The spatial and temporal effects of Fog–Haze pollution on the influenza transmission

Abstract

The energy-intensive industrial economy results in frequent Fog–Haze weather which increases the risk of influenza spread and brings new challenges for the prevention and control of influenza. Therefore, the study of spread mechanics and controlling strategies of influenza based on Fog–Haze will be scientifically meaningful. Considering that when the concentration of Fog–Haze is low, Fog–Haze contributes to the number of infectious individuals and Fog–Haze suppresses the transmission of the influenza virus when the concentration of Fog–Haze is high, we establish the Fog–Haze dynamics model. Then we prove the global existence and boundedness of the solution, and the global asymptotic stability of the solution is given by constructing a suitable Lyapunov functional. Under the Fog–Haze weather, we study the influenza virus transmission model that incorporates the incidence rate to reflect the Fog–Haze-dependent saturation effect and investigate the effect of Fog–Haze pollution on the transmission of influenza. We show that the basic reproduction number [Formula: see text] determines the global dynamics of the system: if [Formula: see text], the disease-free equilibrium is global asymptotically stable; the unique endemic equilibrium is global asymptotically stable if [Formula: see text]. Simulations are carried out to validate the theoretical results. Our study provides further understanding of the dynamics of Fog–Haze and the effect of Fog–Haze pollution on the transmission of influenza.