scholarly journals STABILITY ANALYSIS AND APPROXIMATE SOLUTION OF SIR EPIDEMIC MODEL WITH CROWLEY-MARTIN TYPE FUNCTIONAL RESPONSE AND HOLLING TYPE-Ⅱ TREATMENT RATE BY USING HOMOTOPY ANALYSIS METHOD

2020 ◽  
Vol 10 (4) ◽  
pp. 1482-1515
Author(s):  
Parvaiz Ahmad Naik ◽  
◽  
Jian Zu ◽  
Mohammad Ghoreishi ◽  
Keyword(s):  
Approximate Solution ◽  
Stability Analysis ◽  
Functional Response ◽  
Homotopy Analysis Method ◽  
Epidemic Model ◽  
Analysis Method ◽  
Sir Epidemic Model ◽  
Treatment Rate ◽  
Sir Epidemic ◽  
Homotopy Analysis

scholarly journals Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 114
Author(s):  
Emmanuel A. Bakare ◽  
Snehashish Chakraverty ◽  
Radovan Potucek
Keyword(s):  
Numerical Solution ◽  
Homotopy Analysis Method ◽  
Epidemic Model ◽  
Analysis Method ◽  
Sir Epidemic Model ◽  
Deterministic Models ◽  
Interval Model ◽  
Sir Epidemic ◽  
Homotopy Analysis ◽  
Good Agreement

This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). The SIR epidemic model is proposed and solved under different uncertain intervals by the HAM to obtain the numerical solution of the model. Furthermore, the SIR ODE model was transformed into a stochastic differential equation (SDE) model and the results of the stochastic and deterministic models were compared using numerical simulations. The results obtained were compared with the numerical solution and found to be in good agreement. Finally, various simulations were done to discuss the solution.

scholarly journals Stability Analysis of an Age-Structured SIR Epidemic Model with a Reduction Method to ODEs

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 147 ◽  
Author(s):  
Toshikazu Kuniya
Keyword(s):  
Stability Analysis ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Transmission Function ◽  
Endemic Equilibrium ◽  
Dimensional System ◽  
Relevant Parameter ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Age Structured

In this paper, we are concerned with the asymptotic stability of the nontrivial endemic equilibrium of an age-structured susceptible-infective-recovered (SIR) epidemic model. For a special form of the disease transmission function, we perform the reduction of the model into a four-dimensional system of ordinary differential equations (ODEs). We show that the unique endemic equilibrium of the reduced system exists if the basic reproduction number for the original system is greater than unity. Furthermore, we perform the stability analysis of the endemic equilibrium and obtain a fourth-order characteristic equation. By using the Routh–Hurwitz criterion, we numerically show that the endemic equilibrium is asymptotically stable in some epidemiologically relevant parameter settings.

Stability analysis of a delayed sir epidemic model with diffusion and saturated incidence rate

2020 ◽  
Vol 1 (4) ◽  
Author(s):  
Abdelhadi Abta ◽  
Salahaddine Boutayeb ◽  
Hassan Laarabi ◽  
Mostafa Rachik ◽  
Hamad Talibi Alaoui
Keyword(s):  
Stability Analysis ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

scholarly journals Application of the Homotopy Method for Fractional Inverse Stefan Problem

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5474
Author(s):  
Damian Słota ◽  
Agata Chmielowska ◽  
Rafał Brociek ◽  
Marcin Szczygieł
Keyword(s):  
Heat Flux ◽  
Approximate Solution ◽  
Temperature Distribution ◽  
Continuous Function ◽  
Homotopy Analysis Method ◽  
Input Data ◽  
Sufficient Condition ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The One

The paper presents an application of the homotopy analysis method for solving the one-phase fractional inverse Stefan design problem. The problem was to determine the temperature distribution in the domain and functions describing the temperature and the heat flux on one of the considered area boundaries. It was demonstrated that if the series constructed for the method is convergent then its sum is a solution of the considered equation. The sufficient condition of this convergence was also presented as well as the error of the approximate solution estimation. The paper also includes the example presenting the application of the described method. The obtained results show the usefulness of the proposed method. The method is stable for the input data disturbances and converges quickly. The big advantage of this method is the fact that it does not require discretization of the area and the solution is a continuous function.

Homotopy analysis method approximate solution for fuzzy pantograph equation

2021 ◽  
Vol 14 (3) ◽  
pp. 286
Author(s):  
A.H. Shather ◽  
A.F. Jameel ◽  
N.R. Anakira ◽  
A.K. Alomari ◽  
Azizan Saaban
Keyword(s):  
Approximate Solution ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Pantograph Equation ◽  
Homotopy Analysis

Bifurcation and stability analysis of a discrete SIR epidemic model of fractional order

2022 ◽  
Author(s):  
A. George Maria Selvam ◽  
D. Abraham Vianny ◽  
S. Britto Jacob ◽  
D. Vignesh
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Bifurcation And Stability
Sign in / Sign up

Export Citation Format

Share Document