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. (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.
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. (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.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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=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
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.
(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.
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