Antiderivative of the Verhulst logistic function

Give the antiderivative of the logistic function from the Verhulst model.

antideriv_verhulst(x, initial_density, max_density, growth_rate)

Arguments

x

timestep up to which antiderivative must be computed

initial_density

initial density

max_density

maximal density

growth_rate

growth rate

Value

An object of the same type as x containing the antiderivative of the input values.

Details

The Verhulst model (used to simulate host growth) is defined by \( f(x) = max\_{density} / (1 + (max\_{density}/initial\_{density})*exp(-growth\_{rate}*x)) \). See https://en.wikipedia.org/wiki/Logistic_function for details.

Examples

antideriv_verhulst(119, 0.1, 2, 0.1) / 120
#> [1] 1.484066