scholarly journals SIR Model with Homotopy to Predict Corona Cases

2021 ◽  
Author(s):  
Nahid Fatima
Keyword(s):  
Infectious Diseases ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Sir Model ◽  
Homotopy Method ◽  
Experimental Purpose

In this chapter, we will discuss SIR model to study the spread of COVID-2019 pandemic of India. We will give the prediction of corona cases using homotopy method. The HM is a method for solving the ordinary differential equations. The SIR model consists of three ordinary differential equations. In this study, we have used the data of COVID-2019 Outbreak of India on 20 Jan 2021. In this data, Recovered is 102656163, Active cases are 189245 Susceptible persons are 189347782 for the experimental purpose. Data about a wide variety of infectious diseases has been analyzed with the help of SIR model. Therefore, this model has been already well tested for infectious diseases by various scientists and researchers.

scholarly journals Mathematical Modeling and Simulation of SIR Model for COVID−2019 Epidemic Outbreak: A Case Study of India

2020 ◽  
Author(s):  
Dr. Ramjeet Singh Yadav
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Differential Equations ◽  
Modeling And Simulation ◽  
Ordinary Differential Equations ◽  
Initial Level ◽  
Sir Model ◽  
Euler Method ◽  
Epidemic Outbreak

The present study discusses the spread of COVID−2019 epidemic of India and its end by using SIR model. Here we have discussed about the spread of COVID−2019 epidemic in great detail using Euler method. The Euler method is a method for solving the ordinary differential equations. The SIR model has the combination of three ordinary differential equations. In this study, we have used the data of COVID−2019 Outbreak of India on 8 May, 2020. In this data, we have used 135710 susceptible cases, 54340 infectious cases and 1830 reward/removed cases for the initial level of experimental purpose. Data about a wide variety of infectious diseases has been analyzed with the help of SIR model. Therefore, this model has been already well tested for infectious diseases by various scientists and researchers. Using the data to the number of COVID−2019 outbreak cases in India the results obtained from the analysis and simulation of this proposed SIR model showing that the COVID−2019 epidemic cases increase for some time and there after this outbreak decrease. The results obtained from the SIR model also suggest that the Euler method can be used to predict transmission and prevent the COVID−2019 epidemic in India. Finally, from this study, we have found that the outbreak of COVID−2019 epidemic in India will be at its peak on 25 May 2020 and after that it will work slowly and on the verge of ending in the first or second week of August 2020.

scholarly journals Distributed Control and the Lyapunov Characteristic Exponents in the Model of Infectious Diseases

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
M. Bershadsky ◽  
M. Chirkov ◽  
A. Domoshnitsky ◽  
S. Rusakov ◽  
I. Volinsky
Keyword(s):  
Infectious Diseases ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Distributed Control ◽  
Stationary Point ◽  
Treatment Time ◽  
Simulation Models ◽  
Characteristic Exponents ◽  
Data Comparison ◽  
Lyapunov Characteristic Exponents

The Marchuk model of infectious diseases is considered. Distributed control to make convergence to stationary point faster is proposed. Medically, this means that treatment time can be essentially reduced. Decreasing the concentration of antigen, this control facilitates the patient’s condition and gives a certain new idea of treating the disease. Our approach involves the analysis of integro-differential equations. The idea of reducing the system of integro-differential equations to a system of ordinary differential equations is used. The final results are given in the form of simple inequalities on the parameters. The results of numerical calculations of simulation models and data comparison in the case of using distributive control and in its absence are given.

scholarly journals Numerical Simulations of a Modified SIR Model Fitting Statistical Datafor COVID19

2020 ◽  
Vol 8 ◽  
pp. 115-125
Author(s):  
Flavius Guiaş
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Model Fitting ◽  
Sir Model ◽  
Second Stage ◽  
Convalescence Time ◽  
Official Data ◽  
Infectious State

We consider a system of ordinary differential equations obtained by modifying the classical SIR modelin epidemiology in order to account for the particular features of COVID­19 and the structure of the availablestatistical data. Its main feature is that the infectious state is being split in two different stages. In the first one,which lasts a few days after being infected, the individuals are considered to be contagious and able to spreadfurther the disease. After this, the individuals are considered to be isolated and this second stage lasts until eitherrecovery or death is reported. The parameters of the model are fitted for several countries (Germany, Italy, Spain,Russia, USA, Romania) such that the solution matches the known number of new cases, active cases, recoveriesand deaths. The values of these parameters give insight regarding the evolution of the pandemy and can revealdifferent policies and approaches in reporting the official data. For example one of them can indicate that in certaincountries a substantial amount of cases were reported only post­mortem. The variation across several countries ofanother parameter, which models the average convalescence time (the duration of the second stage of the infectiousstate), points to the fact that the recoveries are reported at different rates, in some cases with significant delays.Since it can be assumed that this is only a matter of reporting, we also perform additional simulations for thesecountries by taking the average convalescence time the value of Germany, which is the smallest within the wholerange. The conclusion is that under this assumption, the evolution of the active cases for example in Italy andSpain, is not significantly different to that in Germany, the comparison being based on the fact that these countriesshowed a similar number of cases within the considered period.

scholarly journals Analysis of Transmission Dynamics of Anthrax in Animals: A Modeling Approach

2019 ◽  
pp. 1-9
Author(s):  
George Thiong’o Githire ◽  
George Kimathi ◽  
Mary Wainaina
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Critical Value ◽  
Sir Model ◽  
Vaccination Rate ◽  
Transmission Dynamics ◽  
Animal Population ◽  
Contact Rates ◽  
Sensitive Parameters ◽  
Disease Free

This paper seeks to develop a SIR model with vaccination compartment in the study of anthrax transmission dynamics in animal population. The model employ ordinary differential equations in the formulation of its equation. The model’s steady states solutions are investigated. The disease free equilibrium and endemic equilibrium of the model are analyzed qualitatively. Vaccination rate below a certain critical value causes the anthrax disease to persist. Recruitment and contact rates are the most sensitive parameters that significantly contribute to the basic reproductive ratio.

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