The study of the synergetic effects of multiple interacting disturbances on the dynamical behavior of a biological system has received extensive attention. However, the interactions among disturbances are highly complex and the impacts are not well understood. In this talk, I will discuss the development of mathematical models to study the effects of exogenous pressures on the dynamics of two distinct biological systems: respiratory neuronal networks and tree ecosystems. In the first part of the talk, I will introduce a framework for studying the control of breathing based on a Boolean representation. The constructed network mimics many features seen in the respiratory neuronal network and provides novel insights and new testable predictions. In the second part of the talk, I will present differential equations models incorporating the link between non-lethal harvesting and habitat reduction. The resulting models allow the derivation of a general formula to determine the rational non-lethal harvesting level and habitat size to ensure the sustainability of the plant ecosystem. Additionally, I will discuss the investigation of the optimal non-lethal sustainable harvesting policies that maximize the economic benefit for local populations, and the survival of the plant ecosystem based on the habitat size.
Dr. Maria Leite received her Ph.D from University of Houston in 2005. She held multiple positions in many Institutes and joined University of South Florida in 2014. Dr. Leite is currently an associate professor of Mathematics at the University of South Florida, St. Petersburg and is visiting Basque Center for Applied Mathematics in Spain. Her research is in the field of dynamical systems with focuses on theory and applications to ecology, neuroscience, epidemiology, biology and data science. Dr. Leite has published about 30 papers and received multiple grants.