scholarly journals Mathematical model of epidemics: SEIR model by using homotopy perturbation method

2019 ◽  
Author(s):  
M. Sivakumar ◽  
R. Senthamarai
Keyword(s):  
Mathematical Model ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Seir Model ◽  
Homotopy Perturbation

Dynamic analysis of the mathematical model of COVID-19 with demographic effects

2020 ◽  
Vol 75 (11-12) ◽  
pp. 389-396 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan ◽  
E. F. Doungmo Goufo ◽  
Amna Anjum ◽  
Ali Anjum
Keyword(s):  
Mathematical Model ◽  
Perturbation Method ◽  
Effective Treatment ◽  
Homotopy Perturbation Method ◽  
Simple Mathematical Model ◽  
Safety Measures ◽  
Seir Model ◽  
Homotopy Perturbation ◽  
The Mathematical Model ◽  
Demographic Effects

AbstractThe coronavirus is currently extremely contagious for humankind, which is a zoonotic tropical disease. The pandemic is the largest in history, affecting almost the whole world. What makes the condition the worst of all is no specific effective treatment available. In this article, we present an extended and modified form of SIR and SEIR model, respectively. We begin by investigating a simple mathematical model that describes the pandemic. Then we apply different safety measures to control the pandemic situation. The mathematical model with and without control is solved by using homotopy perturbation method. Obtained solutions have been presented graphically. Finally, we develop another mathematical model, including quarantine and hospitalization.

scholarly journals A Mathematical Model to Solve the Burgers-Huxley Equation by using New Homotopy Perturbation Method

2019 ◽  
Vol 4 (6) ◽  
pp. 1483-1495
Author(s):  
Dinesh Kumar Maurya ◽  
Ravendra Singh ◽  
Yogendra Kumar Rajoria
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Perturbation Method ◽  
Real World ◽  
Analytical Method ◽  
Homotopy Perturbation Method ◽  
Three Dimension ◽  
Homotopy Perturbation ◽  
Precise Solution ◽  
Huxley Equation

A semi-analytical method has been planned for the precise solution of the differential equation established on the New Homotopy Perturbation Method (NHPM), and to develop a generalized Burger-Huxley (BH) equation, in this paper. By employing NHPM, two case studies show the precise solution of the BH equation. It is shown that the NHPM is yield solution is convergent from with the easy computability term; NHPM is an effective and easy tool for cracking many real world difficulties. The three-dimension and two dimension graphical solutions of the BH equations are also provided to validate the mathematical models. MATLAB software is used to calculate the series obtained from HPM.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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