Investigations
These are working notes, not peer-reviewed papers. Each one starts with a concrete question, pulls from a public dataset, analyzes the data, and shows the math behind the answer.
Mathematical Models of Growth and Spread
From Tumor Kinetics and Epidemic Dynamics to Predator-Prey Oscillation
Modeling Tumor Growth Using Differential Equations
How accurately do classical growth models (exponential, logistic, Gompertz, and von Bertalanffy) describe observed tumor volume trajectories, and which model best captures the deceleration of growth at large volumes?
Predicting Disease Spread: SIR and Beyond
How does the basic SIR model's prediction of epidemic trajectory compare to observed COVID-19 outbreak data, and what extensions are necessary to capture real-world dynamics?
Population Dynamics Simulations: Predator-Prey Systems
Do the oscillatory dynamics of predator-prey systems observed in the field conform to Lotka-Volterra predictions, and what parameter regimes produce stable limit cycles versus chaos?
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