Modeling and Predicting the Influence of PM2.5 on Children’s Respiratory Diseases

Abstract

In this paper, the influence of PM[Formula: see text] on children’s respiratory diseases is taken as the main research focus. Based on the real monitoring data of children’s respiratory diseases in Anhui province, the traditional model is modified substantially, leading to the establishment of two mathematical models. First of all, considering that the PM[Formula: see text] changes over time, a nonautonomous air pollution-related disease model is constructed to study its permanence and extinction. Furthermore, regarding lag days of PM[Formula: see text] exposure, an air pollution-related disease model with the lag effect is installed and its local and global stabilities and Hopf bifurcation are investigated. Meanwhile, the above two models are numerically simulated, respectively. Our study demonstrates that the threshold conditions of permanence and extinction are obtained by the nonautonomous air pollution-related disease model, and the optimal parameters are obtained through the annual revision of the data by integrating the mathematical model, such that the number of children with respiratory diseases in the future can be checked and predicted. Also our study finds that the lag days of PM[Formula: see text] exposure have little effect on children with respiratory diseases in the air pollution-related disease model with a lag effect, but the PM[Formula: see text] has a tremendous influence on the number of patients. Once the lag days are combined with the effect of the PM[Formula: see text], it can have a significant impact on the patients’ number, e.g. an emergence of periodic oscillations, with an approximate period of 11 days in Anhui Province, due to the Hopf bifurcation.

Bifurcation analysis of a respiratory disease model about air pollution direct and indirect effects

“…Moreover, a kind of nonautonomous respiratory disease model with lag effect was established in Shi et al 18 ; the persistence and extinction, and the existence and global attraction of periodic solutions, and the existence and stability of almost periodic solutions were analyzed. Both our conclusions in Shi et al 17,18 and the experience of CDC experts show there must be patients as long as there is air pollution. In addition, the case of susceptible population directly getting sick by inhaling $$$ {\mathrm{PM}}_{2.5} $$$ was considered in Shi et al 17 ; the non‐autonomous model with time delay was introduced in Shi et al, 18 and the other way of catching disease was not considered.…”

“…Both our conclusions in Shi et al 17,18 and the experience of CDC experts show there must be patients as long as there is air pollution. In addition, the case of susceptible population directly getting sick by inhaling $$$ {\mathrm{PM}}_{2.5} $$$ was considered in Shi et al 17 ; the non‐autonomous model with time delay was introduced in Shi et al, 18 and the other way of catching disease was not considered. In this paper, two situations that susceptible people directly got sick by inhaling air pollutants and indirectly fallen ill from infection by patients with respiratory diseases were simultaneously considered for modeling.…”

“…It is found that the combination of PM 2.5 and lag days will affect the change trend of patients' number and produce the Hopf bifurcation with periodic oscillation. 17 It follows that the influence of direct illness on the transmission of respiratory diseases should not be ignored. Moreover, a kind of nonautonomous respiratory disease model with lag effect was established in Shi et al 18 ; the persistence and extinction, and the existence and global attraction of periodic solutions, and the existence and stability of almost periodic solutions were analyzed.…”

“…In 2020, the actual situation of susceptible people who directly got sick from inhaling $$$ {\mathrm{PM}}_{2.5} $$$ is considered by Qi et al Through the combination of mathematical modeling and the actual data, mathematical modeling and predicting are made for the influence of $$$ {\mathrm{PM}}_{2.5} $$$ on children's respiratory diseases. It is found that the combination of $$$ {\mathrm{PM}}_{2.5} $$$ and lag days will affect the change trend of patients' number and produce the Hopf bifurcation with periodic oscillation 17 . It follows that the influence of direct illness on the transmission of respiratory diseases should not be ignored.…”

The Significance of Software Engineering to Forecast the Public Health Issues: A Case of Saudi Arabia

“…As health issues are closely related to good health policies, however, it is important to determine the factors which are affecting the public health (12)(13)(14). While focusing on the child health issues, several researchers attempted to investigate the determinants of child health issues (15)(16)(17). Similarly, Gilliland et al (18) examined the impact of air quality on child health, which proposes that improvement in air quality helps to minimize the lungs issues.…”