The Computational Modelling in Physiology and Medical Sciences (COMPAS) Research Group is based in the School of Computer Science and Applied Mathematics at Wits.
COMPAS brings together applied mathematics, computational modelling, machine learning and artificial intelligence to address problems arising in physiology, medicine and healthcare. Our aim is to develop mathematically rigorous and computationally practical approaches that improve our understanding of physiological systems, disease processes and clinically relevant decision-making.
A central philosophy of COMPAS is that meaningful advances in computational medicine require close interaction between mathematical scientists, data scientists, clinicians and biomedical researchers. We therefore work collaboratively with academic hospitals, clinical researchers and interdisciplinary partners to ensure that the problems we study are motivated by genuine healthcare challenges.
Our Research
Our research is organised around four interconnected themes.
- Computational Respiratory Medicine and Data-Driven Physiological Modelling
Respiratory medicine forms a major focus of COMPAS. We develop mathematical, computational and data-driven models to better understand respiratory physiology, disease and treatment.
Our work includes modelling lung mechanics, ventilator-induced lung injury, respiratory disease processes and paediatric respiratory conditions. We are particularly interested in combining physiological understanding with experimental and clinical data to develop models that can capture patient- and disease-specific behaviour.
An important emerging direction is the development of data-driven constitutive models of the lung, where mathematical descriptions of tissue mechanics are informed directly by physiological and experimental data. In the longer term, this work contributes towards computational representations of the lung that can be used to investigate disease, treatment and personalised physiological behaviour.
- Machine Learning and Artificial Intelligence in Medicine
COMPAS develops and evaluates machine-learning and AI approaches for medical and clinical applications, particularly where complex datasets can be used to improve disease prediction and understanding.
Current research includes respiratory disease prediction, paediatric asthma and RSV, tuberculosis, risk stratification and clinical prediction modelling. Our work extends beyond predictive accuracy to consider explainability, model calibration, uncertainty, threshold optimisation and clinical interpretability.
A key objective is to develop models that are not simply computationally accurate, but that provide meaningful and interpretable information within a clinical or biomedical context.
- Mathematical and Computational Modelling of Physiological Flows
We develop mathematical and computational approaches for understanding fluid-flow and transport processes arising in physiology and medicine.
Applications include intranasal drug delivery, mucociliary transport, arterial stenosis, cardiovascular flows and medically relevant jet-flow problems. These problems involve complex fluid behaviour and frequently require the modelling of non-Newtonian fluids, transport phenomena and coupled physical processes.
Fundamental mathematical methods underpin this research. Our expertise includes nonlinear differential equations, symmetry methods, conservation laws, similarity analysis, analytical and numerical methods, and non-Newtonian fluid mechanics.
This combination allows us to move between fundamental mathematical questions and their application to physiological and medical problems, using mathematical structure to develop reduced models, identify conserved quantities and obtain deeper insight into complex biological flows.
- Mathematical Modelling of Infectious Disease
COMPAS applies mathematical, statistical and computational approaches to problems in infectious disease, with a particular interest in tuberculosis and respiratory infections.
Our research includes TB transmission modelling, diagnostic and prediction modelling, bacteriophage-based interventions, and the analysis of clinical and epidemiological data. We are interested in understanding both individual-level and population-level processes and in determining how mathematical and computational models can contribute to improved disease understanding and intervention strategies.
Our Approach
COMPAS operates at the interface of mathematics, computation and medicine.
Rather than treating mathematical modelling, machine learning and artificial intelligence as separate disciplines, we investigate how mechanistic models, clinical and experimental data, and modern computational methods can complement one another.
Our research ranges from fundamental mathematical analysis and computational fluid mechanics to machine-learning models trained on clinical data and data-driven models of physiological systems.
Across these areas, we place particular emphasis on mathematical rigour, interpretability, physiological relevance, validation and translation to real-world healthcare problems.
Collaboration is central to this approach. We work with clinicians, biomedical researchers, academic hospitals and interdisciplinary research partners to identify important problems and develop computational approaches that remain connected to their physiological and clinical context.
Our Vision
Our vision is to establish COMPAS as a multidisciplinary research environment in which mathematics, computation and medical science come together to address important problems in human health.
We aim to contribute to both fundamental scientific understanding and the development of computational approaches relevant to healthcare challenges in South Africa, Africa and internationally.
Through interdisciplinary collaboration and the training of postgraduate researchers, COMPAS seeks to develop the next generation of researchers capable of working across the traditional boundaries between mathematics, data science and medicine.
