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Stochastic general epidemic model describes the progress of an infectious disease through a closed private community of 28 people. There are two infectious individuals; the others are all susceptible. The contact rate ẞ is 1.8 per day, and the removal rate y is 1.2 per day. (a) Show that the epidemic parameter p is equal to 18. (b) Draw diagrams showing all the epidemic paths for which at most one person catches the disease before the epidemic dies out. Calculate the probability that of the initial 26 uninfected susceptibles, at most one person will catch the disease before the epidemic dies out. (c) Calculate an approximate value for the probability that there will be a major outbreak of the disease.

Stochastic general epidemic model describes the progress of an infectious disease through a closed private community of 28 people. There are two infectious individuals; the others are all susceptible. The contact rate ẞ is 1.8 per day, and the removal rate y is 1.2 per day. (a) Show that the epidemic parameter p is equal to 18. (b) Draw diagrams showing all the epidemic paths for which at most one person catches the disease before the epidemic dies out. Calculate the probability that of the initial 26 uninfected susceptibles, at most one person will catch the disease before the epidemic dies out. (c) Calculate an approximate value for the probability that there will be a major outbreak of the disease.

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...
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Stochastic general epidemic model describes the progress of an infectious disease through a closed private community of 28 people. There are two infectious individuals; the others are all susceptible. The contact rate ẞ is 1.8 per day, and the removal rate y is 1.2 per day. (a) Show that the epidemic parameter p is equal to 18. (b) Draw diagrams showing all the epidemic paths for which at most one person catches the disease before the epidemic dies out. Calculate the probability that of the initial 26 uninfected susceptibles, at most one person will catch the disease before the epidemic dies out. (c) Calculate an approximate value for the probability that there will be a major outbreak of the disease.
Transcribed Image Text:Stochastic general epidemic model describes the progress of an infectious disease through a closed private community of 28 people. There are two infectious individuals; the others are all susceptible. The contact rate ẞ is 1.8 per day, and the removal rate y is 1.2 per day. (a) Show that the epidemic parameter p is equal to 18. (b) Draw diagrams showing all the epidemic paths for which at most one person catches the disease before the epidemic dies out. Calculate the probability that of the initial 26 uninfected susceptibles, at most one person will catch the disease before the epidemic dies out. (c) Calculate an approximate value for the probability that there will be a major outbreak of the disease.
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