Table 1 Model variables and parameters
Notation | Description | Value at \({t}_{0}\) | Sources |
|---|---|---|---|
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 | |