Modelling the effects of ozone concentration and pulse vaccination on seasonal influenza outbreaks in Gansu Province, China

Common air pollutants, such as ozone ( \begin{document}$ \rm{O}_{3} $\end{document} ), sulfur dioxide ( \begin{document}$ \rm{SO}_2 $\end{document} ) and nitrogen dioxide ( \begin{document}$ \rm{NO}_2 $\end{document} ), can affect the spread of influenza. We propose a new non-autonomous impulsive differential equation model with the effects of ozone and vaccination in this paper. First, the basic reproduction number of the impulsive system is obtained, and the global asymptotic stability of the disease-free periodic solution is proved. Furthermore, the uniform persistence of the system is demonstrated. Second, the unknown parameters of the ozone dynamics model are obtained by fitting the ozone concentration data by the least square method and Bootstrap. The MCMC algorithm is used to fit influenza data in Gansu Province to identify the most suitable parameter values of the system. The basic reproduction number \begin{document}$ R_{0} $\end{document} is estimated to be \begin{document}$ 1.2486 $\end{document} ( \begin{document}$ 95\%\rm{CI}:(1.2470, 1.2501) $\end{document} ). Then, a sensitivity analysis is performed on the system parameters. We find that the average annual incidence of seasonal influenza in Gansu Province is 31.3374 per 100,000 people. Influenza cases started to surge in 2016, rising by a factor of one and a half between 2014 and 2016, further increasing in 2019 (54.6909 per 100,000 population). The average incidence rate during the post-upsurge period (2017-2019) is one and a half times more than in the pre-upsurge period (2014-2016). In particular, we find that the peak ozone concentration appears 5–8 months in Gansu Province. A moderate negative correlation is seen between influenza cases and monthly ozone concentration (Pearson correlation coefficient: \begin{document}$ r $\end{document} = -0.4427). Finally, our results show that increasing the vaccination rate and appropriately increasing the ozone concentration can effectively prevent and control the spread of influenza.