# Mathematical Models of Cancer Clinical Trials

Most cancer clinical trials fail: 70% fail in Phase 1, and 60% fail in Phase 2. This is particularly so in the case of combination therapy with two or more drugs. One of the reasons for this failure is that not enough thought is given to the potential interactions between the different drugs. In this talk I will consider the case of two drugs, say A and B. I will present mathematical models of cancer and cancer therapy by systems of PDEs, and use them to address the following questions :
(i)Are A and B positively correlated? That is, if A or B is increased, does the tumor volume decrease? Or, are there “zones or resistance,” that is, regions in the (A,B) plane where an increase in A or B actually increases the tumor volume?
(ii)Given a curve G in the (A,B) plane of “equi-efficacy”，that is , such that for each pair (A,B) on G the cancer volume decreases at the same amount after, say,60 days, which pair has the smallest negative side effects?
(iii)How to schedule the treatment? For example, should the two drugs be given at the same time, or separately, and in which order?
I shall give several examples to address these situations. Although the emphasis of the talk in on mathematical models and simulations, I will also indicate some open mathematical problems in PDEs which arise from the models.

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