University Calendar

Elsa Hansen, Penn State University, presents her seminar.

When resistance to anticancer or antimicrobial drugs evolves in a patient, highly effective chemotherapy can fail, threatening patient health and lifespan. The details of how treatment is administered strongly influences if and when this resistance emerges. This is because an infection or cancer can have both drug-sensitive and drug-resistant populations that compete with each other. Using treatment to remove the drug-sensitive population removes this competition and allows for a fully resistant population to emerge. Here we consider the possibility of using drug to manage the drug-sensitive population while also deliberately maintaining a drug-sensitive population to competitively suppress the drug-resistant population. The mathematical framework highlights that maintaining a drug-sensitive population involves a trade-off and that this trade-off changes as the treatment progresses. Pontryagin’s maximum principle is used to determine the optimal removal of drug-sensitive pathogens. The solution is discussed for a class of models and is shown to involve a certain number of impulses and a combination of three conventional removal strategies.