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)

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)

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)

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)

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)

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)