scholarly journals Adomian Decomposition Method Used to Solve a SIR Epidemic Model of Dengue Fever

2020 ◽  
Author(s):  
Yulius Lede ◽  
Sudi Mungkasi
Keyword(s):  
Dengue Fever ◽  
Epidemic Model ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Adomian Decomposition

scholarly journals Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Fazal Haq ◽  
Muhammad Shahzad ◽  
Shakoor Muhammad ◽  
Hafiz Abdul Wahab ◽  
Ghaus ur Rahman
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Epidemic Model ◽  
Adomian Decomposition Method ◽  
Classical Case ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Adomian Decomposition ◽  
Fractional Differential

The fractional order Susceptible-Infected-Recovered (SIR) epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.

scholarly journals On new computations of the fractional epidemic childhood disease model pertaining to the generalized fractional derivative with nonsingular kernel

2021 ◽  
Vol 7 (3) ◽  
pp. 4552-4573
Author(s):  
Saima Rashid ◽  
◽  
Fahd Jarad ◽  
Fatimah S. Bayones ◽  
◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Decomposition Method ◽  
Disease Model ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Sir Epidemic Model ◽  
Childhood Diseases ◽  
Sir Epidemic ◽  
Adomian Decomposition ◽  
The Stability

<abstract><p>The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With the aid of the Elzaki Adomian decomposition method (EADM), the approximate solutions of the aforesaid model are discussed by exerting the Adomian decomposition method. By employing the fixed point postulates and the Picard–Lindelöf approach, the stability, existence, and uniqueness consequences of the model are demonstrated. Furthermore, we illustrate the essential hypothesis for disease control in order to find the role of unaware infectives in the spread of childhood diseases. Besides that, simulation results and graphical illustrations are presented for various fractional-orders. A comparison analysis is shown with the previous findings. It is hoped that ABC fractional derivative and the projected algorithm will provide new venues in futuristic studies to manipulate and analyze several epidemiological models.</p></abstract>

scholarly journals Efficient Iterative Methods for Solving the SIR Epidemic Model

2021 ◽  
pp. 613-622
Author(s):  
Sawsan Mohsin Abed ◽  
Majeed Ahmed AL-Jawary
Keyword(s):  
Iterative Methods ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Adomian Decomposition ◽  
Banach Contraction ◽  
The Fixed Point Theorem ◽  
Adomian Polynomial

In this article, the numerical and approximate solutions for the nonlinear differential equation systems, represented by the epidemic SIR model, are determined. The effective iterative methods, namely the Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM), and the Banach contraction method (BCM), are used to obtain the approximate solutions. The results showed many advantages over other iterative methods, such as Adomian decomposition method (ADM) and the variation iteration method (VIM) which were applied to the non-linear terms of the Adomian polynomial and the Lagrange multiplier, respectively. Furthermore, numerical solutions were obtained by using the fourth-orde Runge-Kutta (RK4), where the maximum remaining errors showed that the methods are reliable. In addition, the fixed point theorem was used to show the convergence of the proposed methods. Our calculation was carried out with MATHEMATICA®10 to evaluate the terms of the approximate solutions.

APPLICATION OF HOMOTOPY PERTURBATION AND VARIATIONAL ITERATION METHODS TO SIR EPIDEMIC MODEL

2011 ◽  
Vol 11 (01) ◽  
pp. 149-161 ◽  
Author(s):  
ABDOUL R. GHOTBI ◽  
A. BARARI ◽  
M. OMIDVAR ◽  
G. DOMAIRRY
Keyword(s):  
Vaccine Coverage ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Sir Epidemic Model ◽  
Childhood Diseases ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Sir Epidemic ◽  
Adomian Decomposition ◽  
Iteration Methods

Children born are susceptible to various diseases such as mumps and chicken pox. These diseases are the most common form of infectious diseases. In recent years, scientists have been trying to devise strategies to fight against these diseases. Since vaccination is considered the most effective strategy against childhood diseases, the development of the framework that would predict the optimal vaccine coverage level needed to prevent the spread of diseases is crucial. The SIR model is a standard compartmental model that has been used to describe many epidemiological diseases. In this article, two methods namely homotopy perturbation method (HPM) and variational iteration method (VIM) are employed to compute an approximation to the solution of nonlinear system of differential equations governing the problem. The obtained results are compared with those obtained by Adomian decomposition method (ADM). This research reveals that although the obtained results are the same, HPM and VIM are much more robust, more convenient and efficient in comparison to ADM.

Analisis Titik Kesetimbangan Dan Kestabilan Penyebaran Penyakit Malaria di Distrik Manokwari Barat Berdasarkan Model Epidemik SIR

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Fandy Fandy ◽  
Andi Fajeriani Wyrasti ◽  
Tri Widjajanti
Keyword(s):  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Endemic Diseases ◽  
Sir Epidemic

<em>Stability and equilibrium of malaria&rsquo;s epidemics in Manokwari Barat district based on SIR epidemic model will be discussed in this paper. The SIR epidemic model can be applied to make a model of endemic diseases like malaria. Based on this research, there are 2 types of the equilibrium of malaria&rsquo;s epidemics in Manokwari Barat District, endemic and non endemic point.</em>

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