Author: Lee, Hyunsun
Title: Stochastic and spatio-temporal analysis of the Middle East Respiratory Syndrome outbreak in South Korea, 2015 Document date: 2019_6_14
ID: 6cyhjt10_17
Snippet: To derive the probability of ultimate extinction, let z n be the probability that the infection will die out within n generations. We assume that q 0 is positive, otherwise the infection will never die out, and that q j is non-negative for all j > 0. For a random vertex with excess degree j, the probabilities z n and z nÀ1 are compared and depicted in Fig. 6 . The sequence fz n g is monotonically increasing since the probability that an infectio.....
Document: To derive the probability of ultimate extinction, let z n be the probability that the infection will die out within n generations. We assume that q 0 is positive, otherwise the infection will never die out, and that q j is non-negative for all j > 0. For a random vertex with excess degree j, the probabilities z n and z nÀ1 are compared and depicted in Fig. 6 . The sequence fz n g is monotonically increasing since the probability that an infection dies out within n generations is generally larger than or equal to the probability that it dies out within ðn À 1Þ generations. For a certain j, the probability of ultimate extinction of the infection within n generations is the product of q j and z j nÀ1 . Thus the probability z n is the summation over all possible non-negative integers j2J, which is the expected value of z J nÀ1 where J ¼ N∪f0g:
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