arXiv subjects

Philip Gerlee

Publications and source records attributed to Philip Gerlee.

14 recordsLinked to original sources

arXiv2026

Evaluating infectious disease forecasts in a cost-loss situation

In order for epidemiological forecasts to be useful for decision-makers the forecasts need to be properly validated and evaluated. Although several metrics fore evaluation have been proposed and used none of them account for the potential costs and losses that the decision-maker faces. We have adapted a decision-theoretic framework to an epidemiological context which assigns a Value Score (VS) to each model by comparing the expected expense of the decision-maker when acting on the model forecast to the expected expense obtained from acting on historical event probabilities. The VS depends on the cost-loss ratio and a positive VS implies added value for the decision-maker whereas a negative VS means that historical event probabilities outperform the model forecasts. We apply this framework to a subset of model forecasts of influenza peak intensity from the FluSight Challenge and show that most models exhibit a positive VS for some range of cost-loss ratios. However, there is no clear relationship between the VS and the original ranking of the model forecasts obtained using a modified log score. This is in part explained by the fact that the VS is sensitive to over- vs. under-prediction, which is not the case for standard evaluation metrics. We believe that this type of context-sensitive evaluation will lead to improved utilisation of epidemiological forecasts by decision-makers.

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arXiv2025

Evaluation of respiratory disease hospitalisation forecasts using synthetic outbreak data

Forecasts of hospitalisations of infectious diseases play an important role for allocating healthcare resources during epidemics and pandemics. Large-scale analysis of model forecasts during the COVID-19 pandemic has shown that the model rank distribution with respect to accuracy is heterogeneous and that ensemble forecasts have the highest average accuracy. Building on that work we generated a maximally diverse synthetic dataset of 324 different hospitalisation time-series that correspond to different disease characteristics and public health responses. We evaluated forecasts from 14 component models and 6 different ensembles. Our results show that component model accuracy was heterogeneous and varied depending on the current rate of disease transmission. Going from 7 day to 14 day forecasts mechanistic models improved in relative accuracy compared to statistical models. A novel adaptive ensemble method outperforms all other ensembles, but is closely followed by a median ensemble. We also investigated the relationship between ensemble error and variability of component forecasts and show that the coefficient of variation is predictive of future error. Lastly, we validated the results on data from the COVID-19 pandemic in Sweden. Our findings have the potential to improve epidemic forecasting, in particular the ability to assign confidence to ensemble forecasts at the time of prediction based on component forecast variability.

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arXiv2024

Anatomically aware simulation of patient-specific glioblastoma xenografts

Patient-derived cells (PDC) mouse xenografts are increasingly important tools in glioblastoma (GBM) research, essential to investigate case-specific growth patterns and treatment responses. Despite the central role of xenograft models in the field, few good simulation models are available to probe the dynamics of tumor growth and to support therapy design. We therefore propose a new framework for the patient-specific simulation of GBM in the mouse brain. Unlike existing methods, our simulations leverage a high-resolution map of the mouse brain anatomy to yield patient-specific results that are in good agreement with experimental observations. To facilitate the fitting of our model to histological data, we use Approximate Bayesian Computation. Because our model uses few parameters, reflecting growth, invasion and niche dependencies, it is well suited for case comparisons and for probing treatment effects. We demonstrate how our model can be used to simulate different treatment by perturbing the different model parameters. We expect in silico replicates of mouse xenograft tumors can improve the assessment of therapeutic outcomes and boost the statistical power of preclinical GBM studies.

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arXiv2024

Team game adaptive dynamics

Adaptive dynamics describes a deterministic approximation of the evolution of scalar- and function-valued traits. Applying it to the team game developed by Menden-Deuer and Rowlett [Menden-Deuer & Rowlett 2019], we constructed an evolutionary process in the game. We also refined the adaptive dynamics framework itself to a new level of mathamatical rigor. In our analysis, we demonstrated the existence of solutions to the adaptive dynamics for the team game and determined their regularity. Moreover, we identified all stationary solutions and proved that these are precisely the Nash equilibria of the team game. Numerical examples are provided to highlight the main characteristics of the dynamics. The linearity of the team game results in unstable dynamics; non-stationary solutions oscillate and perturbations of the stationary solutions do not shrink. Instead, a linear type of branching may occur. We finally discuss how to experimentally validate these results. Due to the abstract nature of the team game, our results could be applied to derive implications and predictions in several fields including biology, sports, and finance.

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arXiv2021

Predicting regional COVID-19 hospital admissions in Sweden using mobility data

The transmission of COVID-19 is dependent on social contacts, the rate of which have varied during the pandemic due to mandated and voluntary social distancing. Changes in transmission dynamics eventually affect hospital admissions and we have used this connection in order to model and predict regional hospital admissions in Sweden during the COVID-19 pandemic. We use an SEIR-model for each region in Sweden in which the infectivity is assumed to depend on mobility data in terms of public transport utilisation and mobile phone usage. The results show that the model can capture the timing of the first and beginning of the second wave of the pandemic. Further, we show that for two major regions of Sweden models with public transport data outperform models using mobile phone usage. The model assumes a three week delay from disease transmission to hospitalisation which makes it possible to use current mobility data to predict future admissions.

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arXiv2017

Travelling wave analysis of a mathematical model of glioblastoma growth

In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander, PLoS Comp. Bio., 8(6) 2012). The dynamics of this model can be described by a system of partial differential equations, which exhibits travelling wave solutions whose wave speed depends crucially on the rates of phenotypic switching. We show that under certain conditions on the model parameters, a closed form expression of the wave speed can be obtained, and using singular perturbation methods we also derive an approximate expression of the wave front shape. These new analytical results agree with simulations of the cell-based model, and importantly show that the inverse relationship between wave front steepness and speed observed for the Fisher equation no longer holds when phenotypic switching is considered.

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arXiv2017

The impact of cellular characteristics on the evolution of shape homeostasis

The importance of individual cells in a developing multicellular organism is well known but precisely how the individual cellular characteristics of those cells collectively drive the emergence of robust, homeostatic structures is less well understood. For example cell communication via a diffusible factor allows for information to travel across large distances within the population, and cell polarisation makes it possible to form structures with a particular orientation, but how do these processes interact to produce a more robust and regulated structure? In this study we investigate the ability of cells with different cellular characteristics to grow and maintain homeostatic structures. We do this in the context of an individual-based model where cell behaviour is driven by an intra-cellular network that determines the cell phenotype. More precisely, we investigated evolution with 96 different permutations of our model, where cell motility, cell death, long-range growth factor (LGF), short-range growth factor (SGF) and cell polarisation were either present or absent. The results show that LGF has the largest positive impact on the fitness of the evolved solutions. SGF and polarisation also contribute, but all other capabilities essentially increase the search space, effectively making it more difficult to achieve a solution. By perturbing the evolved solutions, we found that they are highly robust to both mutations and wounding. In addition, we observed that by evolving solutions in more unstable environments they produce structures that were more robust and adaptive. In conclusion, our results suggest that robust collective behaviour is most likely to evolve when cells are endowed with long range communication, cell polarisation, and selection pressure from an unstable environment.

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arXiv2016

Estimating the probability of coexistence in cross-feeding communities

The dynamics of many microbial ecosystems are driven by cross-feeding interactions, in which metabolites excreted by some species are metabolised further by others. The population dynamics of such ecosystems are governed by frequency-dependent selection, which allows for stable coexistence of two or more species. We have analysed a model of cross-feeding based on the replicator equation, with the aim of establishing criteria for coexistence in ecosystems containing three species, given the information of the three species' ability to coexist in their three separate pairs, i.e. the long term dynamics in the three two-species component systems. The triple-system is studied statistically and the probability of coexistence in the species triplet is computed for two models of species interactions. The interaction parameters are modelled either as stochastically independent or organised in a hierarchy where any derived metabolite carries less energy than previous nutrients in the metabolic chain. We differentiate between different modes of coexistence with respect to the pair-wise dynamics of the species, and find that the probability of coexistence is close to $\frac12$ for triplet systems with three pair-wise coexistent pairs and for so-called intransitive systems. Systems with two and one pair-wise coexistent pairs are more likely to exist for random interaction parameters, but are on the other hand much less likely to exhibit triplet coexistence. Hence we conclude that certain species triplets are, from a statistical point of view, rare, but if allowed to interact are likely to coexist. This knowledge might be helpful when constructing synthetic microbial communities for industrial purposes.

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arXiv2015

The evolution of carrying capacity in constrained and expanding tumour cell populations

Cancer cells are known to modify their micro-environment such that it can sustain a larger population, or, in ecological terms, they construct a niche which increases the carrying capacity of the population. It has however been argued that niche construction, which benefits all cells in the tumour, would be selected against since cheaters could reap the benefits without paying the cost. We have investigated the impact of niche specificity on tumour evolution using an individual based model of breast tumour growth, in which the carrying capacity of each cell consists of two components: an intrinsic, subclone-specific part and a contribution from all neighbouring cells. Analysis of the model shows that the ability of a mutant to invade a resident population depends strongly on the specificity. When specificity is low selection is mostly on growth rate, while high specificity shifts selection towards increased carrying capacity. Further, we show that the long-term evolution of the system can be predicted using adaptive dynamics. By comparing the results from a spatially structured vs.\ well-mixed population we show that spatial structure restores selection for carrying capacity even at zero specificity, which a poses solution to the niche construction dilemma. Lastly, we show that an expanding population exhibits spatially variable selection pressure, where cells at the leading edge exhibit higher growth rate and lower carrying capacity than those at the centre of the tumour.

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arXiv2014

Bridging scales in cancer progression: Mapping genotype to phenotype using neural networks

In this review we summarize our recent efforts in trying to understand the role of heterogeneity in cancer progression by using neural networks to characterise different aspects of the mapping from a cancer cells genotype and environment to its phenotype. Our central premise is that cancer is an evolving system subject to mutation and selection, and the primary conduit for these processes to occur is the cancer cell whose behaviour is regulated on multiple biological scales. The selection pressure is mainly driven by the microenvironment that the tumour is growing in and this acts directly upon the cell phenotype. In turn, the phenotype is driven by the intracellular pathways that are regulated by the genotype. Integrating all of these processes is a massive undertaking and requires bridging many biological scales (i.e. genotype, pathway, phenotype and environment) that we will only scratch the surface of in this review. We will focus on models that use neural networks as a means of connecting these different biological scales, since they allow us to easily create heterogeneity for selection to act upon and importantly this heterogeneity can be implemented at different biological scales. More specifically, we consider three different neural networks that bridge different aspects of these scales and the dialogue with the micro-environment, (i) the impact of the micro-environment on evolutionary dynamics, (ii) the mapping from genotype to phenotype under drug-induced perturbations and (iii) pathway activity in both normal and cancer cells under different micro-environmental conditions.

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arXiv2013

A filter-flow perspective of hematogenous metastasis offers a non-genetic paradigm for personalized cancer therapy

Research into mechanisms of hematogenous metastasis has largely become genetic in focus, attempting to understand the molecular basis of `seed-soil' relationships. Preceeding this biological mechanism is the physical process of dissemination of circulating tumour cells (CTCs). We utilize a `filter-flow' paradigm to show that assumptions about CTC dynamics strongly affect metastatic efficiency: without data on CTC dynamics, any attempt to predict metastatic spread in individual patients is impossible.

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arXiv2013

Mathematical modeling of the metastatic process

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.

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arXiv2013

A mathematical model of tumor self-seeding reveals secondary metastatic deposits as drivers of primary tumor growth

Two models of circulating tumor cell (CTC) dynamics have been proposed to explain the phenomenon of tumor 'self-seeding', whereby CTCs repopulate the primary tumor and accelerate growth: Primary Seeding, where cells from a primary tumor shed into the vasculature and return back to the primary themselves; and Secondary Seeding, where cells from the primary first metastasize in a secondary tissue and form microscopic secondary deposits, which then shed cells into the vasculature returning to the primary. These two models are difficult to distinguish experimentally, yet the differences between them is of great importance to both our understanding of the metastatic process and also for designing methods of intervention. Therefore we developed a mathematical model to test the relative likelihood of these two phenomena in the subset of tumours whose shed CTCs first encounter the lung capillary bed, and show that Secondary Seeding is several orders of magnitude more likely than Primary seeding. We suggest how this difference could affect tumour evolution, progression and therapy, and propose several possible methods of experimental validation.

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arXiv2009

A Spatial Model of Tumor-Host Interaction: Application of Chemotherapy

In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of endothelial cells and the extra-cellular matrix. When no treatment is applied the model reproduces the typical dynamics of early tumor growth. The initially avascular tumor reaches a diffusion limited size of the order of millimeters and initiates angiogenesis through the release of vascular endothelial growth factor (VEGF) secreted by hypoxic cells in the core of the tumor. This stimulates endothelial cells to migrate towards the tumor and establishes a nutrient supply sufficient for sustained invasion. To this model we apply cytostatic treatment in the form of a VEGF-inhibitor, which reduces the proliferation and chemotaxis of endothelial cells. This treatment has the capability to reduce tumor mass, but more importantly, we were able to determine that inhibition of endothelial cell proliferation is the more important of the two cellular functions targeted by the drug. Further, we considered the application of a cytotoxic drug that targets proliferating tumor cells. The drug was treated as a diffusible substance entering the tissue from the blood vessels. Our results show that depending on the characteristics of the drug it can either reduce the tumor mass significantly or in fact accelerate the growth rate of the tumor. This result seems to be due to complicated interplay between the stromal and tumor cell types and highlights the importance of considering chemotherapy in a spatial context.

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