PhD Math Defence: Dynamics of Coupled Human and Natural Systems in Epidemiology and Ecology

CANDIDATE:    KAMAL JNAWALI

Many natural systems exist in a state of two-way coupling with human systems, where changes in the human system create changes in the natural system, which in turn create changes the human system once again. The study of dynamics of such coupled human-and-natural systems is a growing area of research. For instance, in the case of influenza antiviral drug use during a pandemic, widespread use of antiviral drugs is a main contributor to the evolution of drug-resistant strains, and recent studies show that influenza viruses can acquire drug resistance without incurring a fitness penalty that reduces their transmission rate. This phenomenon illustrates a coupled human-and-natural system since an influenza pandemic causes a human population to respond with antiviral drug use, which in turn changes influenza epidemiology. It also creates the possibility of strategic (game theoretical) interactions between humans making decisions about antiviral drug use strategies. On the other hand, the dynamics of endangered ecosystems can also illustrate a coupled human-and-natural dynamic, where processes such as agricultural expansion, migration and urbanization, road construction, mining and industry can endanger rare ecosystems, which in turn can stimulate human populations to enact conservation measures. Stochastic effects are important for evaluating the likelihood of extinction of a rare ecosystem, but stochasticity has been little studied in the context of extinction in coupled human-and-natural systems. This dissertation develops and analyzes a 2-player game theoretical model of influenza antiviral drug use, with both (i) 2 strategies with payoffs based on a fixed matrix and (ii) a continuous strategy set with payoffs determined by a stochastic differential equation model of influenza transmission and drug resistance. It also develops and analyzes (iii) a stochastic differential equation model to explore extinction and conservation opinion dynamics in a coupled forest-human system. The influenza models predict a coordination game between the two jurisdictions, where both players either choose a socially optimal low antiviral drug treatment rate or a suboptimal high treatment rate. This prediction of two co-existing Nash equilibria is robust to the mutation rate and the effectiveness of the drug in preventing transmission, but it is sensitive to the volume of travel between the two jurisdictions. In the coupled human-forest model, we predict a new mechanism that we call stochasticity-induced persistence, whereby an increase in stochasticity under certain conditions can actually make the natural population more likely to persist, instead of going extinct due to stochastic fade-out. All three models show how coupled human-and-natural systems can have novel dynamics that are not predicted when the human and natural systems are studied in isolation from one another.