# Research on Plant Disease and Pest Diagnosis Model Based on Generalized Stochastic Petri Net
## 4 Simulation Analysis
### Stimulation Analysis of the Pest and Disease Diagnosis Model
#### 4.2.2 Disease Judgment Stage  
A systematic simulation analysis was conducted on the disease judgment phase in the plant pest and disease spread evolution process. First, the relationships between the mild infection rate, moderate infection rate, and severe infection rate with the probability of meeting treatment criteria were explored. Then, the interactions between the mild infection rate, moderate infection rate, and severe infection rate were analyzed. Based on this, the simulation derived the critical surfaces for three different pest and disease early warning thresholds. These findings provide scientific evidence for developing effective pest and disease control strategies. While keeping all other \(\lambda\) values constant except for \(\lambda_{9}\) and \(\lambda_{10}\), the relationship between the mild infection rate, moderate infection rate, and the probability of meeting treatment criteria is derived from Formula (20):  
\[\mathrm{P}(\mathrm{M}_{12})=\frac{945\lambda_{10}\lambda_{10}}{17640\lambda_{ 9}+17640\lambda_{10}+2805\lambda_{9}\lambda_{10}} \tag{21}\]  
The plant pest and disease early warning threshold is set at 0.005. The contour lines in Figure 6 show the regions where the probability of meeting treatment criteria is the same under different infection rate combinations. For example, when \(\lambda_{9}=1.8\) and \(\lambda_{10}=2.4\), \(\mathrm{P}(\mathrm{M}_{12})=0.0209\). This indicates that under this infection rate combination, the probability of meeting treatment criteria is 2.09%. The system needs to activate the early warning mechanism and promptly implement corresponding control measures. This combination is particularly important in the prevention and early intervention stages. By enhancing monitoring, integrated control, and preventive measures, plant health and efficient production can be ensured. Under the condition that all other \(\lambda\) values remain constant except for \(\lambda_{10}\) and \(\lambda_{11}\), the relationship between the moderate infection rate, severe infection rate, and the probability of meeting treatment criteria is derived from Formula (20):  
\[\mathrm{P}(\mathrm{M}_{12})=\frac{105\lambda_{10}\,\lambda_{11}}{1960\lambda_ {10}+1960\lambda_{11}\,+2573\lambda_{10}\lambda_{11}} \tag{22}\]  
Figure 6: Relationship between mild infection rate, moderate infection rate, and probability of meeting treatment criteria. The changes in the contour lines in Figure 7 show the regions where the probability of meeting the treatment criteria is the same under different infection rate combinations. For example, when \(\lambda_{10}=1.8\) and \(\lambda_{11}=2.4\), \(\mathrm{P}(\mathrm{M}_{12})=0.0234\). This indicates that under this infection rate combination, the probability of meeting the treatment criteria is 2.34%. The system needs to activate the early warning mechanism and promptly implement corresponding control measures. Compared to the \(\lambda_{9}\), \(\lambda_{10}\) combination, the combination of \(\lambda_{10}\) and \(\lambda_{11}\) has a greater influence on the probability of meeting the treatment criteria, with more regions reaching higher probabilities. This combination requires special attention in pest and disease control measures. For areas with high rates of moderate and severe infection, the monitoring frequency should be increased. Combined physical, chemical, and biological control methods should be employed to comprehensively manage moderate and severe infections. Under the condition that all other \(\lambda\) values remain constant except for \(\lambda_{11}\) and \(\lambda_{9}\), the relationship between the severe infection rate, mild infection rate, and the probability of meeting treatment criteria is derived from Formula (20):  
\[\mathrm{P}(\mathrm{M}_{12})=\frac{945\lambda_{9}\ \lambda_{11}}{17640\lambda_{9}+17640 \lambda_{11}+24382\lambda_{9}\lambda_{11}} \tag{23}\]  
The changes in the contour lines in Figure 8 show the regions where the probability of meeting the treatment criteria is the same under different infection rate combinations.