Mathematical Modelling of Parasite Dynamics: A Stochastic Simulation-Based Approach and Parameter Estimation via Modified Sequential-Type Approximate Bayesian Computation.

The development of mathematical models for studying newly emerging and re-emerging infectious diseases has gained momentum due to global events. The gyrodactylid-fish system, like many host-parasite systems, serves as a valuable resource for ecological, evolutionary, and epidemiological investigations owing to its ease of experimental manipulation and long-term monitoring. Although this system has an existing individual-based model, it falls short in capturing information about species-specific microhabitat preferences and other biological details for different Gyrodactylus strains across diverse fish populations. This current study introduces a new individual-based stochastic simulation model that uses a hybrid τ -leaping algorithm to incorporate this essential data, enhancing our understanding of the complexity of the gyrodactylid-fish system. We compare the infection dynamics of three gyrodactylid strains across three host populations. A modified sequential-type approximate Bayesian computation (ABC) method, based on sequential Monte Carlo and sequential importance sampling, is developed. Additionally, we establish two penalised local-linear regression methods (based on L1 and L2 regularisations) for ABC post-processing analysis to fit our model using existing empirical data. With the support of experimental data and the fitted mathematical model, we address open biological questions for the first time and propose directions for future studies on the gyrodactylid-fish system. The adaptability of the mathematical model extends beyond the gyrodactylid-fish system to other host-parasite systems. Furthermore, the modified ABC methodologies provide efficient calibration for other multi-parameter models characterised by a large set of correlated or independent summary statistics.

A web-based tool for designing experimental studies to detect hormesis and estimate the threshold dose.

Hormesis has been widely observed and debated in a variety of context in biomedicine and toxicological sciences. Detecting its presence can be an important problem with wide ranging implications. However, there is little work on constructing an efficient experiment to detect its existence or estimate the threshold dose. We use optimal design theory to develop a variety of locally optimal designs to detect hormesis, estimate the threshold dose and the zero-equivalent point (ZEP) for commonly used models in toxicology and risk assessment. To facilitate use of more efficient designs to detect hormesis, estimate threshold dose and estimate the ZEP in practice, we implement computer algorithms and create a user-friendly web site to help the biomedical researcher generate different types of optimal designs. The online tool facilitates the user to evaluate robustness properties of a selected design to various model assumptions and compare designs before implementation.

Optimal designs in regression with correlated errors.

This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. We then demonstrate that we can design the experiments, such that asymptotically the new estimators achieve the same precision as the best linear unbiased estimator computed for the whole trajectory of the process. As a by-product we derive explicit expressions for the BLUE in the continuous time model and analytic expressions for the optimal designs in a wide class of regression models. We also demonstrate that for a finite number of observations the precision of the proposed procedure, which includes the estimator and design, is very close to the best achievable. The results are illustrated on a few numerical examples.

Optimal designs for composed models in pharmacokinetic-pharmacodynamic experiments.

We consider two frequently used PK/PD models and provide closed form descriptions of locally optimal designs for estimating individual parameters. In a novel way, we use these optimal designs and construct locally standardized maximin optimal designs for estimating any subset of the model parameters of interest. We do this by maximizing the minimal efficiency of the estimates across all relevant parameters so that these optimal designs are less dependent on the individual parameter or parameters of interest. Additionally, robust designs are proposed to further reduce the dependence on the nominal values of the parameters. We compare efficiencies of our proposed optimal designs with locally optimal designs and designs used in four real studies from the literature and show that our proposed designs provide advantages over those used in practice.

A geometric characterization of optimal designs for regression models with correlated observations.

We consider the problem of optimal design of experiments for random effects models, especially population models, where a small number of correlated observations can be taken on each individual, while the observations corresponding to different individuals are assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving (1952) from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated by finding optimal designs for a linear model with correlated observations and a nonlinear random effects population model, which is commonly used in pharmacokinetics.

Optimal experimental design strategies for detecting hormesis.

Hormesis is a widely observed phenomenon in many branches of life sciences, ranging from toxicology studies to agronomy, with obvious public health and risk assessment implications. We address optimal experimental design strategies for determining the presence of hormesis in a controlled environment using the recently proposed Hunt-Bowman model. We propose alternative models that have an implicit hormetic threshold, discuss their advantages over current models, and construct and study properties of optimal designs for (i) estimating model parameters, (ii) estimating the threshold dose, and (iii) testing for the presence of hormesis. We also determine maximin optimal designs that maximize the minimum of the design efficiencies when we have multiple design criteria or there is model uncertainty where we have a few plausible models of interest. We apply these optimal design strategies to a teratology study and show that the proposed designs outperform the implemented design by a wide margin for many situations.

Robust and efficient design of experiments for the Monod model.

In this paper the problem of designing experiments for the Monod model, which is frequently used in microbiology, is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are local optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular, standardized maximin D- and E-optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor of two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.