The qualitative apparatus of dynamical systems theory enables one to construct models in an axiomatic fashion, thus allowing to utilize mathematical tools to examine certain scientific hypothesis. Weizmann scientists and collaborators have taken this approach, demonstrating that simple models of the innate immune system can teach us much about the development of infections when the bone-marrow function is damaged by chemotherapy. In 2008, they developed a model describing the short term effect of G-CSF injections on cancer patients immune cells, suggesting new grades for classifying neutropenic patients. They showed that the results depend only on robust properties of the underlying modeling assumptions and not on the detailed models. In 2012, they developed an axiomatic model describing the competition between growing bacteria and their main enemy in the body, the white blood cells. This model leads to designing and conducting in-vitro experiments that examined bacterial growth. These experiments, combined with the mathematical models lead to suggestions of improved treatment strategies for neutropenic patients, suggestions that are yet to be tested by clinical trials.
The phase portrait of chemotherapy induced Neutrophils-G-CSF dynamics.