# Study on the Impact of Ventilation Methods on Droplet Nuclei Transmission in Subway Carriages
## 3 Results
### Analysis of the Infection Risk Prediction Model  
This study primarily investigates droplet transmission from the perspective of ventilation systems and airflow. To better present the research findings, an epidemiological model is introduced to analyze the specific impact of droplet transmission on infection rates. Assessing infection risk may provide greater value for epidemiological and public health research. This study aims to ensure that the cumulative infection risk in the target area remains below a specific threshold within a given time frame through infection-resistant ventilation. A non-steady-state indoor infection risk prediction model based on the Wells-Riley model is employed in this study. As shown in Equation (18), the steady  
Figure 14: The ADPI values of different air supply methods (MV, SFRC) in the subway carriage under different air supply parameters. state Wells-Riley model determines infection risk primarily by considering the number of infected individuals, quanta generation rate, pulmonary ventilation rate, exposure time, and indoor ventilation rate. \[P=\frac{N}{S}=1-e^{-Iqpt/Q} \tag{18}\]  
In the equation, P represents the infection risk; N denotes the number of infected individuals in the next generation; S represents the number of susceptible individuals in the current generation; I is the total number of infected individuals in the current generation; q refers to the quantum generation rate per infected individual (quanta/h), which depends on the type of disease and individual physiological conditions; p is the pulmonary ventilation rate of a susceptible individual (m\({}^{3}\)/h); t represents the total exposure time (hours); and Q is the indoor fresh air ventilation rate (m\({}^{3}\)/h). The steady-state Wells-Riley model is commonly applied when the number of air exchanges during an individual's exposure period is sufficiently high. However, when assessing the impact of short-duration events such as coughing and sneezing on infection risk, the steady-state W-R model tends to significantly overestimate the risk. Therefore, a non-steady-state form of the W-R model must be used to accurately evaluate infection risk. [PERSON] et al. [44] proposed a non-steady-state Wells-Riley (W-R) model based on human behavior, which is suitable for accurately predicting infection risk caused by short-duration events such as sneezing and coughing. The probability of a susceptible individual becoming infected can be calculated using Equation (19). \[P=1-\exp(-\mu)=1-\exp\left[-p\left(\int_{\theta_{1}}^{\theta_{2}}C^{T=1}d \theta+\int_{\theta_{2}}^{\theta_{3}}C^{T=2}d\theta+...+\int_{\theta_{X}}^{ \theta_{X+1}}C^{T=X}d\theta\right)\right] \tag{19}\]  
In the equation, \(\mu\) represents the total number of quanta inhaled by an individual over the total exposure duration. \(\theta\) denotes time (hours), measured from the moment the quanta are initially released. \(C^{T=X}\) represents the instantaneous quantum concentration at the beginning of the X time interval. In this study, infection risk is calculated using the aforementioned non-steady-state Wells-Riley equation. It can be observed from Figure 15 that, for all conditions, the infection risk probability initially increases and then decreases. In the MV system, the infection probability is highest at low air velocity, reaching a peak of 10.4% at t = 60 s when the droplets spread. Afterward, the virus particles gradually move toward the return air outlet and are expelled from the carriage, causing the infection probability to decrease gradually, with a relatively smooth fluctuation. At medium and high air velocities, the fluctuations are more intense. From Figure 6, it is evident that droplets spread more intensively between t = 20 s and t = 40 s, remaining in the space for a longer duration. As they do not flow to the return air outlet in time, a sharp increase in infection probability occurs. Subsequently, due to the effect of wind speed, the droplets flow to the return air outlet and are expelled.