Abstract
The impact of air pollutants on the human respiratory system has received more and more attention. However, due to the differences in human characteristics and the strength of protective measures, different people have different symptoms in air pollution and viral infection environments. In this paper, an SI1I2P dynamic model of respiratory diseases infected by virus under air pollution is established by introducing air pollutant concentration compartment. Qualitative research shows that there are seven equilibria in the system, the daily average emission and clearance rate of pollutants are the key parameters affecting the existence and stability of equilibria. In this paper, by using Sotomayor’s theorem and center manifold theory, it is proved that the system undergoes saddle–node bifurcation or Bogdanov–Takens bifurcation of co-dimension 3 at the boundary equilibrium, and exhibits saddle–node bifurcation at the endemic equilibrium. Numerical simulation results show that wearing masks in haze weather can not only reduce the number of allergic patients, but also reduce the number of viral patients. In addition, reducing the daily average emission of air pollution and increasing its clearance rate can also reduce the number of allergic patients. It is worth mentioning that this measure is more effective in controlling viral respiratory diseases.
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