Recovering Population and Growth Rate of Bacteria Within a Two-Tank Interconnected Chemostat Model using Data Assimilation

The chemostat is a popular laboratory device that is used for growing and maintaining a population of microorganisms. The well-studied single chemostat model is often not realistic for real-world applications such as monitoring populations of microorganisms like lake plankton. Instead, models using a finite number of interconnected chemostats, the so-called gradostat model, often provide more insight for applications that occur in large environments, such as lakes or reservoirs, where liquid mediums are not necessarily well-mixed. Additionally, gradostats have been shown to improve the performances of bioprocesses through decreasing residence time or increasing species persistence. Extensive studies have been done on the behavior and steady state solutions of the general gradostat model. However, it still remains a common problem that, given a noisy set of data observed from one tank, one must estimate and reconstruct the parameters and state variables for the remaining tanks. In this study, we consider a two-tank gradostat model where data is collected from the outflow of the second tank. From here, we develop a data assimilation algorithm to recover the growth rate and population dynamics for the first tank. We conclude with some discussion on extending this model to a larger number of tanks and how data would need to be collected within the larger model to accurately recover the growth and population dynamics.