The fluctuation impact of human mobility on the influenza transmission

Abstract

In this paper, we investigate the fluctuation impact of human mobility on influenza transmissions through a stochastic differential equation (SDE) model with environmental driving forces through both analytical and numerical analysis. We define a stochastic basic reproduction number R0s through a detailed process of calculations for the SDE model. Through R0s, the conditions for the stochastic extinction and persistence of the influenza disease are identified. We show that an epidemic stationary distribution exists in the case of persistence of influenza disease by constructing an appropriate Lyapunov function. We find that: (1) large environment fluctuations can suppress the outbreak of the influenza; (2) R0s determines stochastic distributions; (3) proper noise perturbations can be beneficial to control the spread of the influenza; (4) high economic capability can prohibit the influenza outbreaks; (5) seemingly irregular but appropriate human mobility response can significantly reduce the epidemic prevalence; (6) the positivity of the minimum intrinsic growth rate of human mobility density is the key factor of the stochastic persistence of the influenza disease.