Model variables and parameters*
| Notation | Description | Value | Sources |
|---|---|---|---|
| Variables and their initial values | |||
| Inq2(t) | The number of stay-at-home policy–noncompliant infected individuals with symptoms at day t | 10 | Data21 |
| Sq(t) | The number of stay-at-home policy–compliant susceptible individuals at day t | (n – 1) * 3 | Calculated |
| Eq(t) | The number of stay-at-home policy–compliant exposed individuals at day t | 0 | Assumed |
| Aq(t) | The number of stay-at-home policy–compliant subclinical infected individuals at day t | 0 | Assumed |
| Iq1(t) | The number of stay-at-home policy–compliant prodromal infected individuals at day t | 0 | Assumed |
| Iq2(t) | The number of stay-at-home policy–compliant infected individuals with symptoms at day t | 3 | Data21 |
| H(t) | The number of severe infected individuals in hospitals at day t | 0 | Data21 |
| W(t) | The number of isolated individuals at day t | 0 | Assumed |
| R(t) | The number of recovered individuals at day t | 13 | Data21 |
| D(t) | The number of deaths at day t | 0 | Data21 |
| P | Total population in Toronto | 2 956 024 | Data18 |
| Snq(t) | The number of stay-at-home policy–noncompliant susceptible individuals at day t | 2 955 988 | Estimated |
| Enq(t) | The number of stay-at-home policy–noncompliant exposed individuals at day t | 20 | Estimated |
| Anq(t) | The number of stay-at-home policy–noncompliant subclinical infected individuals at day t | 1 | Estimated |
| Inq1(t) | The number of stay-at-home policy–noncompliant prodromal infected individuals at day t | 2 | Estimated |
| Parameter estimation for COVID-19 in Toronto | |||
| τ1 | Average time spent in the exposed state, Enq, Eq, d | 4 | Refs.24,25 |
| τ2 | Average time spent in prodromal infected state Inq1, Iq1, d | 3 | Ref.25 |
| a | Proportion of infected with prodromal infection | 0.9530 | Ref.2 |
| γa | Recovery rate of subclinical infected | 0.0700 | Ref.2 |
| γm | Recovery rate of infections with mild symptoms | 1/14 | Ref.26 |
| γ | Recovery rate of hospitalized infections | 0.0357 | Ref.26 |
| c0 | Contact rate before stay-at-home policy implemented, 1/day | 11.58 | Ref.27 |
| T1 | Time when the stay-at-home policy is implemented | Mar. 12 | Ref.19 |
| T2 | Time when the preopening begins | May 6 | Ref.19 |
| T3 | Time when the reopening of stage 1 begins | May 19 | Ref.19 |
| T4 | Time of reopening of stage 2 begins | June 24 | Ref.19 |
| n | Average number of household population | 2–3 | Ref.23 |
| q(t) | Stay-at-home rate of Snq, Enq, Anq and Inq1 | – | |
| dc(t) | Completion ratio of diagnosis of all symptomatic infections | – | Refs.21,22 |
| g(t) | Going out rate of Sq, Eq, Aq and Iq1 | – | |
| qnq2(t) | Quarantined rate of Inq2 | – | |
| Q(t) | The proportion of population in stay-at-home state to the total population at time t | – | |
| Estimated parameters | |||
| βnq | Probability of transmission per contact outside household | Feb. 24–May 18: 3.2984e-02 May 19–June 24: 1.9000e-02† | |
| μ | Exponential decreasing rate of contact rate due to stay-at-home policy | 7.5000e-01 | |
| βq | Infection rate of stay-at-home policy–compliant susceptible within household | 1.5030e-02 | |
| Q | Stay-at-home rate of Snq, Enq, Anq and Inq1 before stay-at-home policy implemented | 3.0001e-04 | |
| ɛ | Adjust parameter | 7.0000e-01 | |
| G | Going out rate of Sq, Eq, Aq and Iq1 during the period of stay-at-home policy implementation | 1.0000e-04 | |
| Φh | Hospitalization rate of Inq2, Iq2 | 0.0152 | |
| Φi | Isolation rate of Inq2, Iq2 | 3.9978e-02 | |
| d | Disease-induced death rate in hospitals | 3.4000e-02 | |
| Q | Maximum compliance proportion of stay-at-home policy | 6.5058e-01 | |
| 1/ΔTQ | The average transition rate of stay-at-home policy compliance | 1/9 | |
| G0 | Maximum going out proportion in the period of May 6 to May 19 | 1.5000e-01 | |
| G1 | Maximum going out proportion in the period of May 20 to June 24 | 3.0000e-01 | |
| G2 | Maximum going out proportion in the period of reopening Stage 2 starting June 24 | 3.0000e-01 (assumed) | |
| ΔTG | The average time from stay-at-home policy relaxed to individuals going out | 3 (assumed) | |