Stochastic modeling and analysis of the mutual influence between respiratory diseases and air quality

Respiratory viruses can be transmitted through both human contact and airborne particles. Air pollution exacerbates the spread of airborne diseases, while the societal burden imposed by these diseases drives efforts to improve air quality. This study proposes a stochastic bidirectionally coupled model to capture the mutual influence between respiratory disease transmission and air pollution. It incorporates dual transmission routes and accounts for stochastic factors influencing both disease dynamics and air quality fluctuations. Conditions for the elimination and persistence of both air pollutants and respiratory diseases are derived, with numerical simulations validating the conclusions. When both respiratory diseases and air pollution persist, the stochastic model exhibits a stationary distribution. The findings suggest that stochasticity can promote the elimination of respiratory diseases and contribute to mitigating air pollution. Data fitting validates the accuracy and effectiveness of the coupled model, and numerical results confirm that incorporating coupling relationships provides a more comprehensive understanding of disease transmission dynamics and air quality variations.