# Modeling and Analyzing Transmission of Infectious Diseases Using Generalized Stochastic Petri Nets
## 4 Experimental Analysis  
By using the proposed GSPN model of infectious diseases, the steady-state probability can be analyzed according to the Markov process, and then the average number of tokens (\(U\)) in each place is calculated according to Formula (4). Through analyzing the key transitions including T5, T6, T7, T8, T9, T10, T12, T15, it can find how to change some links to improve the operating efficiency of the entire system. It has important practical significance for improving the efficiency of emergency decision-making for epidemic emergencies. In the experimental analysis, the initial parameters of the firing rates are simulated data, not real infectious disease experimental data. The initial transition firing rates are set as \(\lambda_{4}=\lambda_{11}=\lambda_{13}=\lambda_{14}=\lambda_{16}=\infty\), \(\lambda_{1}=\lambda_{2}=1\), \(\lambda_{3}=5\), \(\lambda_{5}=4\), \(\lambda_{6}=\lambda_{7}=\lambda_{10}=2\), \(\lambda_{8}=\lambda_{9}=3\), \(\lambda_{12}=\lambda_{15}=1\). In order to display the number of people in each stage of the epidemic evolution, we define that \(N\) represents the number unit of the population. The number of people in a place can be calculated by \(U\times N\). Note that the value of each \(\lambda_{i}\) can correspond to the measured or predicted value of the real data. Therefore, epidemiologists can input the parameters of different infectious diseases such as the reproduction number (\(R_{0}\)), the probability of the virus transmission, the probability of contacts, and the proportion of the people, etc. into \(\lambda_{i}\) as the firing rates. Figure 4 shows the impact of epidemic information reporting time (T5) on the evolution of the epidemic. It can be seen that the sum of the average number of tokens \(U(9)+U(10)\) in P9 and P10 gradually increases with the delay time of T5 from 1 h to 9 h. The average number of tokens \(U(12)\) in P12 also gradually increases. It indicates that with the longer the time for virus identification and information collection, the speed of virus infection from the initial infected people through hospitals and communities will gradually increase. Especially when the time of T5 is greater than 8 h, the rate of increase in the number of infections in the hospitals and communities will be significantly accelerated. For the social emergency system, it can improve the efficiency of responding to major infectious diseases by speeding up the collection of information on major epidemic diseases and shortening the virus identification cycle. Figure 5 shows the change in the number of infected people in the hospitals with the basic reproduction number (\(R_{0}\)). As \(R_{0}\) changes from 1 to 10, the virus spreads faster in the hospitals where the early-onset patients are located. The average number of tokens \(U(9)\) of P9 rapidly increases. It indicates that the new infected people in the hospitals increase significantly with the increase of \(R_{0}\). At the same time, the average number of tokens \(U(11)\) and \(U(13)\) in P11 and P13 will gradually rise with the increasing of \(R_{0}\). This shows that hospital infections are the main source of nosocomial infection to quickly spread the virus to other areas of the community. According to the analysis in Figure 5, as hospitals are places of early contact with infected persons, more attention should be paid to the prevention and control works in hospitals, such as immediately isolating infected patients and avoiding contact with other patients, so as to effectively reduce the transmission rate of the virus and thus curb the spread of the virus in hospitals. Establishing the mobile cabin hospitals in China is the effective way to reduce the rate of nosocomial infections. Figure 6 shows the changes in the number of infected people in the infected areas at different values of \(R_{0}\). The mild or no symptoms cases are more likely to cause negligence and accelerate the spread of the virus in the communities.