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Plenary Talks
Plenary Talks
Title: Modeling Human Brain Function and Pathways of Neurodegeneration
Abstract: Neurodegenerative diseases (NDs) are complex disorders characterized by the progressive structural and functional deterioration of the brain. A common hallmark of many NDs is the accumulation of disease-specific misfolded and aggregated proteins, such as amyloid-beta and tau in Alzheimer’s disease, alpha-synuclein in Parkinson’s disease, and TDP-43 in Amyotrophic Lateral Sclerosis. In this presentation, we introduce a novel framework that integrates multiphysics and multiscale mathematical modeling, advanced discretization techniques, and computational learning paradigms to elucidate the mechanisms underlying neurodegeneration. The spatio-temporal dynamics of misfolded proteins are modelled via conformational conversion differential systems discretized with high-order polytopal finite element methods [1]. Additionally, multiphysics mathematical models of cerebral waste-clearance dynamics, a critical factor influencing the onset and progression of NDs, are described, along with an analysis of how pathological processes associated with neurodegeneration may increase epileptiform activity [2, 3].
Title: Modeling Human Brain Function and Pathways of Neurodegeneration
Abstract: Neurodegenerative diseases (NDs) are complex disorders characterized by the progressive structural and functional deterioration of the brain. A common hallmark of many NDs is the accumulation of disease-specific misfolded and aggregated proteins, such as amyloid-beta and tau in Alzheimer’s disease, alpha-synuclein in Parkinson’s disease, and TDP-43 in Amyotrophic Lateral Sclerosis. In this presentation, we introduce a novel framework that integrates multiphysics and multiscale mathematical modeling, advanced discretization techniques, and computational learning paradigms to elucidate the mechanisms underlying neurodegeneration. The spatio-temporal dynamics of misfolded proteins are modelled via conformational conversion differential systems discretized with high-order polytopal finite element methods [1]. Additionally, multiphysics mathematical models of cerebral waste-clearance dynamics, a critical factor influencing the onset and progression of NDs, are described, along with an analysis of how pathological processes associated with neurodegeneration may increase epileptiform activity [2, 3].
References:
[1] M. Corti, F. Bonizzoni, P. F. Antonietti, Structure Preserving Polytopal Discontinuous Galerkin Methods for the Numerical Modeling of Neurodegenerative Diseases, J. Sci. Comput., 100:39 (2024).
[2] I. Fumagalli, M. Corti, N. Parolini, P. F. Antonietti, Polytopal discontinuous Galerkin discretization of brain multiphysics flow dynamics, J. Comput. Phys., 513:113115 (2024).
[3] C. B. Leimer Saglio, S. Pagani, P.F. Antonietti, A p-adaptive polytopal discontinuous Galerkin method for high-order approximation of brain electrophysiology, Comput. Methods Appl. Mech. Eng., 446:118249 (2025).
Title: Quantitative models and approaches in medicine and biology
Title: Quantitative models and approaches in medicine and biology
Abstract: Modern medicine and biology increasingly depend on quantitative models that convert complex observations into testable mechanisms and predictions. In this talk, I will discuss how mathematical modelling, cognitive and computational neuroscience, machine learning, and multimodal imaging can jointly illuminate biological organisation across scales, from molecules and cells to circuits, behaviour, and clinical outcomes. Examples will include dynamical systems for physiological regulation, perceptual decision and multi-stability, network analyses of neural interactions, and data-driven tools for discovering biomarkers. We will also consider methodological challenges, including bias, reproducibility, causal inference, and validation.
Title: Classification of small excitatory-inhibitory networks using network ODE-equivalence
Abstract: In many biological networks there is a key distinction between excitatory and inhibitory connections. Examples where this distinction is of central importance are networks of neurons and gene regulatory networks. In this talk we plan to show how to use a theoretical result on coupled cell networks theory to classify small excitatory-inhibitory networks.
Title: Classification of small excitatory-inhibitory networks using network ODE-equivalence
Abstract: In many biological networks there is a key distinction between excitatory and inhibitory connections. Examples where this distinction is of central importance are networks of neurons and gene regulatory networks. In this talk we plan to show how to use a theoretical result on coupled cell networks theory to classify small excitatory-inhibitory networks.
Joint work with Manuela Aguiar (FEP and CMUP, University of Porto, Portugal) and Ian Stewart (Mathematics Institute, University of Warwick, United Kingdom).
References:
[1] M. Aguiar, A. Dias and I. Stewart. Classification of 2-node Excitatory-Inhibitory Networks. Mathematical Biosciences 373 (2024) 109205 DOI: 10.1016/j.mbs.2024.109205
[2] M. Aguiar, A. Dias and I. Stewart. Classification of 3-node excitatory-inhibitory networks. Mathematical Biosciences 380 (2025) 109372 DOI:10.1016/j.mbs.2024.109372
Title: Persistence of nonautonomous systems of differential equations with unbounded delays
Title: Persistence of nonautonomous systems of differential equations with unbounded delays
Abstract: In this talk, we present sufficient conditions for the persistence of the following class of nonautonomous systems of differential equations with unbounded delays
Abstract: In this talk, we present sufficient conditions for the persistence of the following class of nonautonomous systems of differential equations with unbounded delays
The presented class of systems is general enough to include several important models arising in mathematical biology. As applications of the main result, we derive sufficient conditions for the permanence of Nicholson, Mackey–Glass, and logistic systems. Finally, numerical simulations are provided to illustrate the theoretical results.
The presented class of systems is general enough to include several important models arising in mathematical biology. As applications of the main result, we derive sufficient conditions for the permanence of Nicholson, Mackey–Glass, and logistic systems. Finally, numerical simulations are provided to illustrate the theoretical results.
Joint work with Teresa Faria (Faculdade de Ciências, Departamento de Ciências Matemáticas and CEMS.UL, Universidade de Lisboa)
References:
[1] T. Faria and J.J. Oliveira, Persistence for a class of nonautonomous systems of differential equations with unbounded delays. Mathematical Biosciences 396, 109670 (2026).
Title: Vaccination Dynamics and Human Behaviour Feedback: A Mathematical Perspective
Abstract: Vaccination remains the most effective strategy for preventing and controlling infectious disease outbreaks. However, its success often reduces the perceived risk of infection, contributing to vaccine hesitancy and declining vaccine uptake. This presentation reviews mathematical modelling frameworks that captures the feedback between epidemiological dynamics and vaccination behaviour. In the first framework, within a game-theoretic setting [1], we consider an age-structured population with incomplete immunity and vaccination, assuming rational individuals facing age-dependent disease costs. Nash equilibria are characterized and the social welfare of vaccination strategies is evaluated [2]. To account for behavioural adaptation over time, the framework is extended by incorporating imitation dynamics, whereby individuals revise their vaccination decisions through social learning [3]. Because of the complexity of the resulting age-structured system, a simplified SIR model was first analysed to investigate its qualitative dynamics [4]. This analysis revealed a rich dynamical landscape, including periodic outbreaks and chaotic behaviour driven by the interplay between the imitation rate and perceived infection risk. Interestingly, these chaotic dynamics disappear when the age structure and incomplete immunity is reintroduced [5]. The study of models incorporating incomplete immunity through temporary and partial immune protection revealed that waning immunity acts as a stabilizing mechanism, substantially reducing the parameter region in which chaotic dynamics occur, with chaos persisting only under very low immunity waning rates or high protection against reinfection [6]. Furthermore, the results indicate that shorter immunity periods, combined with high perceived vaccination costs, can lead populations to rapidly abandon vaccination, increasing susceptibility to future outbreaks. Overall, these models demonstrate how demographic heterogeneity, behavioural adaptation, and immunological processes jointly shape vaccination decisions and epidemic dynamics. The results provide valuable insights into the design of public health interventions that are robust to behavioural feedback and changing patterns of population immunity.
Title: Vaccination Dynamics and Human Behaviour Feedback: A Mathematical Perspective
Abstract: Vaccination remains the most effective strategy for preventing and controlling infectious disease outbreaks. However, its success often reduces the perceived risk of infection, contributing to vaccine hesitancy and declining vaccine uptake. This presentation reviews mathematical modelling frameworks that captures the feedback between epidemiological dynamics and vaccination behaviour. In the first framework, within a game-theoretic setting [1], we consider an age-structured population with incomplete immunity and vaccination, assuming rational individuals facing age-dependent disease costs. Nash equilibria are characterized and the social welfare of vaccination strategies is evaluated [2]. To account for behavioural adaptation over time, the framework is extended by incorporating imitation dynamics, whereby individuals revise their vaccination decisions through social learning [3]. Because of the complexity of the resulting age-structured system, a simplified SIR model was first analysed to investigate its qualitative dynamics [4]. This analysis revealed a rich dynamical landscape, including periodic outbreaks and chaotic behaviour driven by the interplay between the imitation rate and perceived infection risk. Interestingly, these chaotic dynamics disappear when the age structure and incomplete immunity is reintroduced [5]. The study of models incorporating incomplete immunity through temporary and partial immune protection revealed that waning immunity acts as a stabilizing mechanism, substantially reducing the parameter region in which chaotic dynamics occur, with chaos persisting only under very low immunity waning rates or high protection against reinfection [6]. Furthermore, the results indicate that shorter immunity periods, combined with high perceived vaccination costs, can lead populations to rapidly abandon vaccination, increasing susceptibility to future outbreaks. Overall, these models demonstrate how demographic heterogeneity, behavioural adaptation, and immunological processes jointly shape vaccination decisions and epidemic dynamics. The results provide valuable insights into the design of public health interventions that are robust to behavioural feedback and changing patterns of population immunity.
Joint work with Paulo Doutor and Maria do Céu Soares (Center for Mathematics and Applications (NOVA Math) and Department of Mathematics, NOVA School of Science and Technology (NOVA FCT)).
Joint work with Paulo Doutor and Maria do Céu Soares (Center for Mathematics and Applications (NOVA Math) and Department of Mathematics, NOVA School of Science and Technology (NOVA FCT)).
References:
[1] C.T. Bauch and D.J.D. Earn, Vaccination and the theory of games. Proceedings of the National Academy of Sciences 101 (36), 13391--13394 (2004).
[2] F.A.C.C. Chalub, P. Doutor, P. Patrício and M.C. Soares, Social vs. individual age-dependent costs of imperfect vaccination. Mathematical Biosciences 375, 109259 (2024).
[3] C.T. Bauch, Imitation dynamics predict vaccinating behaviour. Proceedings of the Royal Society B: Biological Sciences 272 (1573), 1669--1675 (2005).
[4] P. Doutor, R. Castelhano, M.C. Soares, B.V. Guerrero, N. Stollenwerk, M. Aguiar and P. Patrício, Complex Dynamics in an Epidemic Model with Imitation-Driven Vaccination Strategy. SIAM Journal on Applied Dynamical Systems 24 (4), 3045--3062 (2025).
[5] P. Doutor, M. C. Soares, R. Castelhano, P. Patricio, Human Behavior in Models with Imperfect Vaccine in Mathematical Modelling of Multi-scale Control Systems: applications to human diseases (Vol. 14). American Institute of Mathematical Sciences (AIMS) (to appear).
[6] P. Doutor, R. Castelhano, M. C. Soares, B. Kooi, P. Patricio, Imitation dynamics in vaccination under partial and temporary immune protection. Mathematical Biosciences and Engineering, 23(5), 1315-1339 (2026).
Title: Progresses in personalized blood flow simulations using variational approaches
Abstract: Numerical simulations have proved in the past decades to be an important tool to provide additional clinical insight into several cardiovascular pathologies. Some of the remaining challenges are related to the pursuit of precise and personalized descriptions of blood flow. Integrating measured data into the simulations represents a means to achieve such a goal. Among several techniques, variational approaches have been tested with partial success. These approaches consist of trying to obtain, as a control variable, meaningful boundary conditions at artificial boundaries. Here, we present several new advances in this direction. First, we consider the issue of correctly adjusting fixed boundary conditions at artificial boundaries in truncated domains. In particular, we study the minimization of a velocity tracking functional with controls acting on part of the boundary, combined with non-standard outflow conditions of the type direction do-nothing. We then discuss a framework for the time-dependent case, where boundary conditions are adjusted using time-series observations. The proposed approach reduces the discrepancy between simulated and observed data and improves the reconstruction of relevant flow quantities such as velocity, pressure and wall shear stress, even in the presence of noise.
Title: Progresses in personalized blood flow simulations using variational approaches
Abstract: Numerical simulations have proved in the past decades to be an important tool to provide additional clinical insight into several cardiovascular pathologies. Some of the remaining challenges are related to the pursuit of precise and personalized descriptions of blood flow. Integrating measured data into the simulations represents a means to achieve such a goal. Among several techniques, variational approaches have been tested with partial success. These approaches consist of trying to obtain, as a control variable, meaningful boundary conditions at artificial boundaries. Here, we present several new advances in this direction. First, we consider the issue of correctly adjusting fixed boundary conditions at artificial boundaries in truncated domains. In particular, we study the minimization of a velocity tracking functional with controls acting on part of the boundary, combined with non-standard outflow conditions of the type direction do-nothing. We then discuss a framework for the time-dependent case, where boundary conditions are adjusted using time-series observations. The proposed approach reduces the discrepancy between simulated and observed data and improves the reconstruction of relevant flow quantities such as velocity, pressure and wall shear stress, even in the presence of noise.
References:
[1] M. A. Anwar, J. Tiago, Time-dependent strategy for improving aortic blood flow simulations with boundary control and data assimilation. Applied Mathematics and Computation 493 (15), 129266 (2025).
[2] P. M. Nogueira, A.L. Silvestre, J. Tiago, Steady Navier-Stokes Equations with Regularized Directional Do-Nothing Boundary Condition: Optimal Boundary Control for a Velocity Tracking Problem. Applied Mathematics and Optimization. Applied Mathematics and Optimization 91 (24) (2025).
Workshops
Workshops
Title: From Pharmaceutical Challenges to Biomathematical Opportunities
Title: From Pharmaceutical Challenges to Biomathematical Opportunities
Title: Predicting Toxicity of Chemical Mixtures in Soil Invertebrates
Title: Predicting Toxicity of Chemical Mixtures in Soil Invertebrates
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