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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 34EQ
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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.
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