Define a dynamic programming and solving it

Let us assume one patient enters the system at t=0. Starting from t =1, the system decides whether or not to raise an alarm (to treat the patient). The system does that every 1 minute up until t=30. The alarm is raised based on a risk score calculated by a classifier. The system terminates as soon as the patient is classified as positive or reaches t=30. a_t is assumed to be the action taken at time t which is to treat or not treat the patient (binary) There are some assumptions that need to be made before we continue. The first assumption is that at t=30 the status of the patient becomes known (after we make a decision to treat it or not). But any time before t=30 the status becomes known only if we decided to treat the patient. The third assumption is that if the patient is really positive, then as time goes by, the risk score becomes higher. Similarly, if the patient is really negative, then the risk would decrease as time goes by. We want to model this as a stochastic dynamic programming problem. It should be done in Python. Let me know if you are interested