Parasite infection in a cell population: role of the partitioning kernel.

We consider a cell population subject to a parasite infection. Cells divide at a constant rate and, at division, share the parasites they contain between their two daughter cells. The sharing may be asymmetric, and its law may depend on the number of parasites in the mother. Cells die at a rate which may depend on the number of parasites they carry, and are also killed when this number explodes. We study the survival of the cell population as well as the mean number of parasites in the cells, and focus on the role of the parasites partitioning kernel at division.

Stochastic Chlamydia Dynamics and Optimal Spread.

Chlamydia trachomatis is an important bacterial pathogen that has an unusual developmental switch from a dividing form (reticulate body or RB) to an infectious form (elementary body or EB). RBs replicate by binary fission within an infected host cell, but there is a delay before RBs convert into EBs for spread to a new host cell. We developed stochastic optimal control models of the Chlamydia developmental cycle to examine factors that control the number of EBs produced. These factors included the probability and timing of conversion, and the duration of the developmental cycle before the host cell lyses. Our mathematical analysis shows that the observed delay in RB-to-EB conversion is important for maximizing EB production by the end of the intracellular infection.

A stochastic transcriptional switch model for single cell imaging data.

Gene expression is made up of inherently stochastic processes within single cells and can be modeled through stochastic reaction networks (SRNs). In particular, SRNs capture the features of intrinsic variability arising from intracellular biochemical processes. We extend current models for gene expression to allow the transcriptional process within an SRN to follow a random step or switch function which may be estimated using reversible jump Markov chain Monte Carlo (MCMC). This stochastic switch model provides a generic framework to capture many different dynamic features observed in single cell gene expression. Inference for such SRNs is challenging due to the intractability of the transition densities. We derive a model-specific birth-death approximation and study its use for inference in comparison with the linear noise approximation where both approximations are considered within the unifying framework of state-space models. The methodology is applied to synthetic as well as experimental single cell imaging data measuring expression of the human prolactin gene in pituitary cells.

Probabilistic predictions of SIS epidemics on networks based on population-level observations.

We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erdos-Rényi and Barabási-Albert networks. It is known that the contact network influences the spread of an epidemic within a population. Therefore, observations of an epidemic, in this case at the population-level, contain information about the underlying network. This information, in turn, is useful for predicting the future course of an ongoing epidemic. To exploit this in a prediction framework, the exact high-dimensional stochastic model of an SIS epidemic on a network is approximated by a lower-dimensional surrogate model. The surrogate model is based on a birth-and-death process; the effect of the underlying network is described by a parametric model for the birth rates. We demonstrate empirically that the surrogate model captures the intrinsic stochasticity of the epidemic once it reaches a point from which it will not die out. Bayesian parameter inference allows for uncertainty about the model parameters and the class of the underlying network to be incorporated directly into probabilistic predictions. An evaluation of a number of scenarios shows that in most cases the resulting prediction intervals adequately quantify the prediction uncertainty. As long as the population-level data is available over a long-enough period, even if not sampled frequently, the model leads to excellent predictions where the underlying network is correctly identified and prediction uncertainty mainly reflects the intrinsic stochasticity of the spreading epidemic. For predictions inferred from shorter observational periods, uncertainty about parameters and network class dominate prediction uncertainty. The proposed method relies on minimal data at population-level, which is always likely to be available. This, combined with its numerical efficiency, makes the proposed method attractive to be used either as a standalone inference and prediction scheme or in conjunction with other inference and/or predictive models.

Population persistence under two conservation measures: Paradox of habitat protection in a patchy environment.

Anthropogenic modification of natural habitats is a growing threat to biodiversity and ecosystem services. The protection of biospecies has become increasingly important. Here, we pay attention to a single species as a conservation target. The species has three processes: reproduction, death and movement. Two different measures of habitat protection are introduced. One is partial protection in a single habitat (patch); the mortality rate of the species is reduced inside a rectangular area. The other is patch protection in a two-patch system, where only the mortality rate in a particular patch is reduced. For the one-patch system, we carry out computer simulations of a stochastic cellular automaton for a "contact process". Individual movements follow random walking. For the two-patch system, we assume an individual migrates into the empty cell in the destination patch. The reaction-diffusion equation (RDE) is derived, whereby the recently developed "swapping migration" is used. It is found that both measures are mostly effective for population persistence. However, comparing the results of the two measures revealed different behaviors. ⅰ) In the case of the one-patch system, the steady-state densities in protected areas are always higher than those in wild areas. However, in the two-patch system, we have found a paradox: the densities in protected areas can be lower than those in wild areas. ⅱ) In the two-patch system, we have found another paradox: the total density in both patches can be lower, even though the proportion of the protected area is larger. Both paradoxes clearly occur for the RDE with swapping migration.