Logistic model

class pints.toy.LogisticModel(initial_population_size=2)[source]

Logistic model of population growth [1].

\[\begin{split}f(t) &= \frac{k}{1+(k/p_0 - 1) \exp(-r t)} \\ \frac{\partial f(t)}{\partial r} &= \frac{k t (k / p_0 - 1) \exp(-r t)} {((k/p_0-1) \exp(-r t) + 1)^2} \\ \frac{\partial f(t)}{ \partial k} &= -\frac{k \exp(-r t)} {p_0 ((k/p_0-1)\exp(-r t) + 1)^2} + \frac{1}{(k/p_0 - 1)\exp(-r t) + 1}\end{split}\]

Has two model parameters: A growth rate \(r\) and a carrying capacity \(k\). The initial population size \(p_0 = f(0)\) is a fixed (known) parameter in the model.

Extends pints.ForwardModel, pints.toy.ToyModel.

Parameters:initial_population_size (float) – Sets the initial population size \(p_0\).

References

[1]https://en.wikipedia.org/wiki/Population_growth
n_outputs()

Returns the number of outputs this model has. The default is 1.

n_parameters()[source]

See pints.ForwardModel.n_parameters().

simulate(parameters, times)[source]

See pints.ForwardModel.simulate().

simulateS1(parameters, times)[source]

See pints.ForwardModelS1.simulateS1().

suggested_parameters()[source]

See pints.toy.ToyModel.suggested_parameters().

suggested_times()[source]

See pints.toy.ToyModel.suggested_times().