Abstract: Nonlocal aggregation-diffusion equations have emerged as a fundamental mean-field approximation for large interacting particle systems, with applications spanning, for example, opinion dynamics, statistical mechanics, physics, synchronisation, and mathematical biology. While much research has focused on their qualitative properties—existence, uniqueness, linear stability analysis, and long-time behavior—understanding their quantitative structure remains a key challenge: What patterns form? Under which conditions do they emerge? Are phase transitions continuous or discontinuous? How do these transitions influence other properties of the solution(s)? I am interested in the rigorous treatment of such questions from an analytical perspective, using tools from bifurcation theory.
In this talk, I will present a bifurcation analysis applied to some nonlocal aggregation-diffusion equations with applications in ecology, focusing on three recent efforts. The first couples a scalar nonlocal aggregation-diffusion equation (population dynamics) with an ordinary differential equation (a 'spatial map' for the population). In the second case, we study a similar problem that can be transformed from a two-equation PDE-ODE system into a three-equation parabolic-elliptic-ODE system while maintaining the stability and solution structure properties. Finally, I will present some preliminary results for a fully nonlocal two-species aggregation-diffusion system and some current progress toward understanding the global bifurcation structure of these problems from a numerical point of view. Together, these examples highlight the versatility of a robust bifurcation analysis in understanding precise solution behaviour of complex nonlocal PDE models and the different (but related) ways these tools can be applied depending on the problem of interest.
Biological systems are remarkable in their ability to adapt to dynamic environments, encode memory, and learn, spanning scales from intricate signaling pathways within cells to coordinated responses in populations. At the subcellular level, we demonstrated that long-lived memory and non-associative learning can originate in intra-cellular signaling networks from distinct timescales of operation among signaling components, forming the basis for signal integration. In the cellular level, our agent-based modeling revealed that T cells integrate signals from sub-threshold antigenic interactions to form immune synapses. Furthermore, we showed that the enhanced flexibility of bispecific antibodies, designed to simultaneously bind targets on T cells and antigen-presenting cancer or host cells, can reduce their therapeutic potency and synapse formation propensity, with crucial translational implications for cancer and autoimmune therapies. Expanding to the cell-cell interaction network, we simulated germinal centers, the sites of extensive T cell-B cell crosstalk and the formation of memory B cells and antibody-secreting cells, using a state-of-the-art agent-based model. We revealed how germinal centers adapt B cell selection to balance immune diversity with specificity. We also studied regulation of autoimmunity in germinal centers by tingible body macrophages and T follicular regulatory cells. In the level of organism-organism interactions, we led data-driven adaptive modeling integrated with healthcare usage during the SARS-CoV-2 outbreak, influencing key political decisions on non-pharmaceutical interventions globally, including advising former German Chancellor Angela Merkel. A central focus of my research, thus, has been to investigate emergent phenomena across biological scales using an interdisciplinary approach and derive translational insights for disease interventions.
Abstract:
We investigate minimal replicator systems that are able to use information in a functional manner. Specifically, we consider a population of autocatalytic replicators in a flow reactor, subject to fluctuating environments. We derive operational bounds on replicators production in terms of information-theoretic quantities, reflecting contributions from environmental uncertainty, side information, and distribution mismatch. We also derive the optimal strategy, expressed as a function of both intrinsic replicator parameters and environmental statistics. We compare and contrast our findings with existing information-theoretic formalisms such as Kelly gambling. The results are illustrated on a model of real-world self-assembled molecular replicators. For this system, we demonstrate the benefit of internal memory in environments with temporal correlations, and we propose a plausible experimental setup for detecting the signature of functional information. We briefly discuss the role that information processing may play in guiding the evolution of prebiotic replicator networks.
Preprint available at:
https://doi.org/10.48550/arXiv.2501.00396
Cooperation arises at all scales in the natural world, from the cooperative binding of receptors at the supramolecular scale to the migration of animals across continents. In this talk, we will construct and solve simple mathematical models to understand the mechanisms driving cooperative behaviours at the microscopic scale—namely, cooperative propulsion and spontaneous synchronization. The subject of these models is the bacterium Escherichia coli—one of the best studied model organisms in biology—and the slender helical appendages (flagella) that E. coli uses for propulsion. First, we will show that the hydrodynamic interactions between the flagella, coupled with the limited capacity for torque generation of the bacterial flagellar motor, lead to unexpected trends in the swimming speed of multiflagellated bacteria [1]. Next, we will propose and analyse an elastohydrodynamic mechanism that enables rotating flagella to spontaneously synchronize their phases without the involvement of a central pattern generator [2]. In both studies, we combine numerical and asymptotic techniques with pertinent information about the features of E. coli bacteria to gain new biophysical insights. If time allows, we will conclude by drawing analogies between the elastohydrodynamic mechanism for synchronization and another recently developed model based on load-dependent actuation with distributed time delay [3].
References:
[1] M. Tătulea-Codrean and E. Lauga (2024) Physical mechanism reveals bacterial slowdown above a critical number of flagella. J. R. Soc. Interface, 21:20240283.
[2] M. Tătulea-Codrean and E. Lauga (2022) Elastohydrodynamic synchronization of rotating bacterial flagella. Phys. Rev. Lett., 128:208101.
[3] N. Diederen and M. Tătulea-Codrean (2025) Hydrodynamic synchronization of rotating flagella with load-dependent actuation. In preparation.
Computational models are revolutionizing our understanding of infectious disease spread. This presentation explores how integrating mobile phone data, global mobility patterns, socioeconomic strata and epidemiological records can enhance our ability to characterize and predict epidemic dynamics across spatio-temporal scales. I will show how these data can be used to: (i) uncover the initial phases (i.e., cryptic spreading) of the COVID-19 pandemic globally; (ii) quantify social inequalities in the adoption of non-pharmaceutical interventions in a large metropolitan area; and (iii) improve the realism of traditional epidemic models by accounting for multiple dimensions beyond age in the stratification of contact patterns.
When and how should we intervene to manage an emerging infectious disease most effectively? Deciding when to enforce or relax non-pharmaceutical interventions (NPIs) based on real-time outbreak surveillance data is a central challenge in infectious disease epidemiology. Practical surveillance data, often characterised by reporting delays and infection under-ascertainment, can misinform decision-making. This may lead to mistimed NPIs that fail to control disease spread or allow harmful epidemic peaks that overwhelm healthcare capacities.
In this talk, I will introduce EpiControl, a novel model-predictive control algorithm designed to optimise NPI decisions by jointly minimising cumulative future risks and costs across stochastic epidemic projections. I will demonstrate how this algorithm outperforms data-insensitive strategies while also discussing the intrinsic limitations of surveillance quality, disease growth rates, and decision frequency in flattening epidemic peaks or reducing endemic oscillations. Additionally, I will present my ongoing research on integrating population behaviour into the policy-making framework.
Inhalational anthrax, caused by the bacterium Bacillus anthracis, is a disease with very high fatality rates. Due to the significant risk posed if the bacterium was to be intentionally used as a bioweapon, it is important to be able to defend against such an attack and to make optimal decisions about treatment strategies. Mechanistic mathematical models can help to quantify and improve understanding of the underlying mechanisms of the infection. In this talk, I will present a multi-scale mathematical model for the infection dynamics of inhalational anthrax. This approach involves constructing individual models for the intracellular, within-host, and population-level infection dynamics, to define key quantities characterising infection at each level, which can be used to link dynamics across scales. I will begin by introducing a model for the intracellular infection dynamics of B. anthracis, which describes the interaction between B. anthracis spores and host cells. The model can be used to predict the distribution of outcomes from this host-pathogen interaction. For example, it can be used to estimate the number of bacteria released upon rupture of an infected phagocyte, as well as the timing of phagocyte rupture and bacterial release. Next, I will show how these key outputs can be used to connect the intracellular model to a model of the infection at the within-host scale. The within-host model aims to provide an overall understanding of the early progression of the infection, and is parametrised with infection data from studies of rabbits and guinea pigs. Furthermore, this model allows the probability of infection and the time to symptoms to be calculated. Building a model that offers a realistic mechanistic description of different animal responses to the inhalation of B. anthracis spores is an important step towards eventually extrapolating the model to describe the dynamics of human infection. This would enable predictions of how many individuals would become infected in different exposure scenarios and also on what timescale this would occur.
When managing a breeding programme, we want to maximize the selection of desirable traits (such as health or yield). At the same time, we know that related plants or animals are more likely to share traits, so we also need to incorporate minimizing inbreeding and its associated risks. This can be modelled as a bi-objective optimization problem, which happens to have a similar structure to portfolio theory from financial mathematics.
Collaborating with researchers at the Roslin Institute in the Royal (Dick) School of Veterinary Studies, we examined how a range of mathematical tools can be used to explore this problem more accurately and efficiently than the state of the art. These were tested with simulated breeding programmes and led to the creation of an open-source tools for practitioners.
At Leeds, we have been developing within-host models of infection for a number of years. Deterministic models of viral dynamics have been widely used in the past to understand average behaviours, and to quantify the efficacy of treatments. On the other hand, stochastic models allow one to incorporate discrete events (such as cellular burst, where an infected cell dies releasing N virions into the extracellular environment), to look at extinction events (e.g. probably of infection establishment vs short-time recovery of the host, for a given initial dose), and to account for variability in summary statistics such as the reproduction number (i.e., the number of cells infected by a typical infected cell during an infection). These heterogeneities can be important for example when looking at extinction events and/or the impact of small viral doses. Stochastic models also allow one to obtain summary statistics related to the infection dynamics across different scales (intra-cellular, within-host and population levels), and to link these scales via multi-scale modelling approaches. In this talk, I will discuss recent work that we have carried out in this area.
Preparing for the next pandemic: development of mathematical and computational tools for the assessment of the impact of novel antivirals at the individual and population level.
Some first modelling efforts towards the assessment of a new approach to combat pathogenic respiratory viruses using novel broadly neutralising antibodies will be presented.
