scholarly journals The pluses and minuses of 0

2007 ◽  
Vol 4 (16) ◽  
pp. 949-961 ◽  
Author(s):  
M.G Roberts
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Central Place ◽  
Sir Model ◽  
Direct Measure ◽  
Control Effort ◽  
Epidemic Theory ◽  
The Basic Reproduction Number

The concept of the basic reproduction number ( 0 ) occupies a central place in epidemic theory. The value of 0 determines the proportion of the population that becomes infected over the course of a (modelled) epidemic. In many models, (i) an endemic infection can persist only if 0 >1, (ii) the value of 0 provides a direct measure of the control effort required to eliminate the infection, and (iii) pathogens evolve to maximize their value of 0 . These three statements are not universally true. In this paper, some exceptions to them are discussed, based on the extensions of the SIR model.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

Evolution of SARS-CoV-2 in the state of Alagoas-Brazil via an adaptive SIR model

2020 ◽  
pp. 2150040
Author(s):  
I. F. F. Dos Santos ◽  
G. M. A. Almeida ◽  
F. A. B. F. De Moura
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Sir Model ◽  
The State ◽  
Epidemic Dynamics ◽  
Historical Series ◽  
Input Parameters ◽  
Number Formula ◽  
Near Future ◽  
The Basic Reproduction Number

We investigate the spreading of SARS-CoV-2 in the state of Alagoas, northeast of Brazil, via an adaptive susceptible-infected-removed (SIR) model featuring dynamic recuperation and propagation rates. Input parameters are defined based on data made available by Alagoas Secretary of Health from April 19, 2020 on. We provide with the evolution of the basic reproduction number [Formula: see text] and reproduce the historical series of the number of confirmed cases with less than [Formula: see text] error. We offer predictions, from November 16 forward, over the epidemic situation in the near future and show that it will keep decelerating. Furthermore, the same model can be used to study the epidemic dynamics in other countries with great easiness and accuracy.

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 An Age and Space Structured SIR Model Describing the Covid-19 Pandemic

2020 ◽  
Author(s):  
Rinaldo M Colombo ◽  
Mauro Garavello ◽  
Francesca Marcellini ◽  
Elena Rossi
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Sir Model ◽  
Qualitative Properties ◽  
Numerical Integrations ◽  
Key Features ◽  
Virus Spreading ◽  
The Basic Reproduction Number

We present an epidemic model capable of describing key features of the present Covid-19 pandemic. While capturing several qualitative properties of the virus spreading, it allows to compute the basic reproduction number, the number of deaths due to the virus and various other statistics. Numerical integrations are used to illustrate the relevance of quarantine and the role of care houses.

An early estimation of the number of affected people in South Asia due to Covid-19 pandemic using susceptible, infected and recover model

2020 ◽  
Vol 31 (10) ◽  
pp. 2050140
Author(s):  
Md. Enamul Hoque
Keyword(s):  
Simple Model ◽  
South Asia ◽  
South Asian ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Sir Model ◽  
Asian Countries ◽  
Susceptible Population ◽  
The Basic Reproduction Number

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for Bangladesh, India, Pakistan and compared with that of China. Numerical solutions are used to obtain the value of parameters for the SIR model. It is predicted that the active case in Pakistan due to the SARS-CoV-2 will be comparable with that in China whereas it will be low for Bangladesh and India. The basic reproduction number, with fluctuations, for South Asian countries are predicted to be less than that of China. The susceptible population is also estimated to be under a million for Bangladesh and India but it becomes very large for Pakistan.

scholarly journals Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
F. Talay Akyildiz ◽  
Fehaid Salem Alshammari
Keyword(s):  
Fractional Order ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sir Model ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Exponential Kernel ◽  
Disease Free ◽  
The Basic Reproduction Number

AbstractThis paper investigates a new model on coronavirus-19 disease (COVID-19), that is complex fractional SIR epidemic model with a nonstandard nonlinear incidence rate and a recovery, where derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The model has two equilibrium points when the basic reproduction number $R_{0} > 1$ R 0 > 1 ; a disease-free equilibrium $E_{0}$ E 0 and a disease endemic equilibrium $E_{1}$ E 1 . The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number $R_{0} <1$ R 0 < 1 , we show that the endemic equilibrium state is locally asymptotically stable if $R_{0} > 1$ R 0 > 1 . We also prove the existence and uniqueness of the solution for the Atangana–Baleanu SIR model by using a fixed-point method. Since the Atangana–Baleanu fractional derivative gives better precise results to the derivative with exponential kernel because of having fractional order, hence, it is a generalized form of the derivative with exponential kernel. The numerical simulations are explored for various values of the fractional order. Finally, the effect of the ABC fractional-order derivative on suspected and infected individuals carefully is examined and compared with the real data.

scholarly journals Simulating the progression of the COVID-19 disease in Cameroon using SIR models

2020 ◽  
Author(s):  
Ulrich KAMGUEM NGUEMDJO ◽  
Freeman MENO ◽  
Audric DONGFACK ◽  
Bruno VENTELOU
Keyword(s):  
Public Health ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Sir Model ◽  
Health Policies ◽  
Public Health Policies ◽  
Epidemic Curve ◽  
Health Authorities ◽  
Public Health Authorities ◽  
The Basic Reproduction Number

This paper analyses the evolution of COVID 19 disease in Cameroon over the period March 6 April 2020 using SIR model. Specifically, 1) we evaluate the basic reproduction number of the virus. 2) Determine the peak of the infection and the spread-out period of the disease. 3) Simulate the interventions of public health authorities. Data used in this study is obtained from the Ministry of Health of Cameroon. The results suggest that over the period, the reproduction number of the COVID 19 in Cameroon is about 1.5 and the peak of the infection could occur at the end of May 2020 with about 7.7% of the population infected. Besides, implementation of efficient public health policies could help flattens the epidemic curve.

scholarly journals Trend Analysis, Modelling and Impact Assessment of COVID-19 in Nepal

2020 ◽  
Vol 25 (2) ◽  
pp. 1-8
Author(s):  
Shital Bhandary ◽  
Srijan Lal Shrestha ◽  
Ram Prasad Khatiwada ◽  
Deep Narayan Shah ◽  
Nabin Narayan Munankarmi ◽  
...  
Keyword(s):  
Impact Assessment ◽  
Basic Reproduction Number ◽  
Social Distance ◽  
Reproduction Number ◽  
Moving Average ◽  
Statistical Modelling ◽  
Sir Model ◽  
Arima Models ◽  
Autoregressive Integrated Moving Average ◽  
The Basic Reproduction Number

 With the continued global expansion of COVID-19 transmission and the mounting threat of the disease, the timely analysis of its trend in Nepal and forecasting the potential situation in the country has been deemed necessary. We analyzed the trend, modelling, and impact assessment of COVID-19 cases of Nepal from 23rd January 2020 to 30th April 2020 to portray the scenario of COVID-19 during the first phase of lockdown. Exponential smoothing state-space and autoregressive integrated moving average (ARIMA) models were constructed to forecast the cases. Susceptible-infectious-recovered (SIR) model was fit to estimate the basic reproduction number (Ro) of COVID-19 in Nepal. There has been an increase in the number of cases but the overall growth in COVID-19 was not high. Statistical modelling has shown that COVID-19 cases may continue to increase exponentially in Nepal. The basic reproduction number in Nepal being maintained at a low level of 1.08 for the period of 23rd January to 30th April 2020 is an indication of the effectiveness of lockdown in containing the COVID-19 spread. The models further suggest that COVID-19 might persist until December 2020 with peak cases in August 2020. On the other hand, a basic reproduction number of 1.25 was computed for total cases reported for the 22nd March to 30th April 2020 period implying that COVID-19 may remain for at least a year in the country. Thus, maintaining social distance and stay home policy with an implementation of strict lockdown in the COVID-19 affected district is highly recommended.

scholarly journals The first diffusion of the Covid-19 outbreak in Northern Italy: an analysis based on a simplified version of the SIR model

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Mauro Magnoni
Keyword(s):  
Approximate Solution ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Sir Model ◽  
Northern Italy ◽  
Theoretical Formulation ◽  
Relevant Variable ◽  
Infected People ◽  
Italian Regions ◽  
The Basic Reproduction Number

Abstract In this paper an analysis of the first diffusion of the Covid-19 outbreak occurred in late February 2020 in Northern Italy is presented. In order to study the time evolution of the epidemic it was decided to analyze in particular as the most relevant variable the number of hospitalized people, considered as the less biased proxy of the real number of infected people. An approximate solution of the infected equation was found from a simplified version of the SIR model. This solution was used as a tool for the calculation of the basic reproduction number R 0 in the early phase of the epidemic for the most affected Northern Italian regions (Piedmont, Lombardy, Veneto and Emilia), giving values of R 0 ranging from 2.2 to 3.1. Finally, a theoretical formulation of the infection rate is proposed, introducing a new parameter, the infection length, characteristic of the disease.

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