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. 2004 Jun 24;101(27):10229–10234. doi: 10.1073/pnas.0400695101

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Copyright © 2004, The National Academy of Sciences

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Fig. 3. — Probability distributions of observable outbreaks. (a) The probability distribution of the number of cases given that at least one case occurs, p(X|X ≥ 1) = p(X)/[1 - p(0)] = [(1 + √ε)/√ε]p(X), for various pathogenicities. For ε = 1, p(X|X ≥ 1) = 2^-X), and for ε = 0, lim_ε→0 p(X|X ≥ 1) ≈ X^-3/2/2√π (22), i.e., a power law with exponent -3/2. (b) The probability of an outbreak of at least n cases for various pathogenicities. The probabilities are computed as 1 p(X|X ≥ 1). For large n and ε tending to 0, the logarithm of the probability scales with the logarithm of the minimum outbreak size and the scaling factor is -1/2.

Inline graphic — Probability distributions of observable outbreaks. (a) The probability distribution of the number of cases given that at least one case occurs, p(X|X ≥ 1) = p(X)/[1 - p(0)] = [(1 + √ε)/√ε]p(X), for various pathogenicities. For ε = 1, p(X|X ≥ 1) = 2^-X), and for ε = 0, lim_ε→0 p(X|X ≥ 1) ≈ X^-3/2/2√π (22), i.e., a power law with exponent -3/2. (b) The probability of an outbreak of at least n cases for various pathogenicities. The probabilities are computed as 1 p(X|X ≥ 1). For large n and ε tending to 0, the logarithm of the probability scales with the logarithm of the minimum outbreak size and the scaling factor is -1/2.