Martinez, C.; Pere, M.

Fitting dynamic models to population data such as the logistic growth equation is a common practice for describing microbial growth, both in natural ecosystems and under research conditions. However, these models are limited to scenarios where the population stabilizes at equilibrium, making them unsuitable for systems like batch bioreactors, where populations decline after substrate depletion. In this work, we propose two new population models capable of accurately describing such dynamics while maintaining an interpretable structure in which each parameter has a biological meaning. These models incorporate the growth rate as a function of cumulative biomass, rather than solely the biomass concentration, thereby accounting for memory effects. We establish fundamental properties of these models and demonstrate their applicability and accuracy to describe data from batch bioreactors.