Table 1 Model variables and parameters

Variables and their initial values

\(S(t)\)

The number of susceptible individuals at day \(t\)

22,211,296

Assumed

\(E(t)\)

The number of exposed individuals at day \(t\)

1

Assumed

\(A(t)\)

The number of asymptomatic infectious at day \(t\)

0

Assumed

\({I}_{1}(t)\)

The number of presymptomatic infectious individuals at day \(t\)

0

Assumed

\({I}_{2}(t)\)

The number of symptomatic infectious individuals at day \(t\)

0

Assumed

\({I}_{d}(t)\)

The number of confirmed and isolated individuals at day t

0

Assumed

\(R(t)\)

The number of recovered individuals at day t

0

Assumed

\({Q}_{S}(t)\)

The number of traced and quarantined susceptible individuals at day \(t\)

–

\({Q}_{E}(t)\)

The number of traced and quarantined exposed individuals at day \(t\)

–

\({Q}_{I}(t)\)

The number of traced and quarantined presymptomatic and asymptomatic infectious individuals at day \(t\)

–

\(H(t)\)

The number of severe patients that need intensive health care (ICU)

–

\(D\left(t\right)\)

The number of deceased individuals at day t

–

\({I}_{d}({T}_{1})\)

The number of confirmed and isolated individuals at day \({T}_{1}\)

5

Data [31]

Parameters for COVID-19 in Fujian

\({\tau }_{1}\)

Average time spent in the exposed state, \(E\), days, for Delta variant

2

Ref [49]

\({\tau }_{2}\)

Average time spent in the presymptomatic infected state \({I}_{1}\), days, for Delta variant

2

Ref [50]

\(a\)

Proportion of infected people who will develop symptoms

0.8

Ref [51]

\(b\)

Infectiousness of asymptomatic individuals compared to symptomatic infections

0.75

Ref [12]

\(\eta\)

The testing efficiency towards asymptomatic infections \(A\) and presymptomatic infections \({I}_{1}\)

0.67

Ref [52]

\({\xi }_{1}\)

The risk increment of ICU requirement for Delta variant compared to the wildtype

2.34

Ref [53]

\({\xi }_{2}\)

The risk increment of death for Delta variant compared to the wildtype

1.32

Ref [53]

\({p}_{D}\)

Proportion of severe patients in ICU died

18%

Ref [54]

\({u}_{1}\)

Days for developing severe symptoms and need ICU care after diagnosed, days

7–12

Ref [55]

\({u}_{2}\)

Length of stay for severe patients in ICU before died, days

15

Ref [56]

\({u}_{{I}_{2}}\)

The average days from symptom onset to diagnosis in Fujian, days

2

Ref [57]

\({\gamma }_{A}\)

Recovery rate of asymptomatic infectious individuals, days⁻¹

1/6

Ref [58]

\(\gamma\)

Recovery rate of symptomatic infectious individuals, days⁻¹

Stage 1: 0

Assumed

\({\gamma }_{d}\)

Recovery rate of non-ICU patients, days⁻¹

1/7

Ref [58]

\({\gamma }_{H}\)

Recovery rate of ICU patients, days⁻¹

1/11

Ref [59]

\({\alpha }_{1}\)

The adherence rate of citywide testing in Fujian

1

Ref [35]

\({\alpha }_{2}\)

The adherence rate of symptom-driven testing in Fujian

1

Ref [5]

\({p}_{c}\)

The percentage of contact tracing in Fujian

1

Ref [5]

\(P\)

Total number of populations in epidemic areas (Xiamen, Putian, Quanzhou, and Zhangzhou) in Fujian Province

22,211,297

Data [60]

\({T}_{0}\)

Time when the virus imported into epidemic areas in Fujian Province

September 2

Assumed

\({T}_{1}\)

Time when the first confirmed cases detected

September 10

Data [31]

\({T}_{Q}\)

The period of isolation for those traced individuals, days

28

Ref [5]

\(T\)

The time needed to complete one round of citywide test, days

2–3

Ref [35]

\({Z}_{CT}(t)\)

The number of people traced who has primary and secondary contacts of suspected or confirmed cases of COVID-19 at time t

–

\({Z}_{S}(t)\)

Daily new isolated susceptible individuals due to contact tracing

–

\({Z}_{E}(t)\)

Daily new isolated exposed individuals due to contact tracing

–

\({Z}_{A}(t)\)

Daily new isolated asymptomatic individuals due to contact tracing

–

\({Z}_{{I}_{1}}\left(t\right)\)

Daily new isolated presymptomatic infected individuals due to contact tracing

–

\({N}_{PCR}(t)\)

The number of individuals conducting citywide testing at time t

–

\({M}_{A}\left(t\right)\)

Daily new diagnosed asymptomatic infectious individuals from citywide testing

–

\({M}_{{I}_{1}}\left(t\right)\)

Daily new diagnosed presymptomatic infectious individuals from citywide testing

–

\({M}_{{I}_{2}}\left(t\right)\)

Daily new diagnosed symptomatic infectious individuals from symptom-driven testing

–

\({M}_{{I}_{d}}\left(t\right)\)

Daily new diagnosed cases from citywide testing and symptom-driven testing

–

Estimated parameters

\(\beta\)

Probability of transmission per contact

0.0611 (95% CI: 0.0603–0.0804)

\(c\)

The number of contacts per individual per day in each stage

Stage 1: 15.0220 (95% CI: 11.6387–15.4681)

Stage 2: 8.7054 (95% CI: 7.7021–11.4798)

\({T}_{2}\)

Time when the cumulative isolated population reached the maximum in Fujian Province

October 9