Despite decades of application of epidemiological models to respiratory viruses such as influenza and coronavirus, there is no standard model for capturing the life history of disease or immunological response, nor a standard approach to inference. I introduce two deterministic epidemic models applied to SARS-CoV-2 (UK) and pH1N1 2009 (UK and Australia). First, I introduce a discrete-time, deterministic model structured by age of infection, and explore how this model structure influences the performance and uncertainty quantification of both maximum likelihood and Bayesian inference methods in the context of SARS-CoV-2. I then present a two-subtype SIRS-like model and examine the conclusions that can be drawn from sparse immunological, microbiological, and serological data regarding the short- and medium-term impact of pH1N1 2009 vaccination. Finally, I review some remaining questions in seasonal influenza modelling, and discuss future work to calibrate mechanistic models that integrate climate variability, host immune dynamics, and behavioural responses.
Co-infection of a single host by different pathogens is ubiquitous in nature. We consider a population of hosts (e.g., small or large vertebrates) and a population of ticks, both of them susceptible to infection with two different strains of a given virus. We note that for the purposes of our models, we have Crimean-Congo hemorrhagic fever virus (a segmented Bunyavirus) in mind, as the application system. First, we focus on the dynamics of a single infection, proposing a deterministic model to understand the role of co-feeding in the transmission of the virus. We then compute the basic reproduction number by making use of the next generation matrix approach. When considering co-infection by two distinct strains (one resident and one invasive), we make use of differential equations to model the dynamics of susceptible, infected and co-infected species, and we compute the invasion reproduction number of the invasive strain. I discuss some problems with the calculation, and the solution proposed by Samuel Alizon and Marc Lipsitch. The second story involves HIV-1 co-infection. In this instance, we are interested in quantifying the potential for a viral recombinant to get established in a population in which two viral HIV-1 subtypes co-circulate. We make use of epidemiological data in Brazil and China, and together with a mathematical model of co-infection describe and quantify infection dynamics. A feature of the model is an essential asymmetric co-infection step. This allows to include in the model both population and within-host parameters that characterize infection dynamics, since recombination takes place in an individual host, and transmission of the recombinant is a population-level rate. We describe how the ability of the viral recombinant to get stablished depends on both types of parameters. We conclude with a perspective on how to improve the current model and the data sets required for its calibration.
Speaker: Prof Carmen Molina-Paris
Affiliation:
(1) Los Alamos National Laboratory, Los Alamos, New Mexico, USA
(2) School of Mathematics, University of Leeds, Leeds, UK
Global changes are affecting the distribution and demographics of several haematophagus arthropods that are relevant reservoirs and transmitters of infectious diseases to animals and humans. Several vector-borne diseases are emerging and re-emerging in several areas of the world, causing unprecedented outbreaks and concern to ecosystem, animal and public health authorities and people. Understanding the ecology of vectors and pathogens through ecological and epidemiological studies requires the application of mathematical and statistical tools to properly understand the complex interaction network of interactions between environment, animals, pathogens and humans. The examples of West Nile fever virus and Crimean-Congo haemorrhagic fever illustrate recent approaches to understand the ecology of two emerging diseases in Europe.
Speakers: Dr José Francisco Ruiz Fons (1) & Dr Zati Vatansever (2)
(1) Spanish Game & Wildlife Research Institute (IREC); Spanish Scientific Research Council (CSIC) & University of Castilla-La Mancha, Ciudad Real, Spain
(2) Kafkas University, Turkey
Many biological and social systems can be modelled as dynamical processes on networks. An important example are epidemics, where vertices in the network represent people, edges indicate social contacts and the dynamic describes how people’s health (susceptible to infection, infected, recovered etc.) changes in time in response to the health of the people they come into contact with. Biological models based on chemical reaction networks can also be described as dynamics on networks when there is network structure that governs which units can interact, and consequently the law of mass action no longer holds. These examples, and others, can be described exactly as Markov chains, but typically there are too many states for this to be of practical use. Thus it is standard to derive "mean-field" approximations, although this is often done using probabilistic intuition. In this talk I will describe a robust method to approximate a class of dynamical processes on networks based on an explicit average of their exact Markov chain description. While this provides a systematic method to derive mean-field approximations, it remains an open challenge to quantify the error introduced.
Malaria transmission and persistence depend critically on the interaction between parasite dynamics, human immunity, and epidemiological feedbacks. I will review recent work with collaborators developing and analysing structured PDE models spanning both population and within-host scales. At the population level, we couple vector–host epidemiology with the acquisition and loss of anti-disease immunity. Bifurcation analysis reveals the changing structure of endemic equilibria as transmission intensity rises, and our exploration of vaccination strategies, motivated by the RTS,S vaccine, highlights how seasonal transmission profiles may impact interventions. We also investigate multiple potential causes of backward bifurcation in this model. At the within-host level, we examine how parasites allocate resources between proliferation and transmission stages under immune pressure. Using an age‑of‑infection–structured model, we characterize immune-driven clearance thresholds and analyse parasite investment strategies, contrasting constant versus time-varying allocation rules. Our results indicate that adaptive immunity can impose a survival-reproduction tradeoff that explains why malaria parasites cannot evolve ever faster within-host multiplication. Together, these studies illustrate how immunity and feedbacks across scales shape malaria outcomes and inform intervention strategies.
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.
