Disease transmission network
The transmission network is shown in Figure 2. The black dots with connecting lines represent patients with infectious connections (as either an infector or an infected individual), totalling 328 people; the dispersed dots around the edge of the graph represent individuals who were exposed but uninfected. The first patient is marked in red; he infected a total of three susceptible people during the infection period.
Factors affecting the outbreak
R0 As demonstrated in Figure 3A, when R0 increased, the attack rate increased correspondingly. The maximum attack rate increased continuously from 0.3 to 0.96. The median attack rate remained close to 0 when R0 was between 1 and 1.5 but then increased sharply as R0 increased, reaching a maximum value of 0.93 when R0 was 3. When the number of patients reaches three or more, the disease is considered an outbreak. We calculated the probability of an outbreak under different R0 values and found that it rose from close to 0.5 to 0.93. Figure 4A shows that when R0 was equal to 3, 3.5, and 4, the peak values of the median growth rate (the number of new patients per day) were achieved on the 50th day (13 patients), the 46th day (16 patients), and the 41st day (19 patients), respectively, while the median cumulative number of patients on the 120th day at those R0 values was 464, 479, and 488 people, respectively. We defined the day that the first patient was detected as the 1st day.
TOI Figure 3B shows that under the condition of R0=3, the probability of an outbreak increased slightly, from 0.85 to 0.9, and consistently stayed near 0.9. When the TOI was on the 10th day, the probability of having more than 10 patients was only 0.2, indicating that the outbreak was well under control. With a delay in the TOI, the probability of having more than 10, 20, 40, or 80 patients increased. When the TOI was later than the 25th day, an outbreak scenario in which more than 80 people were infected began to emerge, indicating that a later TOI leads to infection of more patients and consequently to greater outbreaks. From the 50th day onwards, the attack rate of the epidemic stabilized and remained at a high level. As demonstrated in Figure 4B, when the TOI was the 40th day and the 50th day, the median growth rate peaked after 4 days (11 patients and 15 patients, respectively) and then dropped rapidly, with corresponding median cumulative numbers of patients of 157 and 300, respectively. When the TOI was on the 60th day, the median cumulative number of patients was 418.
IOI Figure 3C shows that when R0 was 3, the probability of an outbreak rose from 0.32 to 0.92. The maximum attack rate increased from 0.16 to approximately 0.95, and the 75% quantile, median, and 25% quantile of the attack rate began to increase drastically at days 1.5, 2.3, and 3.8, respectively, with all three approaching 0.9 on the 6th day. This result suggests that when the IOI is below a certain threshold, the attack rate of the disease can be controlled at a low level; however, once the IOI exceeds the threshold, the attack rate will increase very quickly. Figure 4C shows that when the TOI was on day 3, 3.5, and 4, the growth rate of patients peaked on the 63rd day (five patients), 58th day (seven patients), and 57th day (nine patients), respectively, while the median cumulative patient numbers were 357, 400, and 423, respectively.
IR Again, at R0=3, the probability of an outbreak showed a continuous reduction from 0.92 to 0.56, as shown in Figure 3D. At the same time, the maximum attack rate was reduced from 0.96 to 0.2, and the 75% quantile, median, and 25% quantile of the attack rate all dropped from the original value of 0.92. When the IR exceeded 0.5, the median attack rate approached zero. As shown in Figure 4D, when the IR was 0.1, 0.15, and 0.2, the growth rates for patient numbers peaked at the 56th day (10 patients), the 57th day (eight patients), and the 60th day (seven patients), and the cumulative patient numbers were 402, 370, and 336 patients, respectively.
We obtained an average generation period of 8.28 days, with a standard deviation of 2.78 days. Figure 5 shows that the median was estimated to be 8.26 days (95% CI: 7.84-8.69 days).
Sensitivity analyses were performed to assess the relationships between the four indexes (R0, TOI, IOI, IR) and one output (attack rate). We obtained 500 samples from a uniform distribution for each parameter range, and the PRCCs for the four indexes were 0.61, 0.17, 0.45, and -0.27, respectively. A value greater than 0 indicates a positive correlation, and a value less than 0 indicates a negative correlation. Values near -1 or +1 indicate that the parameter has a strong impact on the output, whereas values closer to 0 indicate less effect on the output result.