I will present a mathematical model of hematopoietic stem cell dynamics, parameterized with mouse data, to investigate conditions for advantageous mutant emergence. I will first show that a mutant invasion barrier exists in progenitor cell populations, requiring large fitness advantages for successful invasion. I will then demonstrate how age-related changes in stem cell dynamics promote mutant invasion, particularly when mutants construct favorable environments through evolutionary niche construction. Finally, implications for understanding TET2 and JAK2 mutant growth will be discussed, which are associated with chronic health conditions. These two types of mutants often coexist in patients, and their evolutionary dynamics in the presence of invasion barriers helps explain clinical observations.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Symptoms appear only late during cancer development. This makes it difficult to study the disease evolution before clinical manifestation. Using the blood forming (hematopoietic) system as a paradigmatic example, stochastic and deterministic models are proposed to simulate the expansion of pre-malignant and malignant clones. The models account for the hierarchical organization of the blood-forming system and its nonlinear feedback regulations. The models are integrated with patient data from different sources to better understand how cancer progression is shaped by factors such as inflammation and age-related bone marrow changes. A special focus will be on inter-individual heterogeneity in patient trajectories and its potential determinants. Finally, challenges related to the interpretation of patient samples and the personalized prediction of disease progression will be discussed, along with how mathematical models could contribute to overcoming them. A part of the talk is based on a joint work with J. Snyder (NC State), J. Ottesen (Roskilde), M. Andersen (Roskilde), C. Ellervic (Harvard), M.K. Larsen (Roskilde) and H. Hasselbalch (Roskilde)

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Tissue development relies on morphogens—signaling molecules released from localized sources that spread through tissue to guide growth and cell identity. In the vertebrate neural tube, morphogens are produced at opposite poles: BMP and Wnt dorsally, in the surface ectoderm and roof plate, and Shh ventrally, from the notochord and floor plate. This talk brings together our work on how these opposing sources form and function. Using quantitative measurements in embryos and organoids alongside mathematical modeling, we explore how each source is established and how its signal is interpreted over time. We find that although they utilize distinct molecular mechanisms, the roof plate and floor plate both form in two phases – an initial phase shaped by their surroundings, followed by controlled expansion. We also examine how changing signal levels over time help cells choose their identity at the right moment. Together, this work points to principles behind how tissues control and use the dynamics of morphogen signaling.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Most mathematical models of the cancer–immune system rely on phenomenological descriptions of cellular interactions. While such models can be valuable for clinical applications, mechanistic models grounded in fundamental biological and physical principles may provide deeper explanatory insight into the processes that give rise to observed phenomena. In this talk, I will present initial work on a novel mechanistic framework, the Roskilde Immune Pathogen (RIP) model. A central observation is that, under standard second-order mass-action kinetics for cell–cell interactions, much of the system's nonlinear behavior can be shifted from the population level to intracellular signaling and gene-regulatory processes. This motivates the inclusion of simplified but mechanistically founded models of transcriptional dynamics governing macrophage polarization and T-cell differentiation. Despite its relative simplicity, the RIP model reproduces several key observations from cancer immunology, so far qualitatively. These include the three phases of cancer immunoediting (elimination, equilibrium, and escape), recurrent tumor dynamics, and the apparently contradictory associations between tumor-associated macrophages (TAMs) and both favorable and unfavorable clinical outcomes. The results suggest that mechanistic intracellular regulation may provide a unifying explanation for diverse emergent behaviors of the cancer–immune system and offer a foundation for future predictive modeling.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Physiological decline during aging is a multi-scale process spanning molecular drift, cellular loss, and organ-level structural remodeling. To bridge these scales, we developed a computational framework that transforms standard histopathology archives into a rich substrate for quantitative spatial biology. At the single-cell scale, we modeled the spatial relationships of 3.5 billion cells across 16 human organs as spatial graphs. This revealed that functional tissue units undergo a shared aging trajectory, transitioning from dense, specialized arrangements to sparser, heterogeneous structures. At the mesoscale, we developed an unsupervised algorithm to map physical interaction networks between tissue compartments, demonstrating that local interfaces remodel while global organ topology remains resilient. Finally, we integrated these spatial networks with paired molecular data to build deep-learning tissue clocks. These morphological predictors of biological age align with telomere attrition and transcriptomic dysregulation, enabling the prediction of organ-specific decline directly from blood. Together, these paradigms illustrate how large-scale data from primary human tissues can link microscopic cellular arrangements to macroscopic organ physiology and systemic decline.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

The term "Evolutionary rescue", mostly used in evolutionary ecology, denotes adaptation to severe stress that a population would otherwise not survive. Largely independently from the rescue models in evolutionary ecology developed since the 1990s, a second body of theory exists -- models describing the evolution of drug resistance, which is an example of unwanted rescue. In this talk, I will introduce the fundamental one-locus two-alleles model of rescue and highlight how early models for the evolution of resistance to cancer chemotherapy and antibiotic treatment apply the same approaches. I will then show recent examples of how the generalized framework can be applied to identify promising strategies for cancer extinction therapies.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Neuroblastoma is a deadly tumor affecting infants and young children. It is thought to arise in the fetal peripheral nervous system, and single-cell transcriptomic comparisons have likened tumor cells to various sympathoadrenal cell types. However, unlike healthy cells, tumor cells have a disrupted proliferation/differentiation balance and fail to respond to tissue-constraining signals. We aim to analyze the gene-regulatory networks controlling these aberrant cellular phenotypes. For this, we trained logistic regression models on single-cell data of healthy fetal cells and applied them to neuroblastoma. We found that tumor cells formed a continuum, from cells closely resembling healthy cells to those diverging from any reference cell. Intriguingly, some tumor cells simultaneously resembled multiple cell types, indicating mixed transcriptional programs. We would like to discuss approaches to dissect the tumor-normal continuum with workshop participants.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

In the secondary lymphoid tissues, human immunodeficiency virus (HIV) can replicate both in the follicular and the extrafollicular compartments. Yet, virus is concentrated in the follicular compartment in the absence of antiretroviral therapy, in part due to the lack of cytotoxic T lymphocyte (CTL)-mediated activity there. CTL home to the extrafollicular compartment, where they can suppress virus load to relatively low levels. We use mathematical models to show that this compartmentalization can explain seemingly counterintuitive observations. First, it can explain the observed constancy of the viral decline slope during antiviral therapy irrespective of the presence of CTL in SIV-infected macaques, under the assumption that CTL-mediated lysis significantly contributes to virus suppression. Second, it can account for the relatively long times it takes for CTL escape mutants to emerge during chronic infection even if CTL-mediated lysis is responsible for virus suppression. Third, the compartmental structure has important implications for the evolution of viral mutants in general, influencing mutant fixation probabilities and fixation times. The talk will discuss these results, and will further provide an overview of mathematical models that have been used to describe T cell responses.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

CAR-T cell therapy is proving to be an efficient second line treatment against large B-cell lymphoma butheterogeneity in clinical responses is calling for early prediction markers. The fitness of the patient’s circulating T cells that serve to generated the CAR-T cell product is sought to be a key contributor to treatment efficacy. The working hypothesis of our project is that such pretreatment T cell fitness would be best captured through miniaturized functional assays, that may serve as bioassays to predict treatment response. For that purpose, we are implementing a high-content cell imaging pipeline in a 384-well plate format to assess key T cell functional properties pertaining to metabolism, migration, immune synapse, signaling and effector molecule polarization. The generated images are analyzed with Machine Learning methods such as dimension reduction to extract T cell fitness signatures associated with clinical responses. Following a first optimization phase, this pipeline was applied to a cohort of 40 healthy donors spanning a wide age range (18-70 years), which will serve as a reference for the subsequent analysis of patient samples. We are planning to process samples from 100 DLBCL patients from the CeVi Leuka collection with the objective to align image-based signatures of T cell fitness with response to the therapy.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Cancer is an evolving system shaped by the forces of mutation, selection, and genetic drift. Darwinian evolution underpins the life history of all cancers, including those arising in children, driving malignant transformation, metastatic spread, and response to therapy. Understanding these dynamics is therefore crucial for improving treatment. Chromosomal instability (CIN), the frequent alteration of chromosomal structure or number during cell division, is a hallmark of cancer and is associated with aggressive disease. By generating genomic diversity and driving large-scale alterations to the genome, CIN fuels cancer evolution. However, its evolutionary dynamics remain poorly understood. In my talk, I will present our work in paediatric cancers, where we aim to gain new insights into CIN and cancer evolution at single-cell resolution. I will discuss how computational and experimental approaches can help quantify this important driver of cancer evolution and key prognostic feature of many cancers.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Targeted protein degraders offer a powerful way to eliminate disease relevant proteins. A substantial body of modelling work already exists — including contributions by A. Reichel & R. Haid, Bartlett & Gilbert, Guzzetti & Gutierrez, among others — and this talk will summarize and complement these established frameworks with some surprising additional insights. In particular, a simple yet far reaching method for extracting protein half life, offering a practical and broadly applicable way to quantify protein stability, will be presented.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

How can we better model cancer metastasis and/or recurrence in experimental settings? Generating animal models with a single tumor exhibiting both events is a bottleneck in such research. Our novel genetically-engineered mouse model of osteosarcoma addresses this: bone-specific oncogenic manipulations yields primary tumors (80% penetrance) that spontaneously metastasize to the lung (70% incidence), with metastatic nodule sizes following a power-law distribution—hinting at scale-invariant seeding dynamics. Turning off the oncogenic factor drives primary tumor regression, yet recurrence occurs with 100% penetrance if the primary was large, dropping below 50% if initiated smaller, revealing a size-dependent relapse threshold. We will tackle key challenges: mathematically characterizing the stochastic branching of metastatic spread and determining predictive factors for recurrence in residual primary tumor cells. We actively seek to bridge our rigorous in vivo time-series data with predictive computational models, aiming to calibrate parameters governing dormancy, reactivation, and metastatic colonization. We invite interdisciplinary collaboration to transform these biological insights into testable mathematical hypotheses that could ultimately inform adjuvant therapy timing.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

We model the distinct in vivo dynamics of donor-derived Memory Stem CAR T Cells and standard CAR T cells (Gattinoni et al., Cell 2026) with a novel approach of coupling a system of ODEs to a multi-type branching process. The entire cohort difference reduces to one parameter, the stem self- renewal probability, which sits on opposite sides of an analytically derived phase transition and accounts for both the low-dose efficacy and the observed clonal succession. A profile-likelihood analysis shows the data identify the supercritical-versus-subcritical regime rather than a precise value. Because the transition is a threshold, it suggests a categorical release criterion for manufacturing, and the same parameter accounts for the per-cell amplification that underlies the low-dose efficacy.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

We model the distinct in vivo dynamics of donor-derived Memory Stem CAR T Cells and standard CAR T cells (Gattinoni et al., Cell 2026) with a novel approach of coupling a system of ODEs to a multi-type branching process. The entire cohort difference reduces to one parameter, the stem self- renewal probability, which sits on opposite sides of an analytically derived phase transition and accounts for both the low-dose efficacy and the observed clonal succession. A profile- likelihood analysis shows the data identify the supercritical-versus-subcritical regime rather than a precise value. Because the transition is a threshold, it suggests a categorical release criterion for manufacturing, and the same parameter accounts for the per-cell amplification that underlies the low-dose efficacy.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Breastfeeding creates a feedback loop between milk removal by an infant or breastpump, and the stimulation of milk production. In this talk I will present and discuss a hybrid continuous/discrete mechanistic model that captures this process. The model is fitted to and tested against time-course data collected by wearable breast pumps. Model analysis allows to understand which pumping/feeding strategies lead to sustainable milk production, as well as how to optimize one's pumping/feeding strategy.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Breastfeeding creates a feedback loop between milk removal by an infant or breastpump, and the stimulation of milk production. In this talk I will present and discuss a hybrid continuous/discrete mechanistic model that captures this process. The model is fitted to and tested against time-course data collected by wearable breast pumps. Model analysis allows to understand which pumping/feeding strategies lead to sustainable milk production, as well as how to optimize one's pumping/feeding strategy.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Pancreatic cancer is one of the deadliest cancers, and despite decades of research, treatments remain largely ineffective. To make progress, scientists must look beyond the cancer cells themselves and examine everything surrounding them. This work uses mathematical models as a virtual laboratory to study two hidden forces that shape how pancreatic cancer grows: the nerves that infiltrate the tumor and the progressive hardening of the surrounding tissue. Nerves are not passive bystanders; some slow tumor growth, while others accelerate it. Meanwhile, tissue stiffening acts as armor around the tumor, making it harder for treatments to penetrate and be effective. By building mathematical models of these interactions, this work helps explain why the same treatment can succeed in one patient and fail in another and opens the door to more personalized therapeutic strategies.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Pancreatic cancer is one of the deadliest cancers, and despite decades of research, treatments remain largely ineffective. To make progress, scientists must look beyond the cancer cells themselves and examine everything surrounding them. This work uses mathematical models as a virtual laboratory to study two hidden forces that shape how pancreatic cancer grows: the nerves that infiltrate the tumor and the progressive hardening of the surrounding tissue. Nerves are not passive bystanders; some slow tumor growth, while others accelerate it. Meanwhile, tissue stiffening acts as armor around the tumor, making it harder for treatments to penetrate and be effective. By building mathematical models of these interactions, this work helps explain why the same treatment can succeed in one patient and fail in another and opens the door to more personalized therapeutic strategies.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Human blood cell production is maintained by hematopoietic stem cells (HSC) which give rise to all types of mature blood cells. Experimental observation of HSC in their physiologic bone-marrow microenvironment is challenging including malignant mutations of HSC. To investigate the significance of the interaction between the HSC, malignant HSC, the stem cell niche and chronic inflammation, we propose a mechanism-based mathematical model that takes into account several standard-of-care treatments as well as novel inflammation reducing treatments. The model was calibrated to individualized patient-data consisting of longitudinal hematologic and molecular measurements from several patient cohorts. We believe that this approach could have direct clinical relevance, offering expert guidance for clinical decision in terms of disease understanding and optimal treatment scheduling.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Human blood cell production is maintained by hematopoietic stem cells (HSC) which give rise to all types of mature blood cells. Experimental observation of HSC in their physiologic bone- marrow microenvironment is challenging including malignant mutations of HSC. To investigate the significance of the interaction between the HSC, malignant HSC, the stem cell niche and chronic inflammation, we propose a mechanism-based mathematical model that takes into account several standard-of-care treatments as well as novel inflammation reducing treatments. The model was calibrated to individualized patient-data consisting of longitudinal hematologic and molecular measurements from several patient cohorts. We believe that this approach could have direct clinical relevance, offering expert guidance for clinical decision in terms of disease understanding and optimal treatment scheduling.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Adaptive therapy is an evolution-based treatment paradigm has been shown to delay resistance in prostate cancer through treatment breaks that control, rather than minimize, tumor burden. However, patient responses are highly heterogeneous, and there is a significant unmet clinical need for biomarkers to personalize treatment scheduling. We develop and retrospectively validate mathematical biomarkers that predict time to progression (TTP), mean daily dose (MDD), and overall survival (OS) under adaptive therapy from first-cycle prostate-specific antigen (PSA) dynamics.This retrospective modeling and validation study utilized longitudinal clinical trial data from 2 independent cohorts: 45 patients with castrate-sensitive prostate cancer (CSPC) and 13 patients with metastatic castrate-resistant prostate cancer (mCRPC). Patients received either intermittent androgen deprivation therapy (for CSPC) or adaptive abiraterone acetate (for mCRPC). The initial treatment cycle served as the exposure period to extract longitudinal PSA kinetics. Mechanism-based mathematical biomarkers (AT Score, expected TTP, and expected MDD) were derived from first-cycle PSA kinetics. Outcomes included in silico benchmarking experiments and retrospective validation against clinical TTP and OS. Performance was benchmarked against standard phenomenological PSA metrics (e.g., PSA nadir, time to nadir, and doubling time). In the CSPC cohort (N = 40), the AT Score derived from first-cycle data was highly prognostic for prolonged clinical TTP. In the mCRPC cohort (N = 13), the AT Score exhibited a strong rank correlation with clinical TTP and was associated with prolonged TTP. Analysis of long-term survival data in the mCRPC cohort demonstrated that both the AT Score and eTTP were significantly associated with prolonged OS, whereas standard empirical PSA metrics displayed no association with survival. Mechanism-based mathematical biomarkers derived from the initial-cycle PSA dynamics accurately predict patient-specific outcomes and survival, outperforming traditional phenomenological PSA monitoring. We propose these accessible metrics as a mathematically informed decision-support framework to stratify patients into personalized treatment protocols.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Adaptive therapy is an evolution-based treatment paradigm has been shown to delay resistance in prostate cancer through treatment breaks that control, rather than minimize, tumor burden. However, patient responses are highly heterogeneous, and there is a significant unmet clinical need for biomarkers to personalize treatment scheduling. We develop and retrospectively validate mathematical biomarkers that predict time to progression (TTP), mean daily dose (MDD), and overall survival (OS) under adaptive therapy from first-cycle prostate-specific antigen (PSA) dynamics.This retrospective modeling and validation study utilized longitudinal clinical trial data from 2 independent cohorts: 45 patients with castrate-sensitive prostate cancer (CSPC) and 13 patients with metastatic castrate-resistant prostate cancer (mCRPC). Patients received either intermittent androgen deprivation therapy (for CSPC) or adaptive abiraterone acetate (for mCRPC). The initial treatment cycle served as the exposure period to extract longitudinal PSA kinetics. Mechanism-based mathematical biomarkers (AT Score, expected TTP, and expected MDD) were derived from first-cycle PSA kinetics. Outcomes included in silico benchmarking experiments and retrospective validation against clinical TTP and OS. Performance was benchmarked against standard phenomenological PSA metrics (e.g., PSA nadir, time to nadir, and doubling time). In the CSPC cohort (N = 40), the AT Score derived from first-cycle data was highly prognostic for prolonged clinical TTP. In the mCRPC cohort (N = 13), the AT Score exhibited a strong rank correlation with clinical TTP and was associated with prolonged TTP. Analysis of long-term survival data in the mCRPC cohort demonstrated that both the AT Score and eTTP were significantly associated with prolonged OS, whereas standard empirical PSA metrics displayed no association with survival. Mechanism-based mathematical biomarkers derived from the initial-cycle PSA dynamics accurately predict patient-specific outcomes and survival, outperforming traditional phenomenological PSA monitoring. We propose these accessible metrics as a mathematically informed decision-support framework to stratify patients into personalized treatment protocols.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Adoptive cell therapy, also known as cellular immunotherapy, aims at enhancing the cancer-fighting capabilities of the patient’s own immune cells. A promising approach is to genetically engineer immune cells to express a synthetic receptor, namely a chimeric antigen receptor (CAR), capable of targeting specific antigens (e.g. the MET receptor) expressed by cancer cells. Despite the potential of CAR-based immunotherapy to achieve durable clinical responses, a key obstacle to its efficacy is posed by antigen expression heterogeneity both within the same tumour and across patients. In this talk I will show how mathematical modelling, integrated with experimental data, can help predict the efficacy of CAR-based immunotherapy against antigen expression-heterogeneous tumours.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

Adoptive cell therapy, also known as cellular immunotherapy, aims at enhancing the cancer- fighting capabilities of the patient’s own immune cells. A promising approach is to genetically engineer immune cells to express a synthetic receptor, namely a chimeric antigen receptor (CAR), capable of targeting specific antigens (e.g. the MET receptor) expressed by cancer cells. Despite the potential of CAR-based immunotherapy to achieve durable clinical responses, a key obstacle to its efficacy is posed by antigen expression heterogeneity both within the same tumour and across patients. In this talk I will show how mathematical modelling, integrated with experimental data, can help predict the efficacy of CAR-based immunotherapy against antigen expression- heterogeneous tumours.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

To give the right treatment at the right time to the right patient is the mantra of personalized medicine. A framework that could facilitate personalized therapies is the so-called digital twin. I present the latest developments in mathematical and computational modelling in radiation oncology to develop digital twins. To personalize cancer radiation therapy, we must give the right dose and dose fractionation, at the right time, dynamically adapted, to best harness the radiobiological effects of radiation as well as synergy with the patient’s immune system. I present different simple approaches to build predictive pipelines and how to integrate those into clinical decision making towards the concept of real-time adaptive personalized radiation treatments. I will discuss past, present, and future clinical trials of such model-guided treatments.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 9th Workshop "Mathematics for Medicine (against Cancer)" (2026)

To give the right treatment at the right time to the right patient is the mantra of personalized medicine. A framework that could facilitate personalized therapies is the so-called digital twin. I present the latest developments in mathematical and computational modelling in radiation oncology to develop digital twins. To personalize cancer radiation therapy, we must give the right dose and dose fractionation, at the right time, dynamically adapted, to best harness the radiobiological effects of radiation as well as synergy with the patient’s immune system. I present different simple approaches to build predictive pipelines and how to integrate those into clinical decision making towards the concept of real-time adaptive personalized radiation treatments. I will discuss past, present, and future clinical trials of such model-guided treatments.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

In this talk, we study the long-time dynamics of two mesoscopic models for neuronal populations, with a particular focus on the role of synaptic delay and network connectivity. At this scale, the system is described by a probability density representing the distribution of neuronal states, such as the membrane potential or the time elapsed since the last discharge. More precisely, we analyze the behavior of the NNLIF (Nonlinear Noisy Leaky Integrate-and-Fire) model, formulated as a nonlinear Fokker--Planck type equation, and the age-structured model based on the time-since-last-discharge description. While entropy dissipation methods provide a natural analytical framework, they encounter significant limitations, especially in regimes of strong connectivity. We present alternative approaches based on two main ideas: first, the analysis of simplified discrete models, which provide fast and intuitive insight into the nonlinear dynamics; and second, a linearization around equilibrium combined with a reformulation of the problem as a Volterra-type integral equation. These techniques allow us to better understand the influence of delay and connectivity on the long-time behavior of the system. This talk is based on joint works with José A. Cañizo, Alejandro Ramos-Lora, and Nicolás Torres.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Population dynamics are often observed as distributions of individuals with respect to structuring variables such as size or age. The associated inverse problem consists of inferring the underlying vital rates (recruitment/birth, growth, and death) which are typically complex, nonparametric functions due to limited prior knowledge. Physics- Informed Neural Networks (PINNs) provide a natural framework for such problems by combining neural networks as universal function approximators with mechanistic constraints encoded in differential equations. In this talk, we showcase the ability of PINNs to solve inverse problems in the context of size-structured population dynamics governed by coupled PDE-ODE models, in two biological contexts: oocyte dynamics in fish ovaries and adipocyte dynamics in adipose tissue.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Many biological systems exhibit intermittent dynamics across a wide range of scales, where individuals alternate between distinct behavioral states over time, such as motion and rest, or directed and undirected movement. Examples include microswimmers such as bacteria, microalgae, and amoebae, as well as animal groups such as schools of fish and flocks of sheep. In this talk, I will present one unifying model to describe such systems. First, I will discuss the modeling of intermittent biased motion in microswimmers subjected to an external signal c(x). I will outline the minimal ingredients required for a model to reproduce directed motion of particles toward (or away from) the source of the signal. In the second part, I will focus on intermittent collective dynamics in animal groups, particularly small groups of sheep and large schools of fish. In both systems, transitions can occur between a collective stationary state and a collective moving state, despite the very different biological contexts involved. I will show how both scenarios can be described within a common theoretical framework based on active particles with discrete internal states. Finally, I will discuss the strengths and limitations of this approach, and explain why it provides a particularly effective description of these biological systems.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Many partial differential equations describe how a macroscopic density of particles/cells evolves in time. So, it is a natural question to ask whether there’s a microscopic (deterministic) model, which focuses on the interaction between each particles, that leads to a given macroscopic PDE. For second-order aggregation–diffusion equations, this connection has been proved, starting with the porous medium equation in 2001. In this work, we extend that framework to a fourth-order equation, that has applications in cell–cell adhesion in biological systems. This is a joint work with Alejandro Fernandez- Jimenez.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

I will talk about a model for a population that is structured in space and that diffuses heterogeneously. The model is based on a KPP equation with a “q-diffusion”, which is a framework that unifies various standard linear diffusion regimes: Fickian diffusion (q = 0), Stratonovich diffusion (q = 1/2), Fokker-Planck diffusion (q = 1). I will explore how the ability of persistence and how the asymptotic spreading speed depend on the parameter q and on the phase shift between the growth rate r(x) and the diffusion coefficient D(x). Those results demonstrate that persistence and spreading properties generally depend on q: for example, appropriate configurations of r(x) and D(x) can be constructed such that q-diffusion either enhances or diminishes the ability of persistence and the spreading speed with respect to the traditional Fickian diffusion. This work underscores the importance of carefully selecting diffusion models in ecological and epidemiological contexts, highlighting their potential implications for persistence, spreading, and control strategies. Joint work with Y.-J. Kim and L. Roques.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Grid cells, with their striking hexagonal firing patterns, are neurons which play a key role in the internal navigational system of mammals. This talk will concern a nonlocal Fokker- -Planck-type PDE which emerged in a pursuit to better understand the effects of noise on grid cell activity. When this model produces hexagonal neuronal network activity which persists when translated in accordance with the mammal's movement in physical space, the model is in a setting which enables the mammal's ability to orientate itself. But under which conditions could such activity emerge in the model?

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Pancreatic cancer is one of the deadliest cancers, and despite decades of research, treatments remain largely ineffective. To make progress, scientists must look beyond the cancer cells themselves and examine everything surrounding them. This work uses mathematical models as a virtual laboratory to study two hidden forces that shape how pancreatic cancer grows: the nerves that infiltrate the tumor and the progressive hardening of the surrounding tissue. Nerves are not passive bystanders; some slow tumor growth, while others accelerate it. Meanwhile, tissue stiffening acts as armor around the tumor, making it harder for treatments to penetrate and be effective. By building mathematical models of these interactions, this work helps explain why the same treatment can succeed in one patient and fail in another and opens the door to more personalized therapeutic strategies.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)

Collective cell migration is a fundamental process driving essential biological phenomena, including tissue morphogenesis, wound healing, and cancer metastasis. A key driver of these coordinated movements is cellular heterogeneity—be it in size, adhesive properties, signaling, etc. 2D models fail to capture the full interaction between cells, and 3D models can be computationally prohibitive. Based on cellular sub-element modeling, we present a pseudo-3D model to understand the movement of cells in tight groups.

• Thematic program: Quantitative Methods in Biology and Medicine (2026/2027)
• Event: 3rd Workshop on "Mathematical modeling in biology and medicine" (2026)