A simple modification to the classical SIR model to estimate the proportion of under-reported infections using case studies in flu and COVID-19.

Background: Under-reporting and, thus, uncertainty around the true incidence of health events is common in all public health reporting systems. While the problem of under-reporting is acknowledged in epidemiology, the guidance and methods available for assessing and correcting the resulting bias are obscure. Objective: We aim to design a simple modification to the Susceptible - Infected - Removed (SIR) model for estimating the fraction or proportion of reported infection cases. Methods: The suggested modification involves rescaling of the classical SIR model producing its mathematically equivalent version with explicit dependence on the reporting parameter (true proportion of cases reported). We justify the rescaling using the phase plane analysis of the SIR model system and show how this rescaling parameter can be estimated from the data along with the other model parameters. Results: We demonstrate how the proposed method is cross-validated using simulated data with known disease cases and then apply it to two empirical reported data sets to estimate the fraction of reported cases in Missoula County, Montana, USA, using: (1) flu data for 2016-2017 and (2) COVID-19 data for fall of 2020. Conclusions: We establish with the simulated and COVID-19 data that when most of the disease cases are presumed reported, the value of the additional reporting parameter in the modified SIR model is close or equal to one, so that the original SIR model is appropriate for data analysis. Conversely, the flu example shows that when the reporting parameter is close to zero, the original SIR model is not accurately estimating the usual rate parameters, and the re-scaled SIR model should be used. This research demonstrates the role of under-reporting of disease data and the importance of accounting for under-reporting when modeling simulated, endemic, and pandemic disease data. Correctly reporting the "true" number of disease cases will have downstream impacts on predictions of disease dynamics. A simple parameter adjustment to the SIR modeling framework can help alleviate bias and uncertainty around crucial epidemiological metrics (e.g.: basic disease reproduction number) and public health decision making.

Biomathematical modeling of fatigue due to sleep inertia.

Biomathematical models of fatigue capture the physiology of sleep/wake regulation and circadian rhythmicity to predict changes in neurobehavioral functioning over time. We used a biomathematical model of fatigue linked to the adenosinergic neuromodulator/receptor system in the brain as a framework to predict sleep inertia, that is, the transient neurobehavioral impairment experienced immediately after awakening. Based on evidence of an adenosinergic basis for sleep inertia, we expanded the biomathematical model with novel differential equations to predict the propensity for sleep inertia during sleep and its manifestation after awakening. Using datasets from large laboratory studies of sleep loss and circadian misalignment, we calibrated the model by fitting just two new parameters and then validated the model's predictions against independent data. The expanded model was found to predict the magnitude and time course of sleep inertia with generally high accuracy. Analysis of the model's dynamics revealed a bifurcation in the predicted manifestation of sleep inertia in sustained sleep restriction paradigms, which reflects the observed escalation of the magnitude of sleep inertia in scenarios with sleep restriction to less than âˆ¼ 4 h per day. Another emergent property of the model involves a rapid increase in the predicted propensity for sleep inertia in the early part of sleep followed by a gradual decline in the later part of the sleep period, which matches what would be expected based on the adenosinergic regulation of non-rapid eye movement (NREM) sleep and its known influence on sleep inertia. These dynamic behaviors provide confidence in the validity of our approach and underscore the predictive potential of the model. The expanded model provides a useful tool for predicting sleep inertia and managing impairment in 24/7 settings where people may need to perform critical tasks immediately after awakening, such as on-demand operations in safety and security, emergency response, and health care.

Revisiting classical SIR modelling in light of the COVID-19 pandemic.

Background: Classical infectious disease models during epidemics have widespread usage, from predicting the probability of new infections to developing vaccination plans for informing policy decisions and public health responses. However, it is important to correctly classify reported data and understand how this impacts estimation of model parameters. The COVID-19 pandemic has provided an abundant amount of data that allow for thorough testing of disease modelling assumptions, as well as how we think about classical infectious disease modelling paradigms. Objective: We aim to assess the appropriateness of model parameter estimates and prediction results in classical infectious disease compartmental modelling frameworks given available data types (infected, active, quarantined, and recovered cases) for situations where just one data type is available to fit the model. Our main focus is on how model prediction results are dependent on data being assigned to the right model compartment. Methods: We first use simulated data to explore parameter reliability and prediction capability with three formulations of the classical Susceptible-Infected-Removed (SIR) modelling framework. We then explore two applications with reported data to assess which data and models are sufficient for reliable model parameter estimation and prediction accuracy: a classical influenza outbreak in a boarding school in England and COVID-19 data from the fall of 2020 in Missoula County, Montana, USA. Results: We demonstrated the magnitude of parameter estimation errors and subsequent prediction errors resulting from data misclassification to model compartments with simulated data. We showed that prediction accuracy in each formulation of the classical disease modelling framework was largely determined by correct data classification versus misclassification. Using a classical example of influenza epidemics in an England boarding school, we argue that the Susceptible-Infected-Quarantined-Recovered (SIQR) model is more appropriate than the commonly employed SIR model given the data collected (number of active cases). Similarly, we show in the COVID-19 disease model example that reported active cases could be used inappropriately in the SIR modelling framework if treated as infected. Conclusions: We demonstrate the role of misclassification of disease data and thus the importance of correctly classifying reported data to the proper compartment using both simulated and real data. For both a classical influenza data set and a COVID-19 case data set, we demonstrate the implications of using the "right" data in the "wrong" model. The importance of correctly classifying reported data will have downstream impacts on predictions of number of infections, as well as minimal vaccination requirements.

The Combined Treatment with Ketogenic Diet and Metformin Slows Tumor Growth in Two Mouse Models of Triple Negative Breast Cancer.

BACKGROUND: Many tumors contain hypoxic microenvironments caused by inefficient tumor vascularization. Hypoxic tumors have been shown to resist conventional cancer therapies. Hypoxic cancer cells rely on glucose to meet their energetic and anabolic needs to fuel uncontrolled proliferation and metastasis. This glucose dependency is linked to a metabolic shift in response to hypoxic conditions. METHODS: To leverage the glucose dependency of hypoxic tumor cells, we assessed the effects of a controlled reduction in systemic glucose by combining dietary carbohydrate restriction, using a ketogenic diet, with gluconeogenesis inhibition, using metformin, on two mouse models of triple-negative breast cancer (TNBC). RESULTS: We confirmed that MET - 1 breast cancer cells require abnormally high glucose concentrations to survive in a hypoxic environment in vitro. Then, we showed that, compared to a ketogenic diet or metformin alone, animals treated with the combination regimen showed significantly lower tumor burden, higher tumor latency and slower tumor growth. As a result, lowering systemic glucose by this combined dietary and pharmacologic approach improved overall survival in our mouse model by 31 days, which is approximately equivalent to 3 human years. CONCLUSION: This is the first preclinical study to demonstrate that reducing systemic glucose by combining a ketogenic diet and metformin significantly inhibits tumor proliferation and increases overall survival. Our findings suggest a possible treatment for a broad range of hypoxic and glycolytic tumor types, one that can also augment existing treatment options to improve patient outcomes.

Fatigue risk management based on self-reported fatigue: Expanding a biomathematical model of fatigue-related performance deficits to also predict subjective sleepiness.

Biomathematical models of fatigue can be used to predict neurobehavioral deficits during sleep/wake or work/rest schedules. Current models make predictions for objective performance deficits and/or subjective sleepiness, but known differences in the temporal dynamics of objective versus subjective outcomes have not been addressed. We expanded a biomathematical model of fatigue previously developed to predict objective performance deficits as measured on the Psychomotor Vigilance Test (PVT) to also predict subjective sleepiness as self-reported on the Karolinska Sleepiness Scale (KSS). Four model parameters were re-estimated to capture the distinct dynamics of the KSS and account for the scale difference between KSS and PVT. Two separate ensembles of datasets - drawn from laboratory studies of sleep deprivation, sleep restriction, simulated night work, napping, and recovery sleep - were used for calibration and subsequent validation of the model for subjective sleepiness. The expanded model was found to exhibit high prediction accuracy for subjective sleepiness, while retaining high prediction accuracy for objective performance deficits. Application of the validated model to an example scenario based on cargo aviation operations revealed divergence between predictions for objective and subjective outcomes, with subjective sleepiness substantially underestimating accumulating objective impairment, which has important real-world implications. In safety-sensitive operations such as commercial aviation, where self-ratings of sleepiness are used as part of fatigue risk management, the systematic differences in the temporal dynamics of objective versus subjective measures of functional impairment point to a potentially significant risk evaluation sensitivity gap. The expanded biomathematical model of fatigue presented here provides a useful quantitative tool to bridge this previously unrecognized gap.

Polymer-free corticosteroid dimer implants for controlled and sustained drug delivery.

Polymeric drug carriers are widely used for providing temporal and/or spatial control of drug delivery, with corticosteroids being one class of drugs that have benefitted from their use for the treatment of inflammatory-mediated conditions. However, these polymer-based systems often have limited drug-loading capacity, suboptimal release kinetics, and/or promote adverse inflammatory responses. This manuscript investigates and describes a strategy for achieving controlled delivery of corticosteroids, based on a discovery that low molecular weight corticosteroid dimers can be processed into drug delivery implant materials using a broad range of established fabrication methods, without the use of polymers or excipients. These implants undergo surface erosion, achieving tightly controlled and reproducible drug release kinetics in vitro. As an example, when used as ocular implants in rats, a dexamethasone dimer implant is shown to effectively inhibit inflammation induced by lipopolysaccharide. In a rabbit model, dexamethasone dimer intravitreal implants demonstrate predictable pharmacokinetics and significantly extend drug release duration and efficacy (>6 months) compared to a leading commercial polymeric dexamethasone-releasing implant.

Assessing treatment efficacy in the presence of diagnostic errors.

This paper investigates estimating and testing treatment effects in randomized control trials where imperfect diagnostic device is used to assign subjects to treatment and control group(s). The paper focuses on pre-post design and proposes two new methods for estimating and testing treatment effects. Furthermore, methods for computing sample sizes for such design accounting for misclassification of the subjects are devised. The methods are compared with each other and with a traditional method that ignores the imperfection of the diagnostic device. In particular, the likelihood-based approach shows a significant advantage in terms of power, coverage probability and, consequently, in reduction of the required sample size. The application of the results are illustrated with data from an aging trial for dementia and data from electroencephalogram (EEG) recordings of alcoholic and non-alcoholic subjects. Copyright © 2016 John Wiley & Sons, Ltd.

Prediction Accuracy in Multivariate Repeated-Measures Bayesian Forecasting Models with Examples Drawn from Research on Sleep and Circadian Rhythms.

In study designs with repeated measures for multiple subjects, population models capturing within- and between-subjects variances enable efficient individualized prediction of outcome measures (response variables) by incorporating individuals response data through Bayesian forecasting. When measurement constraints preclude reasonable levels of prediction accuracy, additional (secondary) response variables measured alongside the primary response may help to increase prediction accuracy. We investigate this for the case of substantial between-subjects correlation between primary and secondary response variables, assuming negligible within-subjects correlation. We show how to determine the accuracy of primary response predictions as a function of secondary response observations. Given measurement costs for primary and secondary variables, we determine the number of observations that produces, with minimal cost, a fixed average prediction accuracy for a model of subject means. We illustrate this with estimation of subject-specific sleep parameters using polysomnography and wrist actigraphy. We also consider prediction accuracy in an example time-dependent, linear model and derive equations for the optimal timing of measurements to achieve, on average, the best prediction accuracy. Finally, we examine an example involving a circadian rhythm model and show numerically that secondary variables can improve individualized predictions in this time-dependent nonlinear model as well.

Generalized correlation integral vectors: A distance concept for chaotic dynamical systems.

Several concepts of fractal dimension have been developed to characterise properties of attractors of chaotic dynamical systems. Numerical approximations of them must be calculated by finite samples of simulated trajectories. In principle, the quantities should not depend on the choice of the trajectory, as long as it provides properly distributed samples of the underlying attractor. In practice, however, the trajectories are sensitive with respect to varying initial values, small changes of the model parameters, to the choice of a solver, numeric tolerances, etc. The purpose of this paper is to present a statistically sound approach to quantify this variability. We modify the concept of correlation integral to produce a vector that summarises the variability at all selected scales. The distribution of this stochastic vector can be estimated, and it provides a statistical distance concept between trajectories. Here, we demonstrate the use of the distance for the purpose of estimating model parameters of a chaotic dynamic model. The methodology is illustrated using computational examples for the Lorenz 63 and Lorenz 95 systems, together with a framework for Markov chain Monte Carlo sampling to produce posterior distributions of model parameters.

Glutamate transporter control of ambient glutamate levels.

Accurate knowledge of the ambient extracellular glutamate concentration in brain is required for understanding its potential impacts on tonic and phasic receptor signaling. Estimates of ambient glutamate based on microdialysis measurements are generally in the range of ∼2-10µM, approximately 100-fold higher than estimates based on electrophysiological measurements of tonic NMDA receptor activity (∼25-90nM). The latter estimates are closer to the low nanomolar estimated thermodynamic limit of glutamate transporters. The reasons for this discrepancy are not known, but it has been suggested that microdialysis measurements could overestimate ambient extracellular glutamate because of reduced glutamate transporter activity in a region of metabolically impaired neuropil adjacent to the dialysis probe. We explored this issue by measuring diffusion gradients created by varying membrane densities of glutamate transporters expressed in Xenopus oocytes. With free diffusion from a pseudo-infinite 10µM glutamate source, the surface concentration of glutamate depended on transporter density and was reduced over 2 orders of magnitude by transporters expressed at membrane densities similar to those previously reported in hippocampus. We created a diffusion model to simulate the effect of transport impairment on microdialysis measurements with boundary conditions corresponding to a 100µm radius probe. A gradient of metabolic disruption in a thin (∼100µm) region of neuropil adjacent to the probe increased predicted [Glu] in the dialysate over 100-fold. The results provide support for electrophysiological estimates of submicromolar ambient extracellular [Glu] in brain and provide a possible explanation for the higher values reported using microdialysis approaches.

Dynamic circadian modulation in a biomathematical model for the effects of sleep and sleep loss on waking neurobehavioral performance.

Recent experimental observations and theoretical advances have indicated that the homeostatic equilibrium for sleep/wake regulation--and thereby sensitivity to neurobehavioral impairment from sleep loss--is modulated by prior sleep/wake history. This phenomenon was predicted by a biomathematical model developed to explain changes in neurobehavioral performance across days in laboratory studies of total sleep deprivation and sustained sleep restriction. The present paper focuses on the dynamics of neurobehavioral performance within days in this biomathematical model of fatigue. Without increasing the number of model parameters, the model was updated by incorporating time-dependence in the amplitude of the circadian modulation of performance. The updated model was calibrated using a large dataset from three laboratory experiments on psychomotor vigilance test (PVT) performance, under conditions of sleep loss and circadian misalignment; and validated using another large dataset from three different laboratory experiments. The time-dependence of circadian amplitude resulted in improved goodness-of-fit in night shift schedules, nap sleep scenarios, and recovery from prior sleep loss. The updated model predicts that the homeostatic equilibrium for sleep/wake regulation--and thus sensitivity to sleep loss--depends not only on the duration but also on the circadian timing of prior sleep. This novel theoretical insight has important implications for predicting operator alertness during work schedules involving circadian misalignment such as night shift work.

The central cavity in trimeric glutamate transporters restricts ligand diffusion.

A prominent aqueous cavity is formed by the junction of three identical subunits in the excitatory amino acid transporter (EAAT) family. To investigate the effect of this structure on the interaction of ligands with the transporter, we recorded currents in voltage-clamped Xenopus oocytes expressing EAATs and used concentration jumps to measure binding and unbinding rates of a high-affinity aspartate analog that competitively blocks transport (ß-2-fluorenyl-aspartylamide; 2-FAA). The binding rates of the blocker were approximately one order of magnitude slower than l-Glu and were not significantly different for EAAT1, EAAT2, or EAAT3, but 2-FAA exhibited higher affinity for the neuronal transporter EAAT3 as a result of a slower dissociation rate. Unexpectedly, the rate of recovery from block was increased by l-Glu in a saturable and concentration-dependent manner, ruling out a first-order mechanism and suggesting that following unbinding, there is a significant probability of ligand rebinding to the same or neighboring subunits within a trimer. Consistent with such a mechanism, coexpression of wild-type subunits with mutant (R447C) subunits that do not bind glutamate or 2-FAA also increased the unblocking rate. The data suggest that electrostatic and steric factors result in an effective dissociation rate that is approximately sevenfold slower than the microscopic subunit unbinding rate. The quaternary structure, which has been conserved through evolution, is expected to increase the transporters' capture efficiency by increasing the probability that following unbinding, a ligand will rebind as opposed to being lost to diffusion.

Reduced models of algae growth.

The simulation of biological systems is often plagued by a high level of noise in the data, as well as by models containing a large number of correlated parameters. As a result, the parameters are poorly identified by the data, and the reliability of the model predictions may be questionable. Bayesian sampling methods provide an avenue for proper statistical analysis in such situations. Nevertheless, simulations should employ models that, on the one hand, are reduced as much as possible, and, on the other hand, are still able to capture the essential features of the phenomena studied. Here, in the case of algae growth modeling, we show how a systematic model reduction can be done. The simplified model is analyzed from both theoretical and statistical points of view.

A new mathematical model for the homeostatic effects of sleep loss on neurobehavioral performance.

The two-process model of sleep regulation makes accurate predictions of sleep timing and duration for a variety of experimental sleep deprivation and nap sleep scenarios. Upon extending its application to waking neurobehavioral performance, however, the model fails to predict the effects of chronic sleep restriction. Here we show that the two-process model belongs to a broader class of models formulated in terms of coupled non-homogeneous first-order ordinary differential equations, which have a dynamic repertoire capturing waking neurobehavioral functions across a wide range of wake/sleep schedules. We examine a specific case of this new model class, and demonstrate the existence of a bifurcation: for daily amounts of wakefulness less than a critical threshold, neurobehavioral performance is predicted to converge to an asymptotically stable state of equilibrium; whereas for daily wakefulness extended beyond the critical threshold, neurobehavioral performance is predicted to diverge from an unstable state of equilibrium. Comparison of model simulations to laboratory observations of lapses of attention on a psychomotor vigilance test (PVT), in experiments on the effects of chronic sleep restriction and acute total sleep deprivation, suggests that this bifurcation is an essential feature of performance impairment due to sleep loss. We present three new predictions that may be experimentally verified to validate the model. These predictions, if confirmed, challenge conventional notions about the effects of sleep and sleep loss on neurobehavioral performance. The new model class implicates a biological system analogous to two connected compartments containing interacting compounds with time-varying concentrations as being a key mechanism for the regulation of psychomotor vigilance as a function of sleep loss. We suggest that the adenosinergic neuromodulator/receptor system may provide the underlying neurobiology.

Numerical simulation of local pharmacokinetics of a drug after intravascular delivery with an eluting stent.

We use mathematical modelling to delineate the influence of two important factors on local pharmacokinetics of a drug delivered via an eluting stent, namely: (1) diffusional resistance of a stent coating, and (2) reversible binding of a drug to the vascular tissue. A system of differential equations that describes diffusion of the drug out of the polymeric coating of the stent into the vascular tissue and into the bloodstream, as well as reversible binding of the drug within the vascular tissue, was solved numerically and the spatial profiles of the concentration of the drug at various points of time were produced and analysed. Also, kinetic curves of the spatial average concentration of the drug within the wall were constructed, and the areas under those curves (AUC) were calculated. The simulations showed that AUC might be enhanced, if the stent is coated with a continuous layer of a drug-releasing medium with a high diffusional resistance. Both the residence time and the average concentration of the drug within the vascular wall increase in this case mainly because the coating imposes a diffusional barrier between the vascular tissue and the bloodstream, thereby reducing the wash-out. If the drug reversibly binds to the tissue, the residence time increases greatly, but the AUC for the free (unbound) drug remains unchanged, implying that the presence of the drug in the vessel is prolonged at the expense of a proportional reduction in concentration of a free drug within the tissue. These findings justify the design of eluting stents with continuous coatings with enhanced diffusional resistance and the engineering of drugs with enhanced affinity to the vascular matrix. Reversible binding to tissue may be beneficial for prolonging the presence of the drug in the target tissue, and for avoiding potential toxic peak effects of high concentrations of the free (unbound) drug.