Methods S1 - A Simple Stochastic Model with Environmental Transmission Explains Multi-Year Periodicity in Outbreaks of Avian Flu

In the supporting information file, we provide, essentially, detailed mathematical derivations of the different theoretical results presented in the main text. Supporting information is divided in four sections. The first one is devoted to the link between the deterministic and stochastic description of the system and the system-size expansion used to calculate power spectral densities. The second one analyzes the dynamical stability of fixed points of the deterministic system. The third one justifies the functional form used to represent environmental transmission, and finally, the last one includes a sensitivity analysis of the main fluctuation periodicity with respect to two model parameters.
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