The reproduction number R of an epidemic spreading process taking place on a random network with degree distribution P(k) is given by (k(k − 1)) R=A (k) where k indicates the degree of the nodes and the average (...) indicates the average over the degree distribution, P(k). Therefore R is the product between the infectivity A of the virus, due to its biological fitness and the branching ratio of the network, depending on the degree distribution of the network and given by (k(k-1))/(k). According to the value of R the epidemic can be in different regimes: If R>1 the epidemics is in the supercritical regime: the epidemics spreads on a finite fraction of the population, resulting in a pandemics. If R < 1 the epidemics is in the subcritical regime: the epidemics affects a infinitesimal fraction of the population and can be considered suppressed. If R = 1 the epidemics is in the critical regime: this is the regime that separates the previous two regimes. Consider an epidemics with infectivity = 1/4. Investigate how the network topology can determine the regime of the epidemics in the following cases. (C) Take the scale-free network considered in point (B) calculate R and establish in which regime the epidemic process is if m = 2, K = 50.
The reproduction number R of an epidemic spreading process taking place on a random network with degree distribution P(k) is given by (k(k − 1)) R=A (k) where k indicates the degree of the nodes and the average (...) indicates the average over the degree distribution, P(k). Therefore R is the product between the infectivity A of the virus, due to its biological fitness and the branching ratio of the network, depending on the degree distribution of the network and given by (k(k-1))/(k). According to the value of R the epidemic can be in different regimes: If R>1 the epidemics is in the supercritical regime: the epidemics spreads on a finite fraction of the population, resulting in a pandemics. If R < 1 the epidemics is in the subcritical regime: the epidemics affects a infinitesimal fraction of the population and can be considered suppressed. If R = 1 the epidemics is in the critical regime: this is the regime that separates the previous two regimes. Consider an epidemics with infectivity = 1/4. Investigate how the network topology can determine the regime of the epidemics in the following cases. (C) Take the scale-free network considered in point (B) calculate R and establish in which regime the epidemic process is if m = 2, K = 50.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Transcribed Image Text:The reproduction number R of an epidemic spreading process taking place
on a random network with degree distribution P(k) is given by
R=A
(k(k-1))
(k)
where k indicates the degree of the nodes and the average (...) indicates the
average over the degree distribution, P(k).
Therefore R is the product between the infectivity A of the virus, due to its
biological fitness and the branching ratio of the network, depending on the
degree distribution of the network and given by (k(k-1))/(k).
According to the value of R the epidemic can be in different regimes:
• If R > 1 the epidemics is in the supercritical regime: the epidemics
spreads on a finite fraction of the population, resulting in a pandemics.
If R < 1 the epidemics is in the subcritical regime: the epidemics
affects a infinitesimal fraction of the population and can be considered
suppressed.
• If R = 1 the epidemics is in the critical regime: this is the regime that
separates the previous two regimes.
Consider an epidemics with infectivity = 1/4. Investigate how
the network topology can determine the regime of the epidemics
in the following cases.
(C) Take the scale-free network considered in point (B) calculate R and
establish in which regime the epidemic process is if m = 2, K = 50.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 13 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON