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 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 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 Deterministic chaos in pendulum systems with delay

2019 ◽  
Vol 4 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Aleksandr Shvets ◽  
Alexander Makaseyev
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Differential Equations ◽  
Deterministic Chaos ◽  
Phase Portraits ◽  
Characteristic Exponents ◽  
Systems Of Differential Equations ◽  
Lyapunov Characteristic Exponents ◽  
The Mathematical Model ◽  
Equations With Delay

AbstractDynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation".

SHILNIKOV’S SADDLE-NODE BIFURCATION

1996 ◽  
Vol 06 (06) ◽  
pp. 1153-1160 ◽  
Author(s):  
PAUL GLENDINNING ◽  
COLIN SPARROW
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Infinite Number ◽  
Bifurcation Point ◽  
Stationary Point ◽  
Saddle Node Bifurcation ◽  
Codimension Two ◽  
Full Shift ◽  
Parameter Values ◽  
Codimension Two Bifurcation

In 1969, Shilnikov described a bifurcation for families of ordinary differential equations involving n≥2 trajectories bi-asymptotic to a non-hyperbolic stationary point. At nearby parameter values the system has trajectories in correspondence with the full shift on n symbols. We investigate a simple (piecewise-smooth) example with an infinite number of homoclinic loops. We also present a smooth example which shows how Shilnikov’s mechanism is related to the Lorenz bifurcation by considering the unfolding of a previously unstudied codimension two bifurcation point.

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