Mathematical Biology

The relative contributions of wild-bird spillover and local spread to highly pathogenic avian influenza (HPAI) infection in British poultry remain poorly quantified. I first introduce the WiLiMan-ID modelling challenge on Jolly Island to explore how intervention priorities may change as a synthetic outbreak evolves. I then outline a framework for HPAI outbreaks in Great Britain, combining ecological spillover from unobserved wild-bird sources at waterbodies with case-associated local spread around infected premises. The analysis explores whether the model can distinguish local spread from spillover and assess how clustered spillover is, from diffuse background risk to concentrated sources (“virus factories”). The aim is to understand how uncertainty about infection routes affects the expected benefits of housing orders and faster culling.

Urbanization shapes infectious disease dynamics through mobility, infrastructure, and spatial structure. Prior work shows how density and network connectivity influence epidemic spread [1,2], particularly for directly transmitted diseases such as COVID-19 and influenza [1,2,3]. However, many models assume pairwise transmission or use static mobility representations, which are less suitable for waterborne diseases like cholera, where risk depends on overlap between movement and shared infrastructure. While spatial cholera dynamics have been studied [4], few models combine mechanistic disease progression, behaviourally realistic mobility, and spatially explicit infrastructure. Common mobility models (e.g., gravity or radiation [2], commuting data [3]) also fail to capture repeated, preferential use of specific locations.
We develop a spatially explicit agent-based model combining a SEIRS process with a density-augmented Exploration and Preferential Return (d-EPR) mobility framework. Agents move between households and shared infrastructure, repeatedly visiting familiar locations while occasionally exploring new ones. Contamination accumulates at infrastructure sites and infection occurs through repeated exposure. The model is implemented on GIS-based urban layouts to examine how spatial structure, movement, and infrastructure jointly shape epidemic dynamics.
Results show that infection concentrates around shared infrastructure, particularly in main activity hubs. In baseline settings, mobility clusters agents into high-use areas, producing localised growth before outward spread. Mobility reduction limits spatial spread and lowers incidence but increases localised exposure. Decentralisation redistributes activity, reducing pressure on individual sites and lowering transmission by limiting repeated exposure. Across scenarios, concentrated movement leads to a small number of high-burden transmission points and faster outbreaks, while reduced or distributed movement spreads load, lowering peak exposure and flattening incidence. These findings highlight the central role of mobility, infrastructure interactions and suggest that targeted, structure-specific interventions are more effective than uniform approaches.
[1]Aguilar, J., Bassolas, A., Ghoshal, G., Hazarie, S., Kirkley, A., Mazzoli, M., ... & Sadilek, A. (2022). Impact of urban structure on infectious disease spreading. Scientific reports, 12(1), 3816.
[2] Wen, T. H., Hsu, C. S., & Hu, M. C. (2018). Evaluating neighborhood structures for modeling intercity diffusion of large-scale dengue epidemics. International journal of health geographics, 17, 1-15.
[3] Moss, R., Naghizade, E., Tomko, M., & Geard, N. (2019). What can urban mobility data reveal about the spatial distribution of infection in a single city?. BMC public health, 19, 1-16.
[4] Phelps, M. D., Azman, A. S., Lewnard, J. A., Antill´on, M., Simonsen, L., Andreasen, V., & Pitzer, V. E. (2017). The importance of thinking beyond the water-supply in cholera epidemics: A historical urban case-study. PLoS neglected tropical diseases, 11(11), e0006103.

Complex systems are often characterised by their intricate structures and behaviours, which can be challenging to analyse and understand. However, the principle of Occam’s Razor suggests that the simplest explanation is often the best. This idea, encapsulated in the concept of the toy model, is often perceived as a parsimonious or exploratory approach when dealing with problems involving many unknown mechanisms or restricted to aggregated data, and it is not always taken seriously. In this work, we connect the idea of model inference from data to rationalise our intuition about minimal models. Connecting ideas from information geometry and Bayesian inference, we show that toy models are often the optimal way to exploit the information in the data and, hence, are not only mathematically or computationally tractable but also optimal in the sense of information theory. We illustrate these ideas with examples from ecology, epidemiology, or astrochemistry. However, they can be applied to any field where data quality and quantity are limited, or the diversity is poor. We also discuss the implications of these ideas in the context of well-established ideas, such as the renormalisation group theory.

Thermal therapies such as hyperthermia, laser ablation, and high-intensity focused ultrasound rely on delivering controlled heat to biological tissue. The temperature propagation in the tissue cannot be modelled accurately with the  Fourier's law, but should be modelled with the Maxwell–Cattaneo law instead, which gives rise to the hyperbolic bio-heat equation, that incorporates the assumption of the finite speed propagation. In this talk I will discuss inverse source problems for such a hyperbolic model, where the goal is to recover the unknown space-dependent component of the heat source.

Recent rises in cases of several mosquito-borne diseases--such as dengue, Chikungunya, and West Nile virus--in both endemic and non-endemic areas, have increased the interest in the use of mathematical models to understand the spread of vector-borne infections, and the potential effects of control strategies. The classical Ross-–Macdonald framework provides the foundation for much of the mathematical modelling of such diseases. In this talk, I will present a model for a mosquito-borne epidemic outbreak in which human hosts may adopt protective behaviours against mosquito bites. First, I will introduce the basics of the Ross–Macdonald framework. Then, I will extend the model by allowing individuals within the host population to adopt protective behaviours (e.g., using repellents) according to information they receive about disease prevalence. I will show that, in the early phase of an epidemic, behaviour-driven protection may either decrease or increase the reproduction number of the epidemic, depending on several factors. In addition, I will show that, in the long run, behavioural responses may facilitate epidemic control, but may also prolong disease persistence, potentially generating recurrent epidemic waves.

 

Acknowledgements
This work was supported by the project "One Health Basic and Translational Actions Addressing Unmet Needs on Emerging Infectious Diseases" (INF-ACT), BaC "Behaviour and sentiment monitoring and modelling for outbreak control/BEHAVE-MOD" (No. PE00000007, CUP I83C22001810007) funded by the NextGenerationEU. The author is member of the UMI research group MSE, and of the INdAM research group GNCS.

As cancer advances, cells often spread from the primary tumor to other parts of the body and form metastases. I'll present a conceptually elegant model of metastasis formation where each primary cell can initiate metastatic lesions which lesions then evolve as independent branching processes. We assume that the primary tumor is resected upon detection. Of fundamental importance is whether synchronous (detectable) or metachronous (undetectable) mets are present at this detection time, the distribution of their numbers and sizes. If there are only metachronous mets at detection, how long until these mets become detectable, leading to the relapse of the disease? We'll extend this model to cancers in which cells first need to evolve the ability to metastasize. Using sequence data from primary and corresponding met samples we'll propose that these intermediate cells are indeed present for certain primary-met pairs, why not there for others.

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The mitotic cell cycle governs DNA replication and cell division. The effectiveness of radiotherapy and chemotherapy depends on cell-cycle position, with increased resistance during DNA replication and mitosis. Thus, accurate mathematical models of the cell cycle are essential for understanding and predicting treatment response. However, mathematical modellers often face the problem of a lack of publicly available, sufficiently resolved, time-series datasets for parametrising models. In this work, we consider how the ability to collate population summary measurements across the literature, from different cell lines and/or experimental set ups, affects identifiability of parameters for a cell cycle model.

Initially synchronised cell populations gradually desynchronise over successive cycles, converging to balanced exponential growth (BEG) which is characterised by exponential population growth and steady, time-independent phase proportions. These proportions can be obtained from fluorescence-activated cell sorting (FACS) data. The increasing use of the Fluorescent Ubiquitination-based Cell Cycle Indicator (FUCCI) provides higher-resolution information on phase dynamics, such as minimum phase durations and variability.


We present an age-structured PDE model in which cell-cycle phase progression follows a delayed gamma distribution. We derive analytical expressions for BEG phase proportions and other FUCCI-observable quantities, and use them to assess how data availability influences parameter identifiability. When parameters are not uniquely identifiable, we determine identifiable parameter groupings, thereby determining the minimum amount of data that must be available for successfully fitting structured population models of the cell cycle.