scholarly journals Epidemiological implications of the contact network structure for cattle farms and the 20–80 rule

2005 ◽  
Vol 1 (3) ◽  
pp. 350-352 ◽  
Author(s):  
M.E.J Woolhouse ◽  
D.J Shaw ◽  
L Matthews ◽  
W.-C Liu ◽  
D.J Mellor ◽  
...  
Keyword(s):  
Infectious Diseases ◽  
Network Structure ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Important Determinant ◽  
Contact Network ◽  
Cattle Movements ◽  
Cattle Farms ◽  
Degree Of Heterogeneity ◽  
The Basic Reproduction Number

The network of movements of cattle between farm holdings is an important determinant of the potential rates and patterns of spread of infectious diseases. Because cattle movements are uni-directional, the network is unusual in that the risks of acquiring infection (by importing cattle) and of passing infection on (by exporting cattle) can be clearly distinguished, and there turns out to be no statistically significant correlation between the two. This means that the high observed degree of heterogeneity in numbers of contacts does not result in an increase in the basic reproduction number, R 0 , in contrast to findings from studies of other contact networks. Despite this, it is still the case that just 20% of holdings contribute at least 80% of the value of R 0 .

scholarly journals Rich Dynamics of a Brucellosis Model with Transport

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Juan Liang ◽  
Zhirong Zhao ◽  
Can Li
Keyword(s):  
Numerical Simulation ◽  
Sensitivity Analysis ◽  
Infectious Diseases ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Great Influence ◽  
Stable State ◽  
Initial Values ◽  
Si Model ◽  
The Basic Reproduction Number

Brucellosis is one of the major infectious diseases in China. In this study, we consider an SI model of animal brucellosis with transport. The basic reproduction number ℛ0 is obtained, and the stable state of the equilibria is analyzed. Numerical simulation shows that different initial values have a great influence on results of the model. In addition, the sensitivity analysis of ℛ0 with respect to different parameters is analyzed. The results reveal that the transport has dual effects. Specifically, transport can lead to increase in the number of infected animals; besides, transport can also reduce the number of infected animals in a certain range. The analysis shows that the number of infected animals can be controlled if animals are transported reasonably.

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 Early Real-Time Estimation of the Basic Reproduction Number of Emerging Infectious Diseases

2012 ◽  
Vol 2 (3) ◽  
Author(s):  
Bahman Davoudi ◽  
Joel C. Miller ◽  
Rafael Meza ◽  
Lauren Ancel Meyers ◽  
David J. D. Earn ◽  
...  
Keyword(s):  
Infectious Diseases ◽  
Real Time ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Emerging Infectious Diseases ◽  
Time Estimation ◽  
Real Time Estimation ◽  
The Basic Reproduction Number

scholarly journals Superspreaders and High Variance Infectious Diseases

2020 ◽  
Author(s):  
Shmuel Safra ◽  
Yaron Oz ◽  
Ittai Rubinstein
Keyword(s):  
Infectious Diseases ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Branching Processes ◽  
Analytical Formula ◽  
Higher Moments ◽  
High Level ◽  
The Basic Reproduction Number ◽  
Infection Spread

A well-known characteristic of pandemics such as COVID-19 is the high level of transmission heterogeneity in the infection spread: not all infected individuals spread the disease at the same rate and some individuals (superspreaders) are responsible for most of the infections. To quantify this phenomenon requires the analysis of the effect of the variance and higher moments of the infection distribution. Working in the framework of stochastic branching processes, we derive an approximate analytical formula for the probability of an outbreak in the high variance regime of the infection distribution, verify it numerically and analyze its regime of validity in various examples.We show that it is possible for an outbreak not to occur in the high variance regime even when the basic reproduction number R0 is larger than one and discuss the implications of our results for COVID-19 and other pandemics.

scholarly journals Early epidemic spread, percolation and Covid-19

2020 ◽  
Author(s):  
Gonçalo Oliveira
Keyword(s):  
Infectious Diseases ◽  
Explicit Formula ◽  
Basic Reproduction Number ◽  
Percolation Theory ◽  
Reproduction Number ◽  
Epidemic Spread ◽  
Human Interactions ◽  
Early Stages ◽  
Disease Spreading ◽  
The Basic Reproduction Number

AbstractHuman to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by a graph whose edges encode these interactions between individuals, the vertices. This article attempts to account for the case when each individual entails in different kinds of interactions which have therefore different probabilities of transmitting the disease. The majority of these results can be also stated in the language of percolation theory.The main contributions of the article are: (1) Extend to this setting some results which were previously known in the case when each individual has only one kind of interactions. (2) Find an explicit formula for the basic reproduction number R0 which depends only on the probabilities of transmitting the disease along the different edges and the first two moments of the degree distributions of the associated graphs. (3) Motivated by the recent Covid-19 pandemic, we use the framework developed to compute the R0 of a model disease spreading in populations whose trees and degree distributions are adjusted to several different countries. In this setting, we shall also compute the probability that the outbreak will not lead to an epidemic. In all cases we find such probability to be very low if no interventions are put in place.

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.

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