On the basis of the improved SEIR model, we simulated the trajectory of infected cases in various outbreak scenarios under nucleic acid detection measures and estimated the nucleic acid detection quantity based on the model simulation results. This information is valuable for adjusting strategies according to the available detection capacity.

In different scenarios with the same initial infected person, the scale of infection after 200 days of epidemic simulation follows this order: scenario 4, scenario 3, scenario 5, scenario 2, scenario 6, scenario 1 (Table 3).

In the scenario without any interventions, the outbreak peaks at approximately 30 days, with 143,195 people infected, constituting 57.28% of the total population (Fig. 3a) All the infected cases were untested (Fig. 4a). As a result of the lack of intervention, there is a potential demand of 187,148, far exceeding the set nucleic acid detection capacity (Table 4).

The change trend of undetected and detected infected persons under scenarios 1–6 (a–f)

Changes in the proportion of different types of infected persons under scenarios 1–6 (a–f)

Under a scenario with relaxed containment measures and low testing capacity, the epidemic peaks at about 44 days, with 115,419 people infected (Fig. 3b) Among them, 83,518 are undiagnosed cases, 25,589 are positive cases, and 6312 are negative cases (Fig. 4b). Undetected cases account for 77.83% of the total cases. The total demand reaches a peak of 121,201 on the 41st day, surpassing the capacity when testing is low (Table 4).

In a scenario with low testing capacity but strengthened non-pharmaceutical prevention and control measures, the epidemic peaks at 122 days, with 21,096 infected people (Fig. 3c) Among them, 2875 are undetected, 14,511 are positive, and 3710 are negative. Undetected cases account for 31.21% of the total cases (Fig. 4c). The total demand peaks at 11,739 on the 115th day, and the demand can be met even with low detection capacity (Table 4).

With increased testing capacity, intensified non-pharmaceutical prevention and control measures, and vaccination, the epidemic peaks at 108 days, with 19,303 infected people (Fig. 3d). Among them, 2657 are undetected, 15,024 are positive, and 1622 are negative. Undetected cases account for 22.17% of the total cases (Fig. 4d). The total demand peaks at 12,884 on the 97th day, and both high and low detection capabilities can meet the demand at this time (Table 4).

Under strict prevention and control measures and robust testing capacity, the epidemic peaks at 125 days, with 30,942 infected people (Fig. 3e). Among them, 18,468 are undetected, 11,262 are positive, and 1212 are negative. Undetected cases account for 63.60% of the total cases (Fig. 4e). The total demand peaks at 32,537 on the 119th day, and both high and low detection capabilities can meet the demand at this time (Table 4).

In a scenario of high vaccination efficiency and low testing capacity with relaxed prevention and control measures, the epidemic peaks at about 39 days, with 119,103 infected people (Fig. 3f). Among them, 102,870 are undetected, 13,018 are positive, and 3215 are negative. Undetected cases account for 89.07% of the total cases (Fig. 4f). The total demand peaks at 134,320 on the 36th day, and neither high nor low detection capabilities can meet the demand at this time (Table 4).

There were significant differences in the total demand for testing under different scenarios (Fig. 5).

Estimation of demand for nucleic acid testing under scenarios 1–6

Compared with no prevention and control measures, relatively lenient prevention and control measures can reduce the infection peak and prolong the epidemic’s peak time. Building upon the implementation of scenario 1, scenario 2 introduced non-pharmaceutical interventions, vaccination, nucleic acid testing, and other measures, resulting in a reduction of 27,776 infections and 65,947 in total testing demand. By intensifying non-pharmaceutical interventions and increasing the frequency of nucleic acid testing in scenario 3, even under low testing capacity, the epidemic’s peak time was delayed by 78 days. The proportion of undetected cases decreased from 77.83% to 31.21%, and the total demand for testing was significantly reduced, meeting the maximum demand under low testing capacity.

In scenario 4, with improved nucleic acid testing capacity compared to scenario 3, the number of undetected cases and test-negative cases decreased, and the proportion of undetected cases was 22.17%. However, the total demand for testing increased in this scenario. Scenario 5 transitioned from universal testing to voluntary testing on the basis of scenario 4, resulting in a 44% decrease in residents’ willingness to test. Consequently, the number of infected patients increased by 11,640, the proportion of undetected cases surged to 63.60%, and the total demand rose by 2.5 times, surpassing the set capacity of nucleic acid testing.

Under scenario 6, where vaccination coverage increased and residents’ willingness to test decreased on the basis of scenario 2, the number of infected people increased by 3685, the proportion of undetected cases rose by 11.24%, and the total demand for nucleic acid testing increased by 13,119. This analysis underscores the intricate dynamics between prevention and control measures, testing strategies, and their collective impact on epidemic outcomes.