Homework Help is Here – Start Your Trial Now!
Math
Probability
Complex Networks The reproduction number R of an epidemic spreading process taking place on a random network with degree distribution P(k) is given by R = (k(k-1)) (k) (1) 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 λ = 1/4. Investigate how the network topology can determine the regime of the epidemics in the following cases. (A) Consider a Poisson network with average degree c = 3 and a Poisson network with average degree c = 5. Calculate R and establish in which regime the epidemic process is in these networks. = (B) Calculate R for a scale-free network with degree distribution P(k) Ck, minimum degree m, maximum degree K and power-law expo- nent 2.5 using the continuous approximation for the degrees. (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.

Complex Networks The reproduction number R of an epidemic spreading process taking place on a random network with degree distribution P(k) is given by R = (k(k-1)) (k) (1) 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 λ = 1/4. Investigate how the network topology can determine the regime of the epidemics in the following cases. (A) Consider a Poisson network with average degree c = 3 and a Poisson network with average degree c = 5. Calculate R and establish in which regime the epidemic process is in these networks. = (B) Calculate R for a scale-free network with degree distribution P(k) Ck, minimum degree m, maximum degree K and power-law expo- nent 2.5 using the continuous approximation for the degrees. (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)
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...
See similar textbooks
icon
Related questions
Question

Can you answer all parts please 

Complex Networks The reproduction number R of an epidemic spreading process taking place on a random network with degree distribution P(k) is given by R = (k(k-1)) (k) (1) 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 λ = 1/4. Investigate how the network topology can determine the regime of the epidemics in the following cases. (A) Consider a Poisson network with average degree c = 3 and a Poisson network with average degree c = 5. Calculate R and establish in which regime the epidemic process is in these networks. = (B) Calculate R for a scale-free network with degree distribution P(k) Ck, minimum degree m, maximum degree K and power-law expo- nent 2.5 using the continuous approximation for the degrees. (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.
Transcribed Image Text:Complex Networks The reproduction number R of an epidemic spreading process taking place on a random network with degree distribution P(k) is given by R = (k(k-1)) (k) (1) 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 λ = 1/4. Investigate how the network topology can determine the regime of the epidemics in the following cases. (A) Consider a Poisson network with average degree c = 3 and a Poisson network with average degree c = 5. Calculate R and establish in which regime the epidemic process is in these networks. = (B) Calculate R for a scale-free network with degree distribution P(k) Ck, minimum degree m, maximum degree K and power-law expo- nent 2.5 using the continuous approximation for the degrees. (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
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 1 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer