In our study, we used a completely different idea from the SEIR model. The random collision model has the following specific advantages: 1. The model can more precisely describe the process of epidemic transmission. We used the individual subject as the study unit, and in the program, each patient’s file contains a record of the time of infection, attack, isolation, rehabilitation, susceptible persons he might have infected, as well as whether his range of activities was restricted during the day and night. Not only is it conducive to inquire about the disease development process of each patient, but the transmission chain of the infection can be drawn, and therefore, an in-depth analysis of the transmission path of infectious diseases in a crowd is valuable. 2. Randomization is in greater agreement with the transmission characteristics of an infectious disease. Contact between patients and susceptible persons is random rather than continuous. The effective contact rate, incubation period, treatment duration, and immunity of the patients are also in accordance with random distribution. We randomly sampled from the probability distributions, which are shown in Table 1, that were obtained from the actual epidemic situation and distributed to each patient. This sampling can ensure the authenticity and scientific integrity of the research. 3. This method can be extended to other infectious diseases and their occurrence scenarios, e.g., tuberculosis outbreaks in schools or the spread of HIV among gay men; we can also set patient activities in programs, such as in a school, where students attend classes during the day, return home at night, or board at the school. Furthermore, more complex factors affecting epidemic transmission can be designed as part of the program, which has the flexibility and diversity that the traditional SEIR model cannot achieve.
Additionally, in the following four paragraphs, we discuss the impact of four indicators, R0, TOI, IOI, and IR, on the attack rate in the outbreak.
Overall, R0 was positively correlated with the attack rate at a PRCC of 0.61, which was the highest absolute value among the four parameters included in the comparison, indicating that R0 has the strongest influence on attack rate. It is worth noting that the median attack rate does not continue to increase with the increase in R0, which differs from the traditional theory that an epidemic will be triggered once R0>1 [26]; rather, it starts to increase dramatically at a certain critical point. The reason for this dramatic increase is because when the value of R0 is small, even when a source of infection is present within the crowd, the patient’s ability to spread the disease is weak, and he will recover before the disease is transmitted to other susceptible people. As the R0 increases, the speed of disease transmission increases with it, and the cumulative effect is amplified in a manner that corresponds to the increase in the number of disease generations. This phenomenon reminds us that as long as appropriate preventive measures (such as health education, active circulation of indoor air, etc.) are taken to keep the R0 at a low level, serious disease outbreaks can be prevented.
The timely isolation of patients after an outbreak can very effectively control further outbreaks of an epidemic. Our results showed that when the R0 stays constant, with a delay of the TOI, the probability of a total patient number that exceeds 80 people remains very low initially; then, it rises sharply; and finally, it reaches a high level and remains there, differing from the traditional theory that the attack rate continues to rise as TOI is delayed. This pattern reveals that when isolation treatment is carried out at the early/beginning stage of an outbreak, the attack rate can be controlled at a lower level; however, with postponed isolation measures, the total number of patients will increase very quickly, and if isolation is initiated too late, outbreaks of the epidemic become extremely difficult to control. When the TOI occurs before the growth rate peaks, the growth rate displays a phased trend of an initial increase, followed by a rapid decrease and a final slow decrease. This trend is observed because many people became infected before being isolated; although those who became sick after the TOI were isolated within 1 day of the onset of illness, those patients may have had contact with others and thus could have transmitted the virus. A small number of the individuals infected during this period will become new patients after an incubation period, which averages approximately 5 days.
The timely diagnosis and treatment of patients following the early onset of the disease can reduce the number of susceptible people who are infected. The PRCC for the IOI is 0.45, indicating a strong positive correlation. Under a constant R0, the probability of an outbreak gradually increases as the IOI is extended. The median attack rate stays at a very low level at first; when the IOI reaches a threshold, the attack rate increases rapidly but then slows down. According to the traditional theory, however, no such threshold exists. This trend suggests that we can effectively reduce the risk of an outbreak by taking isolation measures within a certain time frame. The earlier that detection, diagnosis, and isolation can be performed, the greater the possibility that the disease attack rate will remain low.
Immunization is an effective approach for preventing infectious diseases. The PRCC between the IR and attack rate is -0.27, indicating that the higher the IR among the population, and lower the attack rate will be. The results section shows that as the IR increases gradually from 0, the probability of outbreaks decreases steadily. In addition, the median attack rate continues to decrease rapidly until it reaches a critical point, after which it remains at an extremely low level; this outcome is convergent from the SEIR model in which the epidemic will not occur once the IR increases to . This outcome occurs because when the IR increases to a certain extent, patients will not be able to continue to infect more susceptible people. This trend indicates that the outbreak of an epidemic can be efficiently restricted if the IR reaches a critical point. However, if it does not reach that critical point, disease prevention will be limited. The relationships between the attack rate and the above four parameters are similar to each other in general, all of which display a sharp rise in attack rate after that parameter reaches a certain critical value, meaning that the risk of an epidemic outbreak is manageable; nonetheless, if the measures taken are not effective, difficulty in controlling the outbreak will increase rapidly.
Although we present some original findings, our study has some limitations. For example, the suitability of the random collision model for some diseases that have a more chronic prevalence among the population (such as tuberculosis and AIDS, among others) still requires further discussion where the SEIR model has been proven valuable. Because cluster outbreaks have fewer influencing factors and shorter durations, it is relatively easy to establish a random collision model. However, for some other chronic diseases, modelling requires the consideration of various factors, including population migration, age structures, and government interventions. In addition, we calculated only the PRCCs between the attack rate and each parameter in the sensitivity analyses; we did not investigate the compounding effects of multiple parameters acting together on the attack rate, a topic that needs to be addressed in future studies.