We extend the mathematical model for algae growth as described in  to include
new effects. The roles of light, nutrients and acidity of the water body are taken
into account. Important properties of the model such as existence and uniqueness
of solution, as well as boundedness and positivity are investigated. We also discuss
the numerical integration of the resulting system of ordinary differential equations
and derive a condition which guarantees positivity of the numerical solution. An
optimization problem is formulated which demonstrates an application of the model.