Research Highlights and Recent Online Talks (scroll down for links):
Dynamics of human behaviour at individual and population levels
Environmental issues are currently at the forefront of our social lives, Most policy makers are now trying to determine the best policies and strategies towards a decrease in harmful emissions and in consumption of nonrenewable resources. Such policies need solid models of individual and population behaviour, since no policy is successful unless it is adopted by a high enough population mass. Thus the question we address here is to quantitatively and qualitatively analyze a population of individuals' decision making process with respect to adoption of green products and technologies.
We study two types of mathematical models of environmental choices in a population, over a given time interval. Each individual is assumed to make both rational decisions(to optimize their well being) and subjective ones (for example decisions based on their personality type and/or their social relations). The first type of model is based on differentiated product market models, partial differential equations and dynamical systems. The other type of model is based on a computational approach, where we simulate the dynamics of a population of individuals with a method called "agent-based", using numerical codes specifically designed for our questions. In a population of consumers making "adopting" decisions based on: product prices, perceived health benefits, global and local social influence, personality type and income, both types of models allow one to compute the adoption level of green products in the population under a wide range of parameters,while allowing for the design of policies that will effectively "move" the population towards a more environmentally friendly behaviour.
Current students working on these topics: Hogg, Kuusela, Gheorghiade.
Hybrid Dynamical Systems
I am working on the applications of dynamic games in vaccination behaviour. More specifically, the problem of modelling strategic interactions of various groups within a population under voluntary vaccination policy. We show that vaccination games (both static and dynamic) have solutions, we compute them and study their behaviour under perturbations. The question of accounting for variations in the perceived relative risk of vaccination versus infection across population groups (i.e., the question of treating a population as a heterogeneous entity) has not been formalized in an epidemiological model using tools of variational analysis before. We look as well at how a known vaccination coverage profile in a population can be obtained from the optimal vaccination strategies of each individual population group over a time interval of interest.
Recently, we started looking at hybrid dynamics relating SIR-type models and vaccination, as well as SIR-type models of HIV infection and their possible formulation in a hybrid systems framework. Last but not least, we study hybrid systems blending emergent dynamics in a population, and discrete decision making events.
Current students working on these topics: Greenhalgh
I am also interested in studying constraint dynamical systems, i.e. systems whose flow is only allowed to evolve within a subset of the underlying space. More specifically, I work on infinite-dimensional projected systems (PDS) which are linked with various formulations of known applied problems, such as optimization problems, games and network problems. These systems effectively give a mathematical meaning to what is called "equilibrium" in the type of problems above, namely their equilibrium is a critical point of a differential equation.
PDS models apply to problems ranging from transportation networks, spatial price equilibria, human migration etc., but current investigation issues regard their use in studying stability of the equilibria under perturbations, as well the extension of these systems to Lp-spaces.
Current students working on these issues: Greenhalgh, Gheorghiade
Online Invited Lectures: Brescia 2011 - part I
Brescia 2011 - part II
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