I tackle problems in biology concerning the evolution of disease and epidemics. My most recent work focused on the disease dynamics of the Daphnia-Metschnikowia system in collaboration with the Cáceres Lab and Zoi Rapti (advisor).
Stemming from the broader work of mathematical epidemiology, I use ordinary and partial differential equations to study how quantities such as disease prevalence and the basic reproduction number change due to variations in the host and environment.
"Stochastic Models for Recurrent Epidemics" (2019)
"The Role of Recovery in Daphnia disease dynamics" (2018)
" Behavioral Adaptation in Daphnia populations" ( 2017)
" Host polymorphism in Daphnia epidemics" (2015)
" Evolutionary Dynamics of Virulence" (2014)
Disease ecology studies the interactions among hosts, pathogens, and the environment and how these shape the spread of disease. These interactions can be quite complex and lead to fascinating dynamics. Our system of study, Daphnia has a lot of interesting and complex features that can be analyzed with precision both biologically and mathematically.
By using mathematical models we can study the underlying biological mechanisms that drive and/or inhibit the spread of disease. This dissertation explores, through a range of models, the many aspects that play a role in Daphnia epidemics. We begin with simple models and build models with higher complexity by adding more realistic biological assumptions.
Visualizing Mathematics and its Applications (2019).
Evaluating models for social group competition (2019).
Modeling prevalence of JUUL and other E-Cigarrete use .
Genetic algorithms to model molecular clocks in Python (2018).