Dynamic of the air pollution pathogenic model and optimization control

Air pollution is contamination of the indoor or outdoor environment by any chemical, physical or biological agent that modifies the natural characteristics of the atmosphere. In this paper, the ability of air pollutants to affect the occurrence of infectious respiratory diseases in a population is studied by establishing an SISP respiratory disease model. It is found that the inhalation rate of pollutants, based on the daily emission level of pollutants, has a huge impact on the development of respiratory diseases. It is also found that the existence of multiple endemic equilibria, local stability and global stability of the equilibria, all depend on a certain quantity of pollutant produced in the environment. Moreover, the sensitivity analysis shows that the daily emission of pollutants and the inhalation rate of pollutants have significant positive correlation on the model while the clearance rate of pollutants have strong negative correlations with the model. Based on these results, an control strategy is produced in order to reduce the impact of air pollution on the occurrence of respiratory diseases in our environment and it goes as follows: the first step is to reduce the conversion rate of susceptible people to infective by reducing the inhalation rate of pollutant through raising public awareness on how to protect oneself from air pollutants in order to prevent respiratory infections; the second step is to reduce the daily emission of pollutants from all sources of emissions and try to keep it as low as possible; and the last step is to improve the clearance rate of pollutants in the environment.