Runge-kutta Numerical Method for Solving Nonlinear Influenza Model

Mohammed, Shatha Jabbar; Mohammed, Maha A.

doi:10.1088/1742-6596/1879/3/032040

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…Many researchers interested in studying epidemiological systems especially in Covid 19 pandemic, SIR COVID -19 model spread in Iraq was studied with stochasticity to die out the epidemic [5], see [6], [7], [8], [9]. Other researchers have studied some numerical methods to solve these systems, such as [10], [11], [12], [6], [7], [8]. Some analytical methods have studied; SIR epidemic model was solved by Banach contraction method, Temimi-Ansari method, and Daftardar-Jafari method in [13], LTAM was applied the first time to solve the epidemic nonlinear model, this method is mixed Laplace transform with Tamimi and Ansari iterative method [14], see also [11], [15], [16], [17].…”

Section: Introductionmentioning

confidence: 99%

Suitable Methods for Solving COVID-19 Model in Iraq

A.Mohammed,

A. Sabea

2023

wjps

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Because the Coronavirus epidemic spread in Iraq, the COVID-19 epidemic of people quarantined due to infection is our application in this work. The numerical simulation methods used in this research are more suitable than other analytical and numerical methods because they solve random systems. Since the Covid-19 epidemic system has random variables coefficients, these methods are used. Suitable numerical simulation methods have been applied to solve the COVID-19 epidemic model in Iraq. The analytical results of the Variation iteration method (VIM) are executed to compare the results. One numerical method which is the Finite difference method (FD) has been used to solve the Coronavirus model and for comparison purposes. The numerical simulation methods which are Mean Monte Carlo Finite difference (MMC_FD) and Mean Latin Hypercube Finite difference (MLH_FD), are also used to solve the proposed epidemic model under study. The obtained results are discussed, tabulated, and represented graphically. Finally, the absolute error is the tool used to compare the numerical simulation solutions from 2020 to 2024 years. The behavior of the Coronavirus in Iraq has been expected for 4 years from 2020 to 2024 using the proposed numerical simulation methods.

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Section: Introductionmentioning

confidence: 99%

Suitable Methods for Solving COVID-19 Model in Iraq

A.Mohammed,

A. Sabea

2023

wjps

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“…In addition, the Adomian decomposition method and variation iteration method were used for alcohol consumption [14]. Some researchers use the numerical Runge-Kutta method to analyze the behavior of obesity [15], smoking habits [13], influenza [16], and COVID-19 [17]. On the other hand, there are those who are interested in studying epidemiological models that have random coefficients and using suitable numerical simulation methods to solve them, such as [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Some Numerical Simulation Techniques for COVID-19 Model in Iraq

Mohammed,

A. Sabea,

Fadiya Mohd Noor

2023

IHJPAS

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The aim of our study is to solve a nonlinear epidemic model, which is the COVID-19 epidemic model in Iraq, through the application of initial value problems in the current study. The model has been presented as a system of ordinary differential equations that has parameters that change with time. Two numerical simulation methods are proposed to solve this model as suitable methods for solving systems whose coefficients change over time. These methods are the Mean Monte Carlo Runge-Kutta method (MMC_RK) and the Mean Latin Hypercube Runge-Kutta method (MLH_RK). The results of numerical simulation methods are compared with the results of the numerical Runge-Kutta 4th order method (RK4) from 2021 to 2025 using the absolute error, which proves that the MLH_RK method is the best and closest to the expected values. The results have been discussed after being tabulated and represented graphically. Epidemic behavior for the next two years until 2025 has been projected using the proposed methods.

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“…Thus, numerical methods are used to obtain approximate solutions. Some of the numerical techniques are Euler (Ashigi et al, 2021;Mohammed et al, 2021;Reza et al, 2022), Euler Predictor Corrector (Onwubuoya et al, 2018a), Non-Standard Finite Difference (Raza et al, 2022;Butt et al, 2023;ur Rehman et al, 2023). The Non-Standard Finite Difference (NSFD) method developed by Ronald E. Mickens is a discrete representation of a continuous model (Mickens andWashington, 2012, Qui et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Application of Non-Standard Finite Difference Method on Covid-19 Mathematical Model With Fear of Infection

Usman,

Ibrahim,

Isah

et al. 2023

FJS

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This study presents a novel application of Non -Standard Finite Difference (NSFD) Method to solve a COVID-19 epidemic mathematical model with the impact of fear due to infection. The mathematical model is governed by a system of first-order non-linear ordinary differential equations and is shown to possess a unique positive solution that is bounded. The proposed numerical scheme is used to obtain an approximate solution for the COVID-19 model. Graphical results were displayed to show that the solution obtained by NSFD agrees well with those obtained by the Runge-Kutta-Fehlberg method built-in Maple 18.

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Runge-kutta Numerical Method for Solving Nonlinear Influenza Model

Cited by 4 publications

References 16 publications

Suitable Methods for Solving COVID-19 Model in Iraq

Suitable Methods for Solving COVID-19 Model in Iraq

Comparison of Some Numerical Simulation Techniques for COVID-19 Model in Iraq

Application of Non-Standard Finite Difference Method on Covid-19 Mathematical Model With Fear of Infection

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