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.

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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