Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts

Chowell, Gerardo

where C 0 ðtÞ describes the incidence growth phase over time t, the solution CðtÞ describes the cumulative number of cases at time t, r is a positive parameter denoting the growth rate, and p, the "deceleration of growth" parameter varied between 0 and 1. If p ¼ 0, this equation describes constant incidence over time and the cumulative number of cases grows linearly while p ¼ 1 leads to the well-known exponential growth model (EXPM) . Intermediate values of p between 0 and 1 describe subexponential (e.g. polynomial) growth patterns. In semi-logarithmic scale, exponential growth patterns are visually evident when a straight line fits well several consecutive generations in the growth pattern, whereas a downward curvature in semilogarithmic scale indicates early sub-exponential growth dynamics.