Stochastic Logistic Model¶
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class
pints.toy.StochasticLogisticModel(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
[1] Simpson, M. et al. 2019. Process noise distinguishes between indistinguishable population dynamics. bioRxiv. https://doi.org/10.1101/533182 [2] Gillespie, D. 1976. A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. Journal of Computational Physics. 22 (4): 403-434. https://doi.org/10.1016/0021-9991(76)90041-3 [3] Erban R. et al. 2007. A practical guide to stochastic simulations of reaction-diffusion processes. arXiv. https://arxiv.org/abs/0704.1908v2 -
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.
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n_outputs()¶ Returns the number of outputs this model has. The default is 1.
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