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This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994. After reading a summary of articles written on the incidents, students are guided through the process of creating a first order differential equation from a verbal model of the factors and analyze the nonautonomous ODE using direction field, parameter evaluation, and exact solution computation to fully describe the population behavior. Students are expected to be familiar with the separable method and direction fields. Students will learn building and improving a model from qualitative descriptions, nondimensionalization, evaluating parameters, and how to use DFIELD software to interactively analyze a first order differential equation. An alternative modeling investigation of this problem leads to a nonlinear system of equations shown in modeling scenario "Algae Self-Replenishment"


Originally published as:

Richard Corban Harwood, "1-65-S-Algal Blooms: Algal Blooms Threatening Lake Chapala,'' Systematic Initiative for Modeling Investigations and Opportunities with Differential Equations, (2016) Available at

A Teacher Version with solutions is available at this source for those who register (free for educators) at