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 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 Multi-Type Branching Processes Modeling of Nosocomial Epidemics

2017 ◽  
Vol 32 (2) ◽  
Author(s):  
Zeinab Mohamed ◽  
Tamer Oraby
Keyword(s):  
Health Care ◽  
Basic Reproduction Number ◽  
Branching Process ◽  
Negative Binomial ◽  
Reproduction Number ◽  
Branching Processes ◽  
Care Facility ◽  
Health Care Facility ◽  
Different Types ◽  
The Basic Reproduction Number

AbstractNosocomial epidemics are infectious diseases which spread among different types of susceptible individuals in a health-care facility. To model this type of epidemics, we use a multi-type branching process with a multivariate negative binomial offspring distribution. In particular, we estimate the basic reproduction number

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 .

Theoretical assessment of the impact of desert aerosols on the dynamical transmission of meningitidis serogroup A

2019 ◽  
Vol 12 (05) ◽  
pp. 1950060
Author(s):  
A. Oumar Bah ◽  
M. Lam ◽  
A. Bah ◽  
S. Bowong
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
High Level ◽  
The Impact ◽  
Theoretical Assessment ◽  
Theoretical Results ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper has been motivated by the following biological question: how influential are desert aerosols in the transmission of meningitidis serogroup A (MenA)? A mathematical model for the dynamical transmission of MenA is considered, with the aim of investigating the impact of desert aerosols. Sensitivity analysis of the model has been performed in order to determine the impact of related parameters on meningitis outbreak. We derive the basic reproduction number [Formula: see text]. We prove that there exists a threshold parameter [Formula: see text] such that when [Formula: see text], the disease-free equilibrium is globally asymptotically stable (GAS). However, when [Formula: see text], the model exhibits the phenomenon of backward bifurcation. At the endemic level, we show that the number of infectious individuals in the presence of desert aerosols is larger than the corresponding number without the presence of desert aerosols. In conjunction with the inequality [Formula: see text] where [Formula: see text] is the basic reproduction number without desert aerosols, we found that the ingestion of aerosols by carriers will increase the endemic level, and the severity of the outbreak. This suggests that the control of MenA passes through a combination of a large coverage vaccination of young susceptible individuals and the production of a vaccine with a high level of efficacy as well as respecting the hygienic rules to avoid the inhalation of desert aerosols. Theoretical results are supported by numerical simulations.

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