Stochastic Logistic Model

class pints.toy.stochastic.LogisticModel(initial_molecule_count=50)[source]

This model describes the growth of a population of individuals, where the birth rate per capita, initially \(b_0\), decreases to \(0\) as the population size, \(\mathcal{C}(t)\), starting from an initial population size, \(n_0\), approaches a carrying capacity, \(k\). This process follows a rate according to [1]

\[A \xrightarrow{b_0(1-\frac{\mathcal{C}(t)}{k})} 2A.\]

The model is simulated using the Gillespie stochastic simulation algorithm [2], [3].

Extends: pints.ForwardModel, pints.toy.ToyModel.

Parameters:

initial_molecule_count (float) – Sets the initial population size \(n_0\).

References

interpolate_mol_counts(time, mol_count, output_times)

Takes raw times and inputs and mol counts and outputs interpolated values at output_times

mean(parameters, times)[source]

Computes the deterministic mean of infinitely many stochastic simulations with times \(t\) and parameters (\(b\), \(k\)), which follows: \(\frac{kC(0)}{C(0) + (k - C(0)) \exp(-bt)}\).

Returns an array with the same length as times.

n_outputs()

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

n_parameters()[source]

Default value must be overwritten because the number of parameters does not correspond with the number of equations.

simulate(parameters, times)

See pints.ForwardModel.simulate().

simulate_raw(rates, max_time)

Returns raw times, mol counts when reactions occur.

suggested_parameters()[source]

See pints.toy.ToyModel.suggested_parameters().

suggested_times()[source]

See pints.toy.ToyModel.suggested_times().