Modelling within-host spatiotemporal dynamics of invasive bacterial disease

Mechanistic determinants of bacterial growth, death, and spread within mammalian hosts cannot be fully resolved studying a single bacterial population. They are also currently poorly understood. Here, we report on the application of sophisticated experimental approaches to map spatiotemporal population dynamics of bacteria during an infection. We analyzed heterogeneous traits of simultaneous infections with tagged Salmonella enterica populations (wild-type isogenic tagged strains [WITS]) in wild-type and gene-targeted mice. WITS are phenotypically identical but can be distinguished and enumerated by quantitative PCR, making it possible, using probabilistic models, to estimate bacterial death rate based on the disappearance of strains through time. This multidisciplinary approach allowed us to establish the timing, relative occurrence, and immune control of key infection parameters in a true host-pathogen combination. Our analyses support a model in which shortly after infection, concomitant death and rapid bacterial replication lead to the establishment of independent bacterial subpopulations in different organs, a process controlled by host antimicrobial mechanisms. Later, decreased microbial mortality leads to an exponential increase in the number of bacteria that spread locally, with subsequent mixing of bacteria between organs via bacteraemia and further stochastic selection. This approach provides us with an unprecedented outlook on the pathogenesis of S. enterica infections, illustrating the complex spatial and stochastic effects that drive an infectious disease. The application of the novel method that we present in appropriate and diverse host-pathogen combinations, together with modelling of the data that result, will facilitate a comprehensive view of the spatial and stochastic nature of within-host dynamics. © 2008 Grant et al.

Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, ReW ≤ 2.5 × 103. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's νt-92; Secundov et al.'s two equation νt-L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with ReW ≈ 2.5 × 103 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov νt-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from ReW = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for ReW ≪ 250 are virtually identical to those for ReW = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model's erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k-l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%. © 2007 Elsevier Inc. All rights reserved.

Campylobacter jejuni colonization and transmission in broiler chickens: a modelling perspective.

Campylobacter jejuni is one of the most common causes of acute enteritis in the developed world. The consumption of contaminated poultry, where C. jejuni is believed to be a commensal organism, is a major risk factor. However, the dynamics of this colonization process in commercially reared chickens is still poorly understood. Quantification of these dynamics of infection at an individual level is vital to understand transmission within populations and formulate new control strategies. There are multiple potential routes of introduction of C. jejuni into a commercial flock. Introduction is followed by a rapid increase in environmental levels of C. jejuni and the level of colonization of individual broilers. Recent experimental and epidemiological evidence suggest that the celerity of this process could be masking a complex pattern of colonization and extinction of bacterial strains within individual hosts. Despite the rapidity of colonization, experimental transmission studies exhibit a highly variable and unexplained delay time in the initial stages of the process. We review past models of transmission of C. jejuni in broilers and consider simple modifications, motivated by the plausible biological mechanisms of clearance and latency, which could account for this delay. We show how simple mathematical models can be used to guide the focus of experimental studies by providing testable predictions based on our hypotheses. We conclude by suggesting that competition experiments could be used to further understand the dynamics and mechanisms underlying the colonization process. The population models for such competition processes have been extensively studied in other ecological and evolutionary contexts. However, C. jejuni can potentially adapt phenotypically through phase variation in gene expression, leading to unification of ecological and evolutionary time-scales. For a theoretician, the colonization dynamics of C. jejuni offer an experimental system to explore these 'phylodynamics', the synthesis of population dynamics and evolutionary biology.

Modelling nonlinear vehicle dynamics with neural networks

The nonlinear modelling ability of neural networks has been widely recognised as an effective tool to identify and control dynamic systems, with applications including nonlinear vehicle dynamics which this paper focuses on using multi-layer perceptron networks. Existing neural network literature does not detail some of the factors which effect neural network nonlinear modelling ability. This paper investigates into and concludes on required network size, structure and initial weights, considering results for networks of converged weights. The paper also presents an online training method and an error measure representing the network's parallel modelling ability over a range of operating conditions. Copyright © 2010 Inderscience Enterprises Ltd.