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 Simulation of several flying situations of paragliders

2021 ◽  
Vol 15 (1) ◽  
pp. 79-89
Author(s):  
Thanh Xuan Nguyen ◽  
Phuong Thi-Thu Phan ◽  
Tien Van Pham
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Modeling And Simulation ◽  
Ordinary Differential Equations ◽  
State Space ◽  
Simulation Modeling ◽  
Time Varying ◽  
Gravity Forces

Paragliding is an adventure and fascinating sport of flying paragliders. Paragliders can be launched by running from a slope or by a winch force from towing vehicles, using gravity forces as the motor for the motion of flying. This motion is governed by the gravity forces as well as time-varying aerodynamic ones which depend on the states of the motion of paraglider at each instant of time. There are few published articles considering mechanical problems of paragliders in their various flying situations. This article represents the mathematical modeling and simulation of several common flying situations of a paraglider through establishing and solving the governing differential equations in state-space. Those flying situations include the ones with constant headwind/tailwind with or without constant upwind; the ones with different scenario for the variations of headwind and tailwind combined with the upwind; the ones with varying pilot mass; and the ones whose several parameters are in the form of interval quantities. The simulations were conducted using a powerful Julia toolkit called DifferentialEquations.jl. The obtained results in each situation are discussed, and some recommendations are presented. Keywords: paraglider; simulation; modeling; state-space; ordinary differential equations; Julia; DifferentialEquations.jl

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 Spread of Epidemic Disease on Edge-Weighted Graphs from a Database: A Case Study of COVID-19

2021 ◽  
Vol 18 (9) ◽  
pp. 4432
Author(s):  
Ronald Manríquez ◽  
Camilo Guerrero-Nancuante ◽  
Felipe Martínez ◽  
Carla Taramasco
Keyword(s):  
Public Health ◽  
Infectious Diseases ◽  
Preventive Measures ◽  
Weighted Graph ◽  
Real Data ◽  
Sir Model ◽  
Weighted Graphs ◽  
Epidemic Disease ◽  
The Real

The understanding of infectious diseases is a priority in the field of public health. This has generated the inclusion of several disciplines and tools that allow for analyzing the dissemination of infectious diseases. The aim of this manuscript is to model the spreading of a disease in a population that is registered in a database. From this database, we obtain an edge-weighted graph. The spreading was modeled with the classic SIR model. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics. Moreover, a deterministic approximation is provided. With database COVID-19 from a city in Chile, we analyzed our model with relationship variables between people. We obtained a graph with 3866 vertices and 6,841,470 edges. We fitted the curve of the real data and we have done some simulations on the obtained graph. Our model is adjusted to the spread of the disease. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics, in this case with real data of COVID-19. This valuable information allows us to also include/understand the networks of dissemination of epidemics diseases as well as the implementation of preventive measures of public health. These findings are important in COVID-19’s pandemic context.

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.

Ordinary differential equations and calculus of variations

2020 ◽  
Author(s):  
Efim Kogan
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Calculus Of Variations ◽  
Applied Mechanics ◽  
Technological Systems ◽  
Technological Means ◽  
Independent Work

The textbook contains theoretical information in a volume of the lecture course are discussed in detail and examples of typical tasks and test tasks and tasks for independent work. Designed for students enrolled in directions of preparation 15.03.03 "Applied mechanics" 01.03.02 "mathematics" (specialization "Mathematical modeling"), major 23.05.01 "Land transport and technological means" (specialization "Dynamics and strength of transport and technological systems"). Can be used by teachers for conducting practical classes.

scholarly journals Using Ordinary Differential Equations to Explore Cancer-Immune Dynamics and Tumor Dormancy

2016 ◽  
Author(s):  
Kathleen P. Wilkie ◽  
Philip Hahnfeldt ◽  
Lynn Hlatky
Keyword(s):  
Mathematical Modeling ◽  
Immune Response ◽  
Differential Equations ◽  
Tumor Growth ◽  
Ordinary Differential Equations ◽  
Systemic Disease ◽  
Growth Dynamics ◽  
Tumor Dormancy ◽  
Cytotoxic Action ◽  
General Method

AbstractCancer is not solely a disease of the genome, but is a systemic disease that affects the host on many functional levels, including, and perhaps most notably, the function of the immune response, resulting in both tumor-promoting inflammation and tumor-inhibiting cytotoxic action. The dichotomous actions of the immune response induce significant variations in tumor growth dynamics that mathematical modeling can help to understand. Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.

scholarly journals Analysis and Prediction of COVID-19 Characteristics Using a Birth-and-Death Model

2020 ◽  
Author(s):  
Narayanan C. Viswanath
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Explicit Expression ◽  
Basic Reproduction Number ◽  
Stationary Point ◽  
Reproduction Number ◽  
Sir Model ◽  
Expected Number ◽  
Infection Period ◽  
The Basic Reproduction Number

AbstractIts spreading speed together with the risk of fatality might be the main characteristic that separates COVID-19 from other infectious diseases in our recent history. In this scenario, mathematical modeling for predicting the spread of the disease could have great value in containing the disease. Several very recent papers have contributed to this purpose. In this study we propose a birth-and-death model for predicting the number of COVID-19 active cases. It relation to the Susceptible-Infected-Recovered (SIR) model has been discussed. An explicit expression for the expected number of active cases helps us to identify a stationary point on the infection curve, where the infection ceases increasing. Parameters of the model are estimated by fitting the expressions for active and total reported cases simultaneously. We analyzed the movement of the stationary point and the basic reproduction number during the infection period up to the 20th of April 2020. These provide information about the disease progression path and therefore could be really useful in designing containment strategies.

scholarly journals CALCULATION OF A THREE-LAYER CYLINDRICAL SHELL TAKING THE CREEP INTO ACCOUNT

2019 ◽  
Vol 6 (4) ◽  
pp. 14-18 ◽  
Author(s):  
Антон Чепурненко ◽  
Anton Chepurnenko ◽  
Батыр Языев ◽  
Batyr Yazyev ◽  
Анастасия Лапина ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Difference Method ◽  
Cylindrical Shells ◽  
Euler Method ◽  
Axisymmetric Loading ◽  
The Finite Difference Method

The article presents the derivation of the resolving equations for the calculation of three-layer cylindrical shells under axisymmetric loading, taking into account creep. The problem is reduced to a system of two ordinary differential equations. The solution is performed numerically using the finite difference method in combination with the Euler method.

scholarly journals A COMPARATIVE EXPLORATION ON DIFFERENT NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

2020 ◽  
Vol 15 (12) ◽  
Author(s):  
Mohammad Asif Arefin
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Euler Method ◽  
Euler’S Method ◽  
Runge Kutta Method ◽  
Accuracy Level ◽  
Runge Kutta ◽  
Matlab Programming

In this paper, the initial value problem of Ordinary Differential Equations has been solved by using different Numerical Methods namely Euler’s method, Modified Euler method, and Runge-Kutta method. Here all of the three proposed methods have to be analyzed to determine the accuracy level of each method. By using MATLAB Programming language first we find out the approximate numerical solution of some ordinary differential equations and then to determine the accuracy level of the proposed methods we compare all these solutions with the exact solution. It is observed that numerical solutions are in good agreement with the exact solutions and numerical solutions become more accurate when taken step sizes are very much small. Lastly, the error of each proposed method is determined and represents them graphically which reveals the superiority among all the three methods. We fund that, among the proposed methods Runge-Kutta 4th order method gives the accurate result and minimum amount of error.

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