Kunci: Model SIR-Q; COVID-19; bilangan Reproduksi Dasar; Model Matematika Fraksional; Metode Grunwald-Letnikov.

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“…Song [7] has discussed the positive periodic solutions of a periodic survival for the red blood cell model. Lakshman and Senthilkumar [8], Dzhalladova and Růžičková [9], Sadani [10] have done the stability analysis of functional differential equations. Khalouta and Kade [11] have studied the solution of the fractional bratu-type equation by fractional residual power series method.…”

Section: Introductionmentioning

confidence: 99%