Logistic model¶
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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.
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