PhD Math Defence: Time-Dependent Decision Making, Prevalence of Disease and Social-Economic Effects via Games and Constraint Dynamics

CANDIDATE:   SAFIA ATHAR

Decisions frame many aspects of our lives. We make decisions daily, as individuals or as a part of like-minded groups. Most of the time we strive to make rational decisions, and we endeavour to reach optimal ones for our own or the population's benefit. Decision-making is intertwined scientifically in research areas such as in optimization, probability theory, game theory and operation research with the objective of helping to identify and reach optimal decisions in a variety of contexts: public policy, engineering, transportation, health, communications, etc. In the presence of risk factors, decision-making becomes more convoluted and needs to be studied carefully by taking into account all the factors involved.

This thesis explores different perspectives on undertaking decisions at the individual level and the population level, under various risk factors either perceived or objective. We also study the impact of the time evolution of individuals', or groups of individuals' decisions, on the prevalence of some infectious diseases (such as HIV, influenza or paediatric diseases), and consequently the population's regional socio-economic well-being. We use game theory, non-smooth dynamics and compartmental models to build and analyse our models. The essential focus of the thesis is to investigate the effects of decision-making at the individual, population and system (population & governing authority) levels on the evolution of the disease. Moreover, we study the potential policies that can be implemented to alleviate some of the socio-economic impacts of the disease.