Generalized logistic growth model (GLM)

The generalized logistic growth model (GLM) is an extension of the simple logistic growth model that captures a range of epidemic growth profiles, including sub-exponential (polynomial) and exponential growth dynamics. GLM characterizes epidemic growth by estimating (i) the intrinsic growth rate, r (ii) a dimensionless “deceleration of growth” parameter, p and (iii) the final epidemic size, k₀. The final epidemic size is sensitive to small variations in the deceleration of growth parameters [56] and would vary as the epidemic progresses. The deceleration parameter modulates the epidemic growth patterns, including the sub-exponential growth (0< p <1), constant incidence (p = 0) and exponential growth dynamics (p = 1). The GLM model is given by the following differential equation:

Where dC(t)dt describes the incidence over time t and the cumulative number of cases at time t is given by C (t) [45]. This simple logistic growth type model typically supports single peak epidemics in the number of new infections followed by a burnt-out period, unless external driving forces such as the seasonal variations in contact patterns exist. This model can underestimate the peak timing and the duration of outbreaks. This model can also underestimate the case incidence before the inflection point has occurred [45,47,53,57].