As a biologist I can suggest you two methods to estimate carbon biomass of phytoplankton (No idea about mathematical model!).
1). To estimate the biovolume of phytoplankton, geometric shape based formulae are available. From the biovolume of each group/species, we should calculate the carbon biomass using published conversion factors.
(Eg. Biovolumes and Size-Classes of Phytoplankton in the Baltic Sea).
So many standard articles are available online about the biomass content of each plankton group.
2). Biomass estimation of the substance/phytoplankton using the equipment CHN analyzer (carbon, hydrogen and nitrogen).
Could you be more specific? What I can tell you now is a bit of a cliché, but you should use the simplest model that reflects the behaviour of your system. Also, you must define what is that you want to measure and use as a input to the model.
What I would understand as a vegetative stage is a more or less stable population. However, within that population you have cells dying and others growing; and if you have a mixed population, there might be interactions and oscillations. you will also have oscillations due to the light cycle, and so on.
Therefore, it is essential to define what is you research question, your goal.