A morbidostat is a more advanced chemostat device for developing a microbial culture, where continuous amount of an antibiotic drug is injected/diluted when the total microbes is more/less than some threshold value. During the course of evolution, we are interested in which mutants prevail because of their drug resistance. We introduce a system of ODEs with a drug-on-off-condition to model the morbidostat. Then we study the mathematical structure of morbidostat, especially on the aspect how the global dynamics depends on the threshold value. This ongoing research is motivated by Prof. Sze-Bi Hsu.