Table 1. Model Parameters: Values and Rationale.
| Parameter | Estimate | Comments | Reference |
|---|---|---|---|
| Fixeda | |||
| N | 4 428 247 | Population: population of Alberta (2020) | Vital statistics13 |
| Λ | 137 d−1 | Birth rate: 52 334 births in Alberta (2018); approximated as μ × N as a simplifying assumption of constant population size | Vital statistics13 |
| μ | 0.0000319 d−1 | Natural mortality rate (population): 25 990 deaths in Alberta (2018) | Vital statistics13 |
| Fittedb | |||
| b 0 | 0.121 d−1 | Average of transmission parameter, β(t): related to basic reproduction number | Weber et al2 |
| b 1 | 0.249 | Amplitude of seasonal variation in transmission parameter, β(t): higher values at northern latitudes (eg, 0.36 Finland vs 0.10 Florida) | Weber et al2 |
| δ | 0.0986 d−1 | Rate of loss of infectiousness: related to the mean duration of infection: approximately 10 d | Weber et al2 |
| γ | 0.00469 d−1 | Rate of loss of immunity: related to the mean duration of immunity: approximately 200 d | Weber et al2 |
| s | 1/2000 | Scaling factor: optimal value chosen to match model endemic equilibrium to mean weekly number of cases | Weber et al2 |
| ϕ | 0 | Phase shift: optimal value chosen to match timing of seasonal peaks | Weber et al2 |
a
Parameters are based on vital statistics and were held constant during model fitting.
b
Initial estimates (shown in table) were optimized for each virus, using ordinary least squares regression to fit model to epidemiological data.