Table 1 Parameter estimates for COVID-19 in Ontario, Canada
Parameter | Definitions | Feb 26 to Mar 21 | Feb 26 to Mar 25 | Feb 26 to Mar 29 | Feb 26 to Apr 13 | Source | |
|---|---|---|---|---|---|---|---|
c | Contact rate | 11.7905 | 11.5539 | 9.1586 | – | Estimated | |
c(t) | \(c_{0}\) | Constant contact rate before \(T_{s}\) | – | – | – | 10.0005 | Estimated |
\(r_{1}\) | Exponential decreasing rate of contact rate | – | – | – | 0.0632 | Estimated | |
\(c_{b}\) | Minimum contact rate after \(T_{s}\) | – | – | – | 3.4999 | Estimated | |
β | Probability of transmission per contact | 0.1450 | 0.1450 | 0.1452 | 0.1438 | Estimated | |
q | Quarantined rate of exposed individuals | 0.0810 | 0.1479 | 0.1754 | 0.1003 | Estimated | |
σ | Transition rate of exposed individuals to the infected class | 1/5 | 1/5 | 1/5 | 1/5 | [10] | |
λ | Rate at which the quarantined uninfected contacts were released into the wider community | 1/14 | 1/14 | 1/14 | 1/14 | [7] | |
ρ | Probability of having symptoms among infected individuals | 0.6 | 0.6 | 0.7847 | 0.6201 | Estimated | |
\(\delta _{I}\) | Transition rate of symptomatic infected individuals to the quarantined infected class | 0.1 | 0.1 | 0.1 | – | Estimated | |
\(\delta _{I}(t)\) | \(\delta _{I0}\) | Constant transition rate of symptomatic infected individuals to the quarantined infected class before \(T_{s}\) | – | – | – | 1/9.2 | Data |
\(r_{2}\) | Exponential increasing rate of the detection rate | – | – | – | 0.7174 | Estimated | |
\(\delta _{If}\) | Fastest transition rate of symptomatic infected individuals to the quarantined infected class after \(T_{s}\) | – | – | – | 0.5642 | Estimated | |
\(\delta _{q}\) | Transition rate of quarantined exposed individuals to the quarantined infected class | 0.1 | 0.1 | 0.1 | 0.1 | Estimated | |
\(\gamma _{I}\) | Recovery rate of symptomatic infected individuals | 0.2 | 0.2 | 0.1999 | 0.1830 | Estimated | |
\(\gamma _{A}\) | Recovery rate of asymptomatic infected individuals | 0.139 | 0.139 | 0.139 | 0.139 | [7] | |
\(\gamma _{H}\) | Recovery rate of quarantined diagnosed individuals | 0.2 | 0.2 | 0.2 | 0.2 | [6] | |
α | Disease-induced death rate | 0.008 | 0.008 | 0.008 | 0.008 | [6] | |
θ | Modification factor of asymptomatic infectiousness | 0.0429 | 0.0465 | 0.0308 | 0.0494 | Estimated | |
\(R_{c}\) | Control reproduction number | 3.2546 | 2.9720 | 2.8464 | – | Estimated | |
Initial values | Definitions | Feb 26 to Mar 21 | Feb 26 to Mar 25 | Feb 26 to Mar 29 | Feb 26 to Apr 13 | Source |
|---|---|---|---|---|---|---|
S(0) | Initial susceptible population | 1.999 × 106 | 1.999 × 106 | 1.999 × 106 | 1.993 × 106 | Estimated |
E(0) | Initial exposed population | 10 | 12 | 10 | 10 | Estimated |
I(0) | Initial symptomatic infected population | 7.6 | 7 | 8.5 | 10 | Estimated |
A(0) | Initial asymptomatic infected population | 15 | 24 | 23 | 24 | Estimated |
\(S_{q}(0)\) | Initial quarantined susceptible population | 0 | 0 | 0 | 0 | Data |
\(E_{q}(0)\) | Initial quarantined exposed population | 0 | 0 | 0 | 0 | Data |
D(0) | Initial quarantined diagnosed population | 5 | 5 | 5 | 5 | Data |
R(0) | Initial recovered population | 0 | 0 | 0 | 0 | Data |