Optimal design for dynamical modeling of pest populations

We apply SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets. To illustrate ideas we use a simple phenomenological citrus red mite population model for pest dynamics. First the optimal sampling distributions for a varying number of data points are determined. We then analyze these optimal distributions by comparing the standard errors of parameter estimates corresponding to each distribution. This allows us to investigate how many data are required to have confidence in model parameter estimates in order to employ dynamical modeling to infer population dynamics. Our results suggest that a field researcher should collect at least 12 data points at the optimal times. Data collected according to this procedure along with dynamical modeling will allow us to estimate population dynamics from presence/absence-based data sets through the development of a scaling relationship. These Likert-type data sets are commonly collected by agricultural pest management consultants and are increasingly being used in ecoinformatics studies. By applying mathematical modeling with the relationship scale from the new data, we can then explore important integrated pest management questions using past and future presence/absence data sets.

Improving the generation and selection of virtual populations in quantitative systems pharmacology models

Quantitative systems pharmacology (QSP) models aim to describe mechanistically the pathophysiology of disease and predict the effects of therapies on that disease. For most drug development applications, it is important to predict not only the mean response to an intervention but also the distribution of responses, due to inter-patient variability. Given the necessary complexity of QSP models, and the sparsity of relevant human data, the parameters of QSP models are often not well determined. One approach to overcome these limitations is to develop alternative virtual patients (VPs) and virtual populations (Vpops), which allow for the exploration of parametric uncertainty and reproduce inter-patient variability in response to perturbation. Here we evaluated approaches to improve the efficiency of generating Vpops. We aimed to generate Vpops without sacrificing diversity of the VPs' pathophysiologies and phenotypes. To do this, we built upon a previously published approach (Allen et al., 2016) by (a) incorporating alternative optimization algorithms (genetic algorithm and Metropolis-Hastings) or alternatively (b) augmenting the optimized objective function. Each method improved the baseline algorithm by requiring significantly fewer plausible patients (precursors to VPs) to create a reasonable Vpop.

Dynamical Systems Modeling to Identify a Cohort of Problem Drinkers with Similar Mechanisms of Behavior Change

One challenge to understanding mechanisms of behavior change (MOBC) completely among individuals with alcohol use disorder is that processes of change are theorized to be complex, dynamic (time varying), and at times non-linear, and they interact with each other to influence alcohol consumption. We used dynamical systems modeling to better understand MOBC within a cohort of problem drinkers undergoing treatment. We fit a mathematical model to ecological momentary assessment data from individual patients who successfully reduced their drinking by the end of the treatment. The model solutions agreed with the trend of the data reasonably well, suggesting the cohort patients have similar MOBC. This work demonstrates using a personalized approach to psychological research, which complements standard statistical approaches that are often applied at the population level.

Dynamic Modeling of Problem Drinkers Undergoing Behavioral Treatment

We use dynamical systems modeling to help understand how selected intra-personal factors interact to form mechanisms of behavior change in problem drinkers. Our modeling effort illustrates the iterative process of modeling using an individual's clinical data. Due to the lack of previous work in modeling behavior change in individual patients, we build our preliminary model relying on our understandings of the psychological relationships among the variables. This model is refined and the psychological understanding is then enhanced through the iterative modeling process. Our results suggest that this is a promising direction in research in alcohol use disorders as well as other behavioral sciences.

An adaptive feedback methodology for determining information content in stable population studies

We develop statistical and mathematical based methodologies for determining (as the experiment progresses) the amount of information required to complete the estimation of stable population parameters with pre-specified levels of confidence. We do this in the context of life table models and data for growth/death for three species of Daphniids as investigated by J. Stark and J. Banks [17]. The ideas developed here also have wide application in the health and social sciences where experimental data are often expensive as well as difficult to obtain.

Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

Androgen deprivation therapy is a common treatment for advanced or metastatic prostate cancer. Like the normal prostate, most tumors depend on androgens for proliferation and survival but often develop treatment resistance. Hormonal treatment causes many undesirable side effects which significantly decrease the quality of life for patients. Intermittently applying androgen deprivation in cycles reduces the total duration with these negative effects and may reduce selective pressure for resistance. We extend an existing model which used measurements of patient testosterone levels to accurately fit measured serum prostate specific antigen (PSA) levels. We test the model's predictive accuracy, using only a subset of the data to find parameter values. The results are compared with those of an existing piecewise linear model which does not use testosterone as an input. Since actual treatment protocol is to re-apply therapy when PSA levels recover beyond some threshold value, we develop a second method for predicting the PSA levels. Based on a small set of data from seven patients, our results showed that the piecewise linear model produced slightly more accurate results while the two predictive methods are comparable. This suggests that a simpler model may be more beneficial for a predictive use compared to a more biologically insightful model, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting. Nevertheless, both models are an important step in this direction.

Data and implication based comparison of two chronic myeloid leukemia models

Chronic myeloid leukemia, a disorder of hematopoietic stem cells, is currently treated using targeted molecular therapy with imatinib. We compare two models that describe the treatment of CML, a multi-scale model (Model 1) and a simple cell competition model (Model 2). Both models describe the competition of leukemic and normal cells, however Model 1 also describes the dynamics of BCR-ABL, the oncogene targeted by imatinib, at the sub-cellular level. Using clinical data, we analyze the differences in estimated parameters between the models and the capacity for each model to predict drug resistance. We found that while both models fit the data well, Model 1 is more biologically relevant. The estimated parameter ranges for Model 2 are unrealistic, whereas the parameter ranges for Model 1 are close to values found in literature. We also found that Model 1 predicts long-term drug resistance from patient data, which is exhibited by both an increase in the proportion of leukemic cells as well as an increase in BCR-ABL/ABL Model 2, however, is not able to predict resistance and accurately model the clinical data. These results suggest that including sub-cellular mechanisms in a mathematical model of CML can increase the accuracy of parameter estimation and may help to predict long-term drug resistance.