Uses of Mathematica in the Study of a Mathematical Model for Influenza Medication Strategies

Zhilan Feng

Purdue University

Abstract

We present an example of using Mathematica to analyze a mathematical model which is used to study the spread and control of influenza. Patients at risk for complications of influenza are commonly treated with antiviral medications, which however also could be used to control outbreaks. The adamantanes and neuraminidase inhibitors are active against influenza A, but avian influenza (H5N1) is resistant to oseltamivir and swine influenza (H1N1) to the adamantanes (but see postscript). To explore influenza medication strategies (pre-exposure or prophylaxis, post-exposure/pre-symptom onset, and treatment at successive clinical stages) that may affect evolution of resistance (select for resistant strains within or facilitate their spread between hosts), we elaborated a published transmission model and chose parameters from the literature. Then we derived the reproduction numbers of sensitive and resistant strains, peak and final sizes, and time to peak. Finally, we made these results accessible via user-friendly Mathematica notebooks.