Logistic Transition Function for new variant prevalence.

Used in the COVID-19 Delta/Alpha variants example but can be used to model any generic new variant that becomes prevalent over the old one over time.

Usage

delta(x, scale, start)

Arguments

x

Numeric vector representing time.

scale

Scaling factor controlling the rate of transition.

start

The time point at which the new variant appears.

Value

A numeric vector representing the transition effect for new variant prevalence, ranging between 0 and 1.

Details

The function applies a hyperbolic tangent transformation to model a new more transmissible pathogen variant (e.g. for COVID-19 delta becoming more prevalent than alpha). The output is shifted and scaled to range between 0 and 1.

Examples

x <- seq(0, 100, by = 1)
scale <- 10
start <- 50
delta_effect <- delta(x, scale, start)
plot(x, delta_effect, type = "l", main = "Logistic Transition Over Time")