Starting Year: 2023
Title: CoSysM3 – Mathematical Modelling of Multi-scale Control Systems: applications to human diseases
Abstract: The CoSysM3 project aims to contribute to the scientific advance in the mathematical modelling of behavioural epidemiology, building new hybrid models and generalising results and methods from the theory of systems and control through its application to infectious and autoimmune diseases. These mathematical challenges, applied to human diseases, are in alignment with Goals 3 and 4 of 2030 Agenda – Good Health and Well-being and Quality Education. Theoretical and numerical mathematical results will be proved, providing in turn solutions to control the spread of epidemics and the effective treatment of some autoimmune
diseases. We propose to develop a new hybrid modelling approach that will allow the simulation of complex epidemic scenarios and their control. CoSysM3 is a Biomathematics research project, with emphasis on human diseases, and will contribute to the introduction of Applied Mathematics topics in the graduation and post-graduation levels, in line with Goal 4 of the 2030 Agenda – Quality Education. Mathematical tools will be used to study biological processes and provide optimal solutions for the prevention and treatment of human diseases. Key mathematical topics in this project are theory of differential equations (ordinary, partial and fractional), optimal control theory, theory of dynamical systems, statistical methods, computational methods, and numerical simulations. The main objectives of the project are detailed in its four tasks: impact of human behaviour in disease control; new generation of hybrid models – computed timed automata and validation; multi-scale modelling of autoimmunity; optimal control and applications to human diseases. In CoSysM3 we intend to study the inclusion of human behaviour in epidemiological models. New challenges are imposed in the control of disease transmission due to behavioural changes in the population. An example is the refusal to vaccinate, which is closely linked to the perception of low risk, when herd immunity is reached. We intend to develop compartmental models that include human behaviour and find interventions that take advantage of voluntary vaccination while maintaining an acceptable social cost, in the context of vaccines that only provide temporary protection. The study of these interventions will give rise to new optimal control problems. Changes in mobility behaviour due to awareness of the risk of infection also have direct consequences on disease control. To describe this influence, we propose to use reaction-diffusion models with behaviour-dependent coefficients and to introduce superdiffusion models for disease transmission to better describe the spread of the disease at a global level. The study of these models implies defining adequate numerical schemes and generalising the concept of the basic reproduction number (R0) to the considered operators. In the sequel, modelling the influence of social behaviours on the dynamics of disease spread supposes a coupling of macroscopic (collective behaviours) and microscopic (individual decisions) approaches, requiring an innovative modelling approach, which combines the classic formalisms retained in each micro-macro category of scale. This combination supposes an enlarged global framework which leads to a new generation of hybrid models that we are dedicated to build. We will rely on the most recent studies to calibrate hybrid epidemic models by comparing them with statistical data. Motivated by the potential of mathematical models in giving valuable predictions about the development of the disease and its medical treatment, CoSysM3 members will continue to develop a research line on mathematical modelling of autoimmune diseases, based on kinetic theory approach to describe an autoimmune episode and extending to optimal policies for the immunotherapeutic treatment. Being based on a kinetic theory approach, these models show a multi-scale description in terms of a kinetic system and its macroscopic analogue. They have the advantage of describing, not only the collective behaviour of the populations, but also the cellular activity and the individual behaviour of cells. We will exploit the micro-macro interplay of these models and study other challenging problems at the level of modelling descriptions, rigorous analysis and biological predictions based on numerical simulations. One of the main goals of CoSysM3 is to develop control strategies that minimize the negative impact of certain social behaviours on epidemic dynamics. By extending optimal control methods to the study of hybrid epidemic models and micro-macro models for autoimmune diseases, new challenges are foreseen that may contribute to the generalization of systems and control theory to new contexts.
Funding Source: FCT – Fundação para a Ciência e a Tecnologia, I.P.
Typology: R&D Project
Reference: 2022.03091.PTDC
Principal Investigator (PI): Cristiana Silva
PI’s institution: Universidade Aveiro
NOVA Math members involved: Paula Patrício, Paulo Doutor, magda Rebelo, Fabio Chalub, M Céu Soares