Project Info

Multiscale Modeling and Simulation of the in-host Dynamics of HIV infection

Stephen Pankavich

Project Goals and Description:

Recently, a mathematical model of the in-host dynamics of HIV, consisting of a system of seven nonlinear differential equations, was introduced. This model was the first to simulate the entire life span of HIV disease pathogenesis, and once parameters were fit, it accurately matched clinical data from infected patients. However, in order to achieve such an accurate description, a specific term with no clear biological meaning was included within the differential equations. The general purpose of this project is to investigate this anomalous term: specifically, by considering common biological factors within the model and using multiscale analysis to elucidate their impact. Of particular interest is whether the model responds realistically (i.e. the equations act "biologically") to small perturbations, which would add credence to the nonbiological term's credibility; or whether the model "breaks down" when subjected to the addition of these new common biological factors, which would imply that the addition of the new term is inconsistent with the inherent nature of the model.

More Information:

Grand Challenge: Advance health informatics.

Publications on my research website:

Primary Contacts:

Steve Pankavich,

Student Preparation


Interested students should have familiarity with ordinary and partial differential equations (MATH 225 and MATH 455), linear algebra (MATH 332), and scientific computing (MATH 307). Additionally, they should be open to learning more about the background biology necessary to formulate the problem of interest.




The student will gain modeling skills by creating and modifying existing mathematical models and hone their computational skills by coding in MATLAB.


The student will meet weekly with me and my group in this area - either a graduate student or another undergraduate researcher at Mines.


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