Table 1.
Variable and parameter definitions
| definition | value | comment | |
|---|---|---|---|
| S | susceptibles, people who can catch the virus | 0.9998N | initial condition |
| E | exposed, people who have caught the disease but are not yet infectious | 0 | initial condition |
| P | pre-symptomatic, people who are infectious but have not had the disease long enough to show symptoms | 0 | initial condition |
| IS | infected-symptomatic, people who are infectious and have started showing symptoms | 2.00 × 10−4N | initial condition |
| IA | infected-asymptomatic, people who are infectious but never show symptoms | 0 | initial condition |
| RS | removed-symptomatic, people who were symptomatic and infectious, but are no longer infectious | 0 | initial condition |
| RA | removed-asymptomatic, people who were asymptomatic and infectious, but are no longer infectious | 0 | initial condition |
| N | population of Ontario | 13 448 494 | 2016 census |
| Ncrit | critical population at which healthcare resources are overwhelmed | 81 301 | chosen |
| R0 | basic reproduction number | 2.40 | [16,17] |
| β | transmission rate of disease after coming in contact with the infected class | 0.223 d−1 | see (2.10) |
| δ | reduction in transmission due to social distancing in class 1 | 0.250 | chosen |
| α | reduction in transmission due to being asymptomatic | 0.500 | chosen |
| σ | rate at which exposed class enter pre-symptomatic class | 2.00 d−1 | [16] |
| ϕ | rate at which pre-symptomatic class can begin showing symptoms | 4.60−1 d−1 | [16,18,19] |
| Q | proportion of infected individuals who show symptoms | 0.690 | median value |
| γ | rate at which an infected person is no longer infectious | 10.0−1 d−1 | [20] |
| μmax | maximal rate at which someone moves from a less socially distant class to a more socially distant class | 1.00 d−1 | chosen |
| νmax | maximal rate at which someone moves from a more socially distant class to a less socially distant class | 1.00 d−1 | chosen |
| μI | rate at which people showing symptoms choose to isolate | 0.010 d−1 | chosen |
| q0 | proportion of S0 socially distancing into S1 | 0.9 | chosen |
| q2 | proportion of S2 relaxing social distancing into S1 | 0.6 | chosen |
| qI | proprotion of symptomatic individuals IS0 who isolate into IS1 | 0.6 | chosen |
| ρA | testing rate for someone not showing symptoms to test positive | 8.70 × 10−3 d−1 | see appendix B |
| ρS | testing rate for someone showing symptoms to test positive | 3.48 × 10−2 d−1 | see appendix B |
| Mc | critical active cases to induce social distancing | 2.09 × 103/Ncrit | see appendix B |
| M0 | active cases that lead to half the maximal rate of social distancing | 4.18 × 103/Ncrit | see appendix B |
| kc | critical approximate disease doubling rate to induce social distancing | 16.2−1 d−1 | see appendix B |
| k0 | approximate disease doubling rate that leads to half the maximal rate of social distancing | 4.06−1 d−1 | see appendix B |
| Cc | critical cost to induce social relaxation | 50 d | chosen |
| C0 | cost that leads to half the maximal rate of social relaxation | 100 d | chosen |