scholarly journals Analytical Parameter Estimation of the SIR Epidemic Model. Applications to the COVID-19 Pandemic

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 59
Author(s):  
Dimiter Prodanov
Keyword(s):  
Explicit Solution ◽  
Numerical Algorithms ◽  
Iterative Algorithms ◽  
Case Fatality ◽  
Mathematical Community ◽  
Parametric Estimation ◽  
Model Parameters ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
And Control

The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the mathematical community to derive an explicit solution. The present paper reports novel analytical results and numerical algorithms suitable for parametric estimation of the SIR model. Notably, a series solution of the incidence variable of the model is derived. It is proven that the explicit solution of the model requires the introduction of a new transcendental special function, describing the incidence, which is a solution of a non-elementary integral equation. The paper introduces iterative algorithms approximating the incidence variable, which allows for estimation of the model parameters from the numbers of observed cases. The approach is applied to the case study of the ongoing coronavirus disease 2019 (COVID-19) pandemic in five European countries: Belgium, Bulgaria, Germany, Italy and the Netherlands. Incidence and case fatality data obtained from the European Centre for Disease Prevention and Control (ECDC) are analysed and the model parameters are estimated and compared for the period Jan-Dec 2020.

scholarly journals Optimal Control of an SIR Model with Delay in State and Control Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed Elhia ◽  
Mostafa Rachik ◽  
Elhabib Benlahmar
Keyword(s):  
Optimal Control ◽  
Influenza A ◽  
Optimization Strategy ◽  
Sir Epidemic Model ◽  
Optimal Control Strategy ◽  
Control Variables ◽  
Sir Epidemic ◽  
Influenza A H1n1 ◽  
Using Data ◽  
And Control

We will investigate the optimal control strategy of an SIR epidemic model with time delay in state and control variables. We use a vaccination program to minimize the number of susceptible and infected individuals and to maximize the number of recovered individuals. Existence for the optimal control is established; Pontryagin’s maximum principle is used to characterize this optimal control, and the optimality system is solved by a discretization method based on the forward and backward difference approximations. The numerical simulation is carried out using data regarding the course of influenza A (H1N1) in Morocco. The obtained results confirm the performance of the optimization strategy.

scholarly journals Bifurcation Analysis of an SIR Epidemic Model with the Contact Transmission Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guihua Li ◽  
Gaofeng Li
Keyword(s):  
Theoretical Basis ◽  
Prevention And Control ◽  
Transmission Function ◽  
Threshold Value ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Contact Transmission ◽  
Disease Spreading ◽  
Intervention Policy ◽  
And Control

We consider an SIR endemic model in which the contact transmission function is related to the number of infected population. By theoretical analysis, it is shown that the model exhibits the bistability and undergoes saddle-node bifurcation, the Hopf bifurcation, and the Bogdanov-Takens bifurcation. Furthermore, we find that the threshold value of disease spreading will be increased, when the half-saturation coefficient is more than zero, which means that it is an effective intervention policy adopted for disease spreading. However, when the endemic equilibria exist, we find that the disease can be controlled as long as we let the initial values lie in the certain range by intervention policy. This will provide a theoretical basis for the prevention and control of disease.

CHAOS ANALYSIS AND CONTROL FOR A CLASS OF SIR EPIDEMIC MODEL WITH SEASONAL FLUCTUATION

2013 ◽  
Vol 06 (01) ◽  
pp. 1250063 ◽  
Author(s):  
YI ZHANG ◽  
QINGLING ZHANG ◽  
FUZHEN ZHANG ◽  
FENGLAN BAI
Keyword(s):  
Epidemic Model ◽  
Influenza A ◽  
Control Method ◽  
Seasonal Fluctuation ◽  
H1n1 Influenza ◽  
Sir Epidemic Model ◽  
Chaotic Motions ◽  
Sir Epidemic ◽  
The Common ◽  
And Control

In this paper, the problems of chaos and chaos control for a class of susceptible-infected-removed (SIR) epidemic model with seasonal fluctuation are investigated. The seasonality in outbreak is natural among infectious diseases, as the common influenza, A type H1N1 influenza and so on. It is shown that there exist chaotic phenomena in the epidemic model. Furthermore, the tracking control method is used to control chaotic motions in the epidemic model. A feedback controller is designed to achieve tracking of an ideal output. Thus, the density of infected individuals can converge to zero, in other words, the disease can be disappeared. Finally, numerical simulations illustrate that the controller is effective.

scholarly journals Prediction of Corona Virus Disease 2019 based on SIR model in China

2020 ◽  
Author(s):  
jiangang mu
Keyword(s):  
Virus Disease ◽  
Disease Process ◽  
Sir Model ◽  
Control Measures ◽  
Future Trends ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Corona Virus ◽  
Prevention And Control Measures ◽  
And Control

Abstract Background From the end of 2019 to the beginning of 2020, the Corona Virus Disease 2019 epidemic occurred in Wuhan, China, and quickly spread to the whole country. We used SIR epidemic model to predict the epidemic trend in China. Materials and Methods Respectively fitted the Corona Virus Disease 2019 epidemic trend equations in China, Hubei, and Wuhan, predicted future trends, based on the hypothesis of the infectious disease process by the SIR model and the official announcement data of the Chinese Health Commission . Results There will be no new cases in the non-Hubei area nationwide after March 8; there will be no new cases in Hubei that non Wuhan after March 12; Wuhan will there be no new cases after March 22 ; Conclusions The epidemic will end soon in China, under the prevention and control measures are not relaxed.

THE 2019 NOVEL PANDEMIC OF CORONAVIRUS DISEASE (COVID-19): A STUDY OF EXISTING EVIDENCE IN THE INDIAN POPULATION

2020 ◽  
Vol 7 (2) ◽  
pp. 199-204
Author(s):  
Shrikant Verma ◽  
Mohammad Abbas ◽  
Sushma Verma ◽  
Syed Tasleem Raza ◽  
Farzana Mahdi
Keyword(s):  
Disease Transmission ◽  
Indian Population ◽  
Respiratory Infections ◽  
Clinical Signs ◽  
Case Fatality ◽  
Public Health Emergency ◽  
The World ◽  
And Control ◽  
General Wellbeing ◽  
Different Parts

A novel spillover coronavirus (nCoV), with its epicenter in Wuhan, China's People's Republic, has emerged as an international public health emergency. This began as an outbreak in December 2019, and till November eighth, 2020, there have been 8.5 million affirmed instances of novel Covid disease2019 (COVID-19) in India, with 1,26,611 deaths, resulting in an overall case fatality rate of 1.48 percent. Coronavirus clinical signs are fundamentally the same as those of other respiratory infections. In different parts of the world, the quantity of research center affirmed cases and related passings are rising consistently. The COVID- 19 is an arising pandemic-responsible viral infection. Coronavirus has influenced huge parts of the total populace, which has prompted a global general wellbeing crisis, setting all health associations on high attentive. This review sums up the overall landmass, virology, pathogenesis, the study of disease transmission, clinical introduction, determination, treatment, and control of COVID-19 with the reference to India.

Analisis Titik Kesetimbangan Dan Kestabilan Penyebaran Penyakit Malaria di Distrik Manokwari Barat Berdasarkan Model Epidemik SIR

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Fandy Fandy ◽  
Andi Fajeriani Wyrasti ◽  
Tri Widjajanti
Keyword(s):  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Endemic Diseases ◽  
Sir Epidemic

<em>Stability and equilibrium of malaria&rsquo;s epidemics in Manokwari Barat district based on SIR epidemic model will be discussed in this paper. The SIR epidemic model can be applied to make a model of endemic diseases like malaria. Based on this research, there are 2 types of the equilibrium of malaria&rsquo;s epidemics in Manokwari Barat District, endemic and non endemic point.</em>

scholarly journals Using Unstated Cases to Correct for COVID-19 Pandemic Outbreak and Its Impact on Easing the Intervention for Qatar

Biology ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 463
Author(s):  
Narjiss Sallahi ◽  
Heesoo Park ◽  
Fedwa El Mellouhi ◽  
Mustapha Rachdi ◽  
Idir Ouassou ◽  
...  
Keyword(s):  
Public Health ◽  
A Priori ◽  
Epidemiological Models ◽  
Sir Epidemic Model ◽  
Gulf Region ◽  
Epidemiological Modeling ◽  
Public Health Policies ◽  
Sir Epidemic ◽  
The Impact ◽  
Case Data

Epidemiological Modeling supports the evaluation of various disease management activities. The value of epidemiological models lies in their ability to study various scenarios and to provide governments with a priori knowledge of the consequence of disease incursions and the impact of preventive strategies. A prevalent method of modeling the spread of pandemics is to categorize individuals in the population as belonging to one of several distinct compartments, which represents their health status with regard to the pandemic. In this work, a modified SIR epidemic model is proposed and analyzed with respect to the identification of its parameters and initial values based on stated or recorded case data from public health sources to estimate the unreported cases and the effectiveness of public health policies such as social distancing in slowing the spread of the epidemic. The analysis aims to highlight the importance of unreported cases for correcting the underestimated basic reproduction number. In many epidemic outbreaks, the number of reported infections is likely much lower than the actual number of infections which can be calculated from the model’s parameters derived from reported case data. The analysis is applied to the COVID-19 pandemic for several countries in the Gulf region and Europe.

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