A stochastic model explains the periodicity phenomenon of influenza on network.

Influenza is an infectious disease with obvious periodic changes over time. It is of great practical significance to explore the non-environment-related factors that cause this regularity for influenza control and individual protection. In this paper, based on the randomness of population number and the heterogeneity of population contact, we have established a stochastic infectious disease model about influenza based on the degree of the network, and obtained the power spectral density function by using the van Kampen expansion method of the master equation. The relevant parameters are obtained by fitting the influenza data of sentinel hospitals. The results of the numerical analysis show that: (1) for the infected, the infection period of patients who go to the sentinel hospitals is particularly different from the others who do not; (2) for all the infected, there is an obvious nonlinear relationship between their infection period and the visiting rate of the influenza sentinel hospitals, the infection rate and the degree. Among them, only the infection period of patients who do not go to the sentinel hospitals decreased monotonously with the infection rate (increased monotonously with the visiting rate), while the rest had a non-monotonic relationship.