This assignment will be due on Wednesday January 16th , and is based on the Article on HIV-1 Dynamics by Perelson et al on pages 15-22 of your text. Warning: this assignment includes some aspects that will require tools that will be learned in the next few lectures, the most important of which are the numerical techniques of solving the equations that naturally arise.
1. Equations 1-3 model a perfect drug. Describe the sense in which the modifications described in comment 9 (listed at the end of the paper) change the model to that of an imperfect drug. Choose some reasonable parameters and numerically solve the imperfect equation. How does its solution compare will the perfect equationÕs solution? How might you decide from the experimental data whether the drug would be better modeled via an imperfect model?
2. In the article it is assumed that T remains at approximately its steadystate value. To justify this assumption the authors quote [1] and [5]. Look into [1] and [5] and determine how this assumption was actually justified. Devise and justify a model where T is allowed to vary and attempt to numerically solve it.
3. The authors claim that a model for drug treatment of viral load is introduced in [2] where essentially the k in equation 1 and 2 is set to zero (comment 11). Look into [2] and describe how to justify this choice of model. Describe what is special about the drugs used to treat HIV that requires the use of the model in this paper. Graph the model from [2] and describe a relevant difference between the function V(t) that this model describes and the V(t) function described in the Perelson et al paper. Describe how this difference is expressed in the authorsÕ conclusion.