Activities will help students appreciate the importance of initial values in the existence of solutions.
This activity is inspired by some current research on having surgery before therapy.
As a student of differential equations, there are two verbs in this definition that should engage you: grow (uncontrollably) and spread (to other parts of the body). These two dynamic verbs provide rationale for why many mathematical oncologists use differential equations to investigate cancer growth, spread, and treatments.
Currently, cancer treatments include surgery and various kinds of therapy: radiotherapy, chemotherapy, immunotherapy, hormonal therapy, and even viro-therapy. In this activity, you will explore a basic question: does the order of treatment matter? In particular, suppose that the oncologist has recommended surgery and chemotherapy to treat a cancer.
Should the surgery happen before chemotherapy, or after chemotherapy? We shall use a highly simplified differential equation to explore this question. Please remember that this activity is for classroom exploration only and the results of the exploration should not be used in making medical decisions.
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