In Medicine: Modeling of Growth of Tumors
See also: Gompertz curve#Growth of tumorsAnother application of logistic curve is in medicine, where the logistic differential equation is used to model the growth of tumors. This application can be considered an extension of the above mentioned use in the framework of ecology (see also the Generalized logistic curve, allowing for more parameters). Denoting with X(t) the size of the tumor at time t, its dynamics are governed by:
which is of the type:
where F(X) is the proliferation rate of the tumor.
If a chemotherapy is started with a log-kill effect, the equation may be revised to be
where c(t) is the therapy-induced death rate. In the idealized case of very long therapy, c(t) can be modeled as a periodic function (of period T) or (in case of continuous infusion therapy) as a constant function, and one has that
i.e. if the average therapy-induced death rate is greater than the baseline proliferation rate then there is the eradication of the disease. Of course, this is an oversimplified model of both the growth and the therapy (e.g. it does not take into account the phenomenon of clonal resistance).
Read more about this topic: Logistic Function
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