Inverse Gillespie for inferring stochastic reaction mechanisms from intermittent samples

Transition from growth to decay of an epidemic due to lockdown

We study the transition of an epidemic from growth phase to decay of the active infections in a population when lockdown health measures are introduced to reduce the probability of disease transmission. Although in the case of uniform lockdown, a simple compartmental model would indicate instantaneous transition to decay of the epidemic, this is not the case when partially isolated active clusters remain with the potential to create a series of small outbreaks. We model this using the Gillespie stochastic simulation algorithm based on a connected set of stochastic susceptible-infected-removed/recovered networks representing the locked-down majority population (in which the reproduction number is less than 1) weakly coupled to a large set of small clusters in which the infection may propagate. We find that the presence of such active clusters can lead to slower than expected decay of the epidemic and significantly delayed onset of the decay phase. We study the relative contributions of these changes, caused by the active clusters within the population, to the additional total infected population. We also demonstrate that limiting the size of the inevitable active clusters can be efficient in reducing their impact on the overall size of the epidemic outbreak. The deceleration of the decay phase becomes apparent when the active clusters form at least 5% of the population.

S-Leaping: An Adaptive, Accelerated Stochastic Simulation Algorithm, Bridging [Formula: see text]-Leaping and R-Leaping

We propose the S-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the [Formula: see text]-leaping and R-leaping algorithms. These algorithms are known to be efficient under different conditions; the [Formula: see text]-leaping is efficient for non-stiff systems or systems with partial equilibrium, while the R-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system's set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the [Formula: see text]-leaping with the effective sampling procedure from the R-leaping algorithm. The S-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the S-leaping outperforms both methods. We demonstrate the performance and the accuracy of the S-leaping in comparison with the [Formula: see text]-leaping and R-leaping on a number of benchmark systems involving biological reaction networks.

Deterministic inference for stochastic systems using multiple shooting and a linear noise approximation for the transition probabilities

Estimating model parameters from experimental data is a crucial technique for working with computational models in systems biology. Since stochastic models are increasingly important, parameter estimation methods for stochastic modelling are also of increasing interest. This study presents an extension to the ‘multiple shooting for stochastic systems (MSS)’ method for parameter estimation. The transition probabilities of the likelihood function are approximated with normal distributions. Means and variances are calculated with a linear noise approximation on the interval between succeeding measurements. The fact that the system is only approximated on intervals which are short in comparison with the total observation horizon allows to deal with effects of the intrinsic stochasticity. The study presents scenarios in which the extension is essential for successfully estimating the parameters and scenarios in which the extension is of modest benefit. Furthermore, it compares the estimation results with reversible jump techniques showing that the approximation does not lead to a loss of accuracy. Since the method is not based on stochastic simulations or approximative sampling of distributions, its computational speed is comparable with conventional least‐squares parameter estimation methods.

Reconstructing the hidden states in time course data of stochastic models

Parameter estimation is central for analyzing models in Systems Biology. The relevance of stochastic modeling in the field is increasing. Therefore, the need for tailored parameter estimation techniques is increasing as well. Challenges for parameter estimation are partial observability, measurement noise, and the computational complexity arising from the dimension of the parameter space. This article extends the multiple shooting for stochastic systems' method, developed for inference in intrinsic stochastic systems. The treatment of extrinsic noise and the estimation of the unobserved states is improved, by taking into account the correlation between unobserved and observed species. This article demonstrates the power of the method on different scenarios of a Lotka-Volterra model, including cases in which the prey population dies out or explodes, and a Calcium oscillation system. Besides showing how the new extension improves the accuracy of the parameter estimates, this article analyzes the accuracy of the state estimates. In contrast to previous approaches, the new approach is well able to estimate states and parameters for all the scenarios. As it does not need stochastic simulations, it is of the same order of speed as conventional least squares parameter estimation methods with respect to computational time.