Problem 3We propose another model of early propagation of an epidemic, by counting the number of indi-viduals spreading the disease as follows: At day 0, there is one person infected. From a day to thenext, every infected individual independently:1) remains a spreader with probability (w.p.) p, and has either infected exactly one new individual(who becomes a spreader) with conditional probability q, or has not spread the disease with con-ditional probability 1-q.2) gets definitively removed from the pool of spreaders without infecting anyone else (w.p. 1-p).a. Justify why this model can be described as a branching process (what is the number of spreadersat time n + 1 given the number of spreaders at time n, what is the reproduction law). Find thegenerating function of the reproduction law.b. We define the contact number o as the average number of individuals directly contaminatedby an infected individual before this individual is removed from the pool of spreaders. Show thato= (hint: you can first consider how long on average can an infected person spread thedisease)C. Show that the epidemic has a probability> 0 to propagate forever if and only if > 1, andthat in this case, this probability is 1-

We are given a growth model of an epidemic. At day 0, there is one person infected. From a day to…

Answered: We propose another model of early…

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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