where P{l} denotes a discrete probability distribution with mean l. If the only information on case evolution is their average number then the maximum entropy distribution for P{} is Poisson, which we adopt throughout this paper. If additional information on the magnitude of fluctuations were also known, a generalized distribution should be employed, such as a negative binomial [33] , which can account for clumping effects (we reproduce all estimations from the main paper using a negative binomial in Supplementary Material S1, Table S2 ). To use expression [11] in practice, we need to evaluate the integral Y. Assuming the introductions from the reservoir per unit time to be approximately constant between t and t+t, the integral can be calculated to first order as Y(t,t,B) = t dB/dt and, [11] is written as