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)¶
- simulate_raw(rates, max_time)¶
Returns raw times, mol counts when reactions occur.