The impact of ambient air pollution on an influenza model with partial immunity and vaccination

In this paper, we investigate the effects of ambient air pollution (AAP) on the spread of influenza in an AAP-dependent dynamic influenza model. The value of this study lies in two aspects. Mathematically, we establish the threshold dynamics in the term of the basic reproduction number $ \mathcal{R}_0 $: If $ \mathcal{R}_0 < 1 $, the disease will go to extinction, while if $ \mathcal{R}_0 > 1 $, the disease will persist. Epidemiologically, based on the statistical data in Huaian, China, we find that, in order to control the prevalence of influenza, we must increase the vaccination rate, the recovery rate and the depletion rate, and decrease the rate of the vaccine wearing off, the uptake coefficient, the effect coefficient of AAP on transmission rate and the baseline rate. To put it simply, we must change our traveling plan and stay at home to reduce the contact rate or increase the close-contact distance and wear protective masks to reduce the influence of the AAP on the influenza transmission.