Workshop on Dynamical Systems: Theory, Modelling and AI 19–21 November 2025 

Day-2 programme

[Differential Equations in Natural World and in Physics]

Ecological and Epidemic Modeling with Nonlinear Systems, Economic Dynamics and Market Models via DEs, DEs in Climate and Environmental Science

Workshop Abstracts

Title: From Pest Dynamics to Public Health: Integrating Operations Research with Dynamical Systems Modelling 

Speaker: Linke Potgieter (Stellenbosch University, Stellenbosch)

Bio: Prof. Linke Potgieter is an Associate Professor at Stellenbosch University with research expertise in operations research. Her work focuses on developing and analysing models for integrated pest management, sterile insect release strategies, biological control, healthcare systems and epidemiology.

Abstract: This talk explores how operations research(OR)-integrated dynamical systems models can provide practical decision support for ecological and public health challenges. Examples ranging from managing invasive species (e.g., Eldana saccharina) to controlling measles epidemics are provided, transitioning from non-spatial to spatially explicit agent-based models. Non-spatial mean-field models, yield OR-based guidance on release ratio, timing, and economic viability for control measures like the sterile insect technique. Spatio-temporal reaction-diffusion models incorporate heterogeneity, informing strategic spatial allocation of releases and agricultural landscape management. In epidemic modeling, OR optimises resource allocation, such as vaccines and response teams, to minimise new infections during an epidemic.

Title: Fragmentation–coagulation problems with spatial transport and

diffusion

Speaker: Jacek Banasiak  (University of Pretoria, Pretoria)

Bio: Prof. Jacek Banasiak is the DST/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the University of Pretoria. He is a renowned Polish mathematician whose work spans applied analysis, mathematical modelling, and bioscience-related systems.

Abstract: Fragmentation–coagulation equations, first introduced by Marian Smoluchowski in 1916, describe the evolution of the distribution of sizes of clusters of particles that can clump together or split. The equations describe a wide range of phenomena, from animal grouping and fish schools, through droplet formation in aerosols, dissolution processes, to rock crushing and planetesimal formation. Most work in the field has been done for spatially homogenous problems in many cases, however, neglecting spatial effects is not justified. While, in general, the problem is very complex, its simpler, yet still important in application, versions yield to relatively straightforward analysis, which we will discuss in this talk.

References J. Banasiak, W. Lamb, and P. Lauren¸cot, Analytic methods for coagulationfragmentation models. Vol. 1&2, Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, FL, 2020.

Title: A coagulation toy model for silicosis

Speaker: Fernando P. da Costa (Univ. Aberta, and CAMGSD, Técnico, Univ. Lisboa, Portugal)

Bio: Prof. Fernando Manuel Pestana da Costa completed his Habilitation in 2009 and is currently a Professor at Universidade Aberta, Lisboa, Portugal. He has published 34 peer-reviewed journal articles, six conference papers, and two books, along with 53 technical contributions. He has participated in 25 scientific events, including 17 international meetings, and has supervised one Ph.D. thesis and twelve master’s dissertations in Mathematics and Physics. His research spans differential equations, mathematical modelling, and the analysis of coagulation–fragmentation systems, with additional contributions to self-similar solutions, asymptotic behaviour, Lotka–Volterra equations, and non-autonomous differential equations. Throughout his career, he has collaborated with 73 co-authors across various scientific projects, and he maintains an active interest in the teaching and dissemination of mathematics.

Abstract: We present a system with a countable number of ordinary differential equations of coagulation type that can be considered a simple model for the silicosis mechanism. Silicosis is a respiratory disease due to the ingestion of quartz dust and their accumulation in the lungs. The mathematical model consists in an ODE for the concentration of free quartz particles, an ODE for the concentration of macrophages without quartz (cells of the immune system that identify, capture and try to expel entities strange to the body), and a countable number of ODEs each one describing the concentration of macrophages with a number $i\in\mathbb{N}$ of captured quartz particles. We briefly describe basic results such as existence, uniqueness, regularity, and semigroup results of the set of solutions. Then we study the dynamics of the infinite dimensional system in the case of a particular class of rate coefficients that allows for the decoupling of the full infinite dimensional system into a finite dimensional one and a lower triangular infinite system. By the analysis of the finite dimensional subsystem, we conclude that it has a saddle-node bifurcation, possessing two equilibria when a bifurcation coefficient which is the ratio of the input rate of quartz to the rate of creation of empty macrophages is below a critical value, and no equilibria above that value. The stability properties of the bifurcating branches of the full infinite dimensional system are studied.

Note: Based on works with P. Antunes, M. Drmota, M. Grinfeld, J.T. Pinto, and R. Sasportes.

Title: Eco-evolutionary modelling with adaptive dynamics

Speaker: Pietro Landi (Stellenbosch University, Stellenbosch)

Bio: Dr. Pietro Landi is a Lecturer in Applied Mathematics at Stellenbosch University. He holds a Ph.D. from the Politecnico di Milano in Italy and specializes in ordinary differential equations, difference equations, and dynamical systems. His research expertise spans mathematical modelling, nonlinear dynamics, and the analysis of complex evolutionary processes.

Abstract: Adaptive dynamics is a mathematical modelling framework based on ordinary differential equations to describe evolutionary dynamics driven by the underlying ecological interactions. When such interactions are mediated by phenotypes (traits), adaptive dynamics allows the definition of invasion fitness and selection gradient, that drive the evolution of the traits. Furthermore, when selection vanishes, higher order derivatives of the fitness determine the possibility of evolutionary branching and phenotypic diversification. This framework is applied to a variety of ecological models. 

Title: A Geometric Approach to the Linearization of Differential Equations

Speaker: Andronikos Paliathanasis (Stellenbosch University, Stellenbosch)

Bio: Dr Andronikos Paliathanasis is a researcher in theoretical and mathematical physics, with a background in the geometric and algebraic analysis of differential equations, symmetry methods, and their applications in cosmology and gravitational theories. Dr. Andronikos Paliathanasis is a Research Fellow in the School for Data Science and Computational Thinking at Stellenbosch University. 

Abstract: We introcuce a novel geometric framework for the linearization of point-like Hamiltonian dynamical systems. By employing the Jacobi metric together with the Eisenhart–Duval lift, we establish a direct correspondence between linearization techniques and maximally symmetric spacetimes. This perspective highlights the role of variational symmetries in constrained Hamiltonian systems and shows how they can be systematically used to construct new linearized models. As an application, we explore the shared solution space of General Relativity within this framework, offering new insights into the structure of Einstein’s field equations. 

Title: What are isotope-enabled hydrological models, and why are they useful?

Speaker: Andrew Watson (Stellenbosch University, Stellenbosch)

Bio: Andrew Watson is a Senior Researcher in the School for Climate Studies at Stellenbosch University. His work focuses on Climate Change and Hydrological Modelling.

Abstract: Hydrological models are important tools for understanding water resource availability and crucial for decision-making during extreme conditions, such as extended dry and wet periods, but where data availability impacts which models can be used and applied. In detailed process simulation models used in hydrology, such as numerical models which are often used in groundwater and climate simulations, input data requirements are often extensive. Simplistic conceptual models which are more reproducible often lack crucial process evaluation, such as soil-water and baseflow simulations. Here we show how stable water isotopes of δ2H and δ 18O which contain crucial information about water movement and sources can be used to improve the simulations of conceptual models. These tracers can circumvent huge data requirements of complex models where the mathematical functions of isotope composition according to phase change have been well established.

Title: Bayesian inference of interaction rates in a metabolite-bacteria network using time-series counts

Speaker: Jack Jansma (Department of Mathematical Sciences, Centre for Invasion Biology, Stellenbosch University, Matieland 7600, South Africa)

Bio: Dr. Jack Jansma is a Postdoctoral Fellow in Mathematical Sciences, with research interests at the interface of mathematics and microbiology. His work focuses on the dynamic interplay between host and microbe, interactions within microbial communities, and the mathematical modelling of microbial systems.

Abstract: The human gut hosts a vast and diverse set of microbes that indirectly interact with each other through consuming and producing compounds, called metabolites. Disruptions in this network between gut microbes and their human host can contribute to the onset and progression of various disorders, including obesity, inflammatory bowel syndrome and Parkinson’s disease. Understanding the intricate and dynamic interactions between microbes, metabolites and the host is essential for developing microbiota-targeted interventions to improve human health. To this end a precise mathematical framework is crucial to capturing the complex dynamics of the system.

Here, we develop a dynamic network model of coupled ordinary differential equations and present a computational workflow that integrates computer algebra with Bayesian inference for model identification. Our approach infers interaction rates—quantifying metabolite consumption and production—from experimental time-series count data within a Bayesian framework, incorporating prior knowledge and uncertainty quantification. This workflow enables in silico predictions of system behaviour under perturbations and offers a robust method to integrate high-dimensional biological data with mechanistic models. By refining our understanding of gut microbial dynamics, this framework facilitates the assessment of microbiota-targeted therapeutic interventions.

Keywords: Gut microbiota, Bayesian inference, Ordinary differential equations

Title: Emergence of structure in plant–pollinator adaptive networks

Speaker: Mukhtar Yahaya (Stellenbosch University, Stellenbosch)

Bio: Mukhtar Yahaya is a Ph.D. candidate at Stellenbosch University. His work focuses on Informatics and modelling of transformative ecosystems.

Abstract: Specialisation enhances the efficiency of plant–pollinator networks through the exchange of conspecific pollen transfer for floral resources. Floral resources form the currency of plant–pollinator interactions, but the understanding of how floral resources affect the structure of plant–pollinator networks remains modest. We develop a mutualistic Lotka–Volterra consumer-resource model to investigate the influence of floral resource availability on plant–pollinator network structure. The model incorporates animal adaptive foraging behaviour, floral resource dynamics, and density-dependent dynamics. Specialisation, nestedness and modularity of simulated networks generated from the model under a wide range of parameters were explained using the generalised linear model. We found that the distinction between floral resource dynamics and plant density dynamics was necessary for partial specialisation of plant–pollinator networks. This is because floral resource dynamics constrained animal preference due to its depletion by animal species. Floral resource abundance had a positive effect on network specialisation, but animal density had a negative effect on network specialisation. Floral resource dynamics thus play key roles in the structure of plant–pollinator networks, distinctive from plant species density dynamics.

Title: Perception-based agent movement in uncertain environments using Integro-PDEs

Speaker: Richard Gibbs (Stellenbosch University, Stellenbosch)

Bio: Richard Gibbs is a Ph.D. candidate at Stellenbosch University. His work focuses on Perceptions and games of adaptive foragers.

Abstract: The movement behaviour of animals is remarkably efficient at consistently fulfilling multiple goals. However, this does not mean that animals possess a complete or even accurate understanding of their environment. Rather, an animal's environmental perception is built (and updated) through its subjective experience. It is then this perception - rather than the real world – that informs large-scale movement decisions. As such, an animal’s home-range (its terminal space-use pattern) is inherently linked to the formation and upkeep of its environmental perception. By pairing a system of Integro-PDEs of individual-level memory dynamics with an adaptive, state-based movement protocol, we propose a novel mechanistic model of animal movement behaviour. This model explicitly considers the shared relationship between an agent’s movement and the dynamics of environmental perception. We briefly show how the model allows an agent to efficiently and adaptively maintain its state whilst foraging from a wide range of 1D resource landscapes with varying degrees of spatial and/or temporal heterogeneity. We also highlight key environmental and cognitive factors which may drive the agent towards sub-par behaviour by falling into ecological traps of varying severity.

Title: Bridging Spectral Methods and Machine Learning in Fractional Dynamical Systems

Speaker: Imran Talib (Virtual University, Lahore, Pakistan)

Bio: Dr. Imran Talib is an Assistant Professor of Mathematics at the Virtual University of Pakistan, specializing in scientific computing, fractional calculus, and neural network–based numerical methods. He earned his PhD in Mathematics from the University of Management and Technology, where he developed advanced spectral and operational matrix–based algorithms for integer- and fractional-order differential equations. With over a decade of teaching and research experience, Dr. Talib has published extensively in high-impact journals and has collaborated with leading mathematicians worldwide. His work integrates rigorous theoretical analysis with high-performance computational techniques, particularly in solving complex fractional, delay, and nonlinear dynamical systems. He has supervised eight MS and two PhD theses, delivered invited talks internationally, and continues to advance innovative numerical frameworks that bridge classical mathematical theory with modern machine learning and neural network approaches.

Abstract: Spectral numerical techniques such as the Spectral Tau method, Spectral Collocation method, and the fully Operational Matrix approach based on the operational matrices of orthogonal polynomials have been extensively applied to solve fractional-order ordinary and partial differential equations arising in dynamical systems. These methods are well known for their global convergence and high accuracy. However, their practical implementation is heavily dependent on the construction of operational matrices, which increases both the computational cost and the theoretical effort required. In the fully Operational Matrix framework, both derivative and integral operational matrices must be constructed. Similarly, the Tau and Collocation methods require derivative or integral operational matrices, with additional challenges such as the selection of suitable collocation points in the collocation method or the formulation of a residual function in the Tau method. These requirements often make the methods less user friendly and computationally expensive, particularly when extending them to large-scale problems. Moreover, the operational matrix approach, while avoiding residual functions and collocation point selection, remains highly dependent on the construction of multiple operational matrices. For example, initial value problems typically require derivative and integral operational matrices, whereas boundary value problems necessitate additional operational matrices to handle monomial terms. Problems with variable coefficients also demand the construction of further operational matrices. This heavy reliance reduces the flexibility and efficiency of the classical spectral framework. In this talk, we develop a hybrid methodology that merges the accuracy of spectral approaches with the adaptability of machine learning. Specifically, operational matrices of fractional derivatives in the Caputo sense are constructed using orthogonal polynomial bases and incorporated into the architecture of neural networks, where the bases elements serve as activation functions. The network weights are trained using the Extreme Learning Machine algorithm, which ensures fast convergence and significantly lowers computational costs. Numerical experiments, including fractional-order ordinary and partial differential equations, demonstrate that the proposed hybrid approach not only addresses the limitations of conventional spectral methods but also provides an efficient tool for simulating fractional- order dynamical systems. This framework unifies spectral techniques with neural computation, opening new directions for the accurate modelling of complex dynamical phenomena.

Title: Quantum complexity of neutrino flavour oscillation

Speaker: Luyanda Mazwi (Univerity of Johannesburg, Johannesburg )

Bio: Mr. Luyanda Mazwi is a Junior Lecturer in Physics at University of Johannesburg. 

Abstract: Neutrino flavour oscillation presents the potential to probe physics beyond the standard model. The unresolved questions related to neutrino oscillation are the neutrino mass hierachy and what are the constraints on some of the paramters governing flavour oscillation, in particular the mixing angle θ23 and the Charge-Parity violating phase δcp. In this study we aim to apply one of the measures from Quantum Information theory, Quantum complexity to neutrino flavour oscillation in an attempt to answer these questions. Quantum complexity, is the measure of ”difficulty” in constructing a particular quatum state from a set of universal unitary operators (or quantum gates). In particular, we will make use of Nielsen complexity, a geometric approach to computing complexity. We use complexity to measure the difficulty in moving from the identity operator at an initial time of t = 0 to the time evolution unitary operator produced by the Hamiltonian in the flavour basis at time t. We make use of a group manifold approach, and attempt to calculate the complexity of firstly two flavour and then three flavour neutrino oscillation. We then show how these oscillation parameters affect the complexity of these oscillations.