Validation framework for epidemiological models with application to COVID-19 models.

Mathematical models have been an important tool during the COVID-19 pandemic, for example to predict demand of critical resources such as medical devices, personal protective equipment and diagnostic tests. Many COVID-19 models have been developed. However, there is relatively little information available regarding reliability of model predictions. Here we present a general model validation framework for epidemiological models focused around predictive capability for questions relevant to decision-making end-users. COVID-19 models are typically comprised of multiple releases, and provide predictions for multiple localities, and these characteristics are systematically accounted for in the framework, which is based around a set of validation scores or metrics that quantify model accuracy of specific quantities of interest including: date of peak, magnitude of peak, rate of recovery, and monthly cumulative counts. We applied the framework to retrospectively assess accuracy of death predictions for four COVID-19 models, and accuracy of hospitalization predictions for one COVID-19 model (models for which sufficient data was publicly available). When predicting date of peak deaths, the most accurate model had errors of approximately 15 days or less, for releases 3-6 weeks in advance of the peak. Death peak magnitude relative errors were generally in the 50% range 3-6 weeks before peak. Hospitalization predictions were less accurate than death predictions. All models were highly variable in predictive accuracy across regions. Overall, our framework provides a wealth of information on the predictive accuracy of epidemiological models and could be used in future epidemics to evaluate new models or support existing modeling methodologies, and thereby aid in informed model-based public health decision making. The code for the validation framework is available at https://doi.org/10.5281/zenodo.7102854.

Modeling the immune system response: an application to leishmaniasis.

In this paper, we present a mathematical model of the immune response to parasites. The model is a type of predator-prey system in which the parasite serves as the prey and the immune response as the predator. The model idealizes the entire immune response as a single entity although it is comprised of several aspects. Parasite density is captured using logistic growth while the immune response is modeled as a combination of two components, activation by parasite density and an autocatalytic reinforcement process. Analysis of the equilibria of the model demonstrate bifurcations between parasites and immune response arising from the autocatalytic response component. The analysis also points to the steady states associated with disease resolution or persistence in leishmaniasis. Numerical predictions of the model when applied to different cases of Leishmania mexicana are in very close agreement with experimental observations.

Thermal detection of a prevascular tumor embedded in breast tissue.

This paper presents a mathematical model of heat transfer in a prevascular breast tumor. The model uses the steady state temperature of the breast at the skin surface to determine whether there is an underlying tumor and if so, verifies whether the tumor is growing or dormant. The model is governed by the Pennes equations and we present numerical simulations for versions of the model in two and three dimensions.

A mathematical model of the compression of a spinal disc.

A model is developed of the stress-strain response of an intervertebral disc to axial compression. This is based on a balance of increased intradiscal pressure, resulting from the compression of the disc, and the restraining forces generated by the collagen fibres within the annulus fibrosus. A formula is derived for predicting the loading force on a disc once the nucleus pressure is known. Measured material values of L3 and L4 discs are used to make quantitative predictions. The results compare reasonably well with experimental results.

Comparison of the energy-response factor of LiF and Al2O3 in radiotherapy beams.

A Monte Carlo study of the energy-response factor of aluminium oxide (Al2O3) and lithium fluoride (LiF) TLDs in kilovoltage and megavoltage photon beams relative to 60Co gamma rays has been performed using EGSnrc Monte Carlo simulations. The sensitive volume of the detector was simulated as a disc of diameter 2.85 mm and thickness 1 mm. The phantom material was water and the irradiation depth was 2.0 cm in kilovoltage photon beams and 5.0 cm for megavoltage photon beams. The results show that the energy-response of the Al2O3 and LiF-TLDs is constant within 3% for photon beam energies in the energy range of 60Co gamma rays to 25 MV X rays. However, both detectors show an enhanced response for kilovoltage photon beams, which in the case of 50 kV X rays is 3.2 times higher than that for 60Co gamma rays. The energy-response factor was 1.46 for LiF irradiated in 50 kV X rays. The Al2O3 detector has an energy-response that is 2.2 times higher than that of LiF in 50 kV X rays decreasing to 1.19 for 250 kV X rays. The results show that the addition of 0.1 or 1% of carbon by weight (as dopant) into the Al2O3 does not change the Monte Carlo determined energy-response factor by more than 1%.

Energy response of an aluminium oxide detector in kilovoltage and megavoltage photon beams: an EGSnrc Monte Carlo simulation study.

A Monte Carlo study of the energy response of an aluminium oxide (Al(2)O(3)) detector in kilovoltage and megavoltage photon beams relative to (60)Co gamma rays has been performed using EGSnrc Monte Carlo simulations. The sensitive volume of the Al(2)O(3) detector was simulated as a disc of diameter 2.85 mm and thickness 1 mm. The phantom material was water and the irradiation depth chosen was 2.0 cm in kilovoltage photon beams and 5.0 cm in megavoltage photon beams. The results show that the energy response of the Al(2)O(3) detector is constant within 3% for photon beam energies in the energy range of (60)Co gamma rays to 25 MV X rays. However, the Al(2)O(3) detector shows an enhanced energy response for kilovoltage photon beams, which in the case of 50 kV X rays is 3.2 times higher than that for (60)Co gamma rays. There is essentially no difference in the energy responses of LiF and Al(2)O(3) detectors irradiated in megavoltage photon beams when these Al(2)O(3) results are compared with literature data for LiF thermoluminescence detectors. However, the Al(2)O(3) detector has a much higher enhanced response compared with LiF detectors in kilovoltage X-ray beams, more than twice as much for the case of 50 kV X rays.