Modeling Ertapenem: the impact of body mass index on distribution of the antibiotic in the body.

Ertapenem is an antibiotic commonly used to treat a broad spectrum of infections and is part of a broader class of antibiotics called carbapenems. Unlike other carbapenems, ertapenem has a longer half-life and thus only has to be administered once a day. Previously, a physiologically-based pharmacokinetic (PBPK) model was developed to investigate the uptake, distribution, and elimination of ertapenem following a single one gram dose in normal height, normal weight males. Due to the absorption properties of ertapenem, the amount of fat in the body can influence how the drug binds, how quickly the drug passes through the body, and thus how effective the drug might be. Thus, we have revised the model so that it is applicable to males and females of differing body mass index (BMI). Simulations were performed to consider the distribution of the antibiotic in males and females with varying body mass indexes. These results could help to determine if there is a need for altered dosing regimens in the future.

Correctly modeling plant-insect-herbivore-pesticide interactions as aggregate data.

We consider a population dynamics model in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). The experimental data is clearly aggregate in nature. In previous efforts [1], the aggregate nature of the data was ignored. In this paper, we embrace this aspect of the experiment and correctly model the data as aggregate data, comparing the results to the previous approach. We discuss cases in which the approach may provide similar results as well as cases in which there is a clear difference in the resulting fit to the data.

Spatio-temporal analysis of foraging behaviors of Anelosimus studiosus utilizing mathematical modeling of multiple spider interaction on a cooperative web.

In this paper, we develop a model for predation movements of a subsocial spider species, Anelosimus studiosus. We expand on a previous model to include multiple spider interaction on the web as well as a latency period during predation. We then use the model to test different spatial configurations to determine the optimal spacing of spiders within a colony for successful capture during predation. The model simulations indicate that spiders uniformly spacing out along the edge of the web results in the most successful predation strategy. This is similar to the behavior observed by Ross (2013) in which it was determined to be statistically significant that during certain times of the day, spiders were positioned along the edge more than expected under complete spatial randomness.

A physiologically-based pharmacokinetic model for the antibiotic ertapenem.

Ertapenem is an antibiotic commonly used to treat a broad spectrum of infections, which is part of a broader class of antibiotics called carbapenem. Unlike other carbapenems, ertapenem has a longer half-life and thus only has to be administered once a day. A physiologically-based pharmacokinetic (PBPK) model was developed to investigate the uptake, distribution, and elimination of ertapenem following a single one gram dose. PBPK modeling incorporates known physiological parameters such as body weight, organ volumes, and blood flow rates in particular tissues. Furthermore, ertapenem is highly bound in human blood plasma; therefore, nonlinear binding is incorporated in the model since only the free portion of the drug can saturate tissues and, hence, is the only portion of the drug considered to be medicinally effective. Parameters in the model were estimated using a least squares inverse problem formulation with published data for blood concentrations of ertapenem for normal height, normal weight males. Finally, an uncertainty analysis of the parameter estimation and model predictions is presented.

A stochastic simulation model for Anelosimus studiosus during prey capture: a case study for determination of optimal spacing.

In this paper, we develop a stochastic differential equation model to simulate the movement of a social/subsocial spider species, Anelosimus studiosus, during prey capture using experimental data collected in a structured environment. In a subsocial species, females and their maturing offspring share a web and cooperate in web maintenance and prey capture. Furthermore, observations indicate these colonies change their positioning throughout the day, clustered during certain times of the day while spaced out at other times. One key question was whether or not the spiders spaced out ``optimally'' to cooperate in prey capture. In this paper, we first show the derivation of the model where experimental data is used to determine key parameters within the model. We then use this model to test the success of prey capture under a variety of different spatial configurations for varying colony sizes to determine the best spatial configuration for prey capture.

A comparison of computational efficiencies of stochastic algorithms in terms of two infection models.

In this paper, we investigate three particular algorithms: a stochastic simulation algorithm (SSA), and explicit and implicit tau-leaping algorithms. To compare these methods, we used them to analyze two infection models: a Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunodeficiency Virus (HIV) within host infection model. While the first has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative efficiency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational efficiency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modification of tau-Leaping methods are preferred.

Modeling the effects of introducing a new antibiotic in a hospital setting: A case study.

The increase in antibiotic resistance continues to pose a public health risk as very few new antibiotics are being produced, and bacteria resistant to currently prescribed antibiotics is growing. Within a typical hospital setting, one may find patients colonized with bacteria resistant to a single antibiotic, or, of a more emergent threat, patients may be colonized with bacteria resistant to multiple antibiotics. Precautions have been implemented to try to prevent the growth and spread of antimicrobial resistance such as a reduction in the distribution of antibiotics and increased hand washing and barrier preventions; however, the rise of this resistance is still evident. As a result, there is a new movement to try to re-examine the need for the development of new antibiotics. In this paper, we use mathematical models to study the possible benefits of implementing a new antibiotic in this setting; through these models, we examine the use of a new antibiotic that is distributed in various ways and how this could reduce total resistance in the hospital. We compare several different models in which patients colonized with both single and dual-resistant bacteria are present, including a model with no additional treatment protocols for the population colonized with dual-resistant bacteria as well as models including isolation and/or treatment with a new antibiotic. We examine the benefits and limitations of each scenario in the simulations presented.