STEP@USF

Using knowledge about serum levels of certain drugs over time and their latency in the human body, determine the decay rate of a drug in the human body in order to calculate the right amount of that drug that should be administered to patients.

Theory:

• Derivatives of exponential functions (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 131)
• Pharmacokinetic models (Stephen P. and John Guckenheimer. Dynamic Models in Biology. New Jersey: Princeton University Press, 2006. 13)
  • Type of compartment model that addresses the absorption, redistribution, and transformation of drugs or other ingested substances within the body

References:

• Bradshaw-Pierce, E. L. et al. 2008. Pharmacokinetic-directed dosing of vandetanib and docetaxel in a mouse model of human squamous cell carcinoma. Molecular Cancer Therapeutics. 7(9): 3006-3017.
• Hurwitz, S. J. et al. 2008. Development of an Optimized Dose for Coformulation of Zidovudine with Drugs That Select for the K65R Mutation Using a Population Pharmacokinetic and Enzyme Kinetic Simulation Model. Antimicrobial Agents and Chemotherapy. 52(12): 4241-4250.
• Yin, O. Q. P. et al. 2008. A Mechanism-Based Population Pharmacokinetic Model for Characterizing Time-Dependent Pharmacokinetics of Midostaurin and its Metabolites in Human Subjects. Clinical Pharmacokinetics. 47(12): 807-816.

What conditions allow a single infected person to create an epidemic in a homogeneous population of susceptible individuals if the pathogenic organism is fast-replicating and has a sequenced genome that is littered with other bacterial genes?

Theory:

• differential equation models for infectious disease (Stephen P. and John Guckenheimer. Dynamic Models in Biology. New Jersey: Princeton University Press, 2006. 183-215)
• a simple epidemic model (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 387-389)
• removal rates
• integrals

References:

What is the cumulative change in area of habitat, number of endangered species, biomass, etc. over an interval.

Theory:

• Integration (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 231)
• Cumulative change (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 270)

References:

Most fertilizers have three major nutrients necessary for plant growth: nitrogen, phosphorus, and potassium (denoted as N-P-K). Choose a crop that you would be interested in growing (e.g. flowers, corn, potatoes, etc.) and determine which major nutrient (i.e. nitrogen, phosphorus, and potassium) is most important for your crop. Determine the amount of fertilizer you would need to maximize your crop yield.

Theory:

• Optimization (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 192)

References:

A cancer cell is a cell that grows out of control. Unlike normal cells, cancer cells ignore signals to stop dividing, to specialize, or to die and be shed. Model and compare the growth rates of normal cells to those of cancer cells.

Theory:

• Derivative as an instantaneous rate of change (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 95)
• von Bertalanffy model (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 359)

References: