In our study, we used an idea completely different 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 programme, each patient’s file contains a record of the time of infection, attack, isolation, and rehabilitation; susceptible persons he might have infected; and whether his range of activities was restricted during the day and night. Not only is this approach conducive to inquiring about the disease development process in each patient, but the transmission chain of the infection can be drawn, and therefore, in-depth analysis of the transmission path of an infectious disease in a crowd is possible. 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 programmes, 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 integrated into the programme, which shows 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. Notably, the median attack rate did not continue to increase with an increase in R0, which differs from the SEIR theory that an epidemic will be triggered once R0>1 ; rather, it began 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, a 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, 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 and active circulation of indoor air) are taken to keep the R0 at a low level, serious disease outbreaks can be prevented.
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 in the TOI, the probability of a total patient number that exceeds 80 people remains very low initially, then rises sharply, and finally reaches a high level and remains there, which differs from the SEIR theory that the attack rate continues to rise as the 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 postponement of 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 occurred before the growth rate peaked, the growth rate displayed a phased trend of an initial increase, followed by a rapid decrease and a final slow decrease. This trend was 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.
Timely diagnosis and treatment of patients following early onset of the disease can reduce the number of susceptible people who are infected. The PRCC for the IOI was 0.45, indicating a strong positive correlation. Under a constant R0, the probability of an outbreak gradually increased as the IOI was extended. The median attack rate remained very low at first, but when the IOI reached a threshold, the attack rate increased rapidly and then slowed. However, according to the SEIR theory, 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 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 was –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 increased gradually from 0, the probability of outbreaks decreased steadily. In addition, the median attack rate continued to decrease rapidly until it reached a critical point, after which it remained at an extremely low level; this outcome diverges 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. In general, the relationships between the attack rate and the above four parameters were similar: all displayed a sharp rise in the attack rate after the parameter reached a certain critical value, indicating 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 diseases that have a more chronic prevalence among the population (such as tuberculosis and AIDS, among others) still requires further discussion, although the value of the SEIR model for these diseases has been confirmed. Because cluster outbreaks have fewer influencing factors and shorter durations, it is relatively easy to establish a random collision model. However, for certain other chronic diseases, modelling requires the consideration of various additional 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.