The reproduction number R of an epidemic spreading process taking place on a random network with degree distribution P(k) is given by R=λ- (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. (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. =
The reproduction number R of an epidemic spreading process taking place on a random network with degree distribution P(k) is given by R=λ- (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. (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. =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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=λ-
(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.
(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.
=
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