Title: Adherence to antiretroviral HIV drugs: how many doses can you 
miss before resistance emerges?

Abstract.
The emergence of drug resistance is one of the most prevalent 
reasons for treatment failure in HIV therapy. Drug resistance 
is facilitated in large part by a patient's degree of 
adherence to prescribed therapy. A mathematical model is 
developed to quantify the relationship between drug levels 
and resistance, using impulsive differential equations to 
model the nature of drugs. Since drug levels may be low, 
intermediate or high, the corresponding model of virus and T 
cells will vary as the drugs traverse different regions. It 
can be shown that intermediate drug levels will facilitate 
the emergence of drug resistance while providing no 
measurable increase in the T cell count for the patient. Only 
when drug levels are sufficiently high will the virus be 
controlled. Parameter space of drug dosages and dosing 
intervals is explored, in order to prescribe dosing intervals 
and dosages to prevent or reduce resistance. The model is 
then used to quantify adherence, which has been described by 
the U.S. Department of Health and Human Services as the most 
urgent unanswered question in HIV research. Drug thresholds 
are developed in order to determine the number of doses that 
a strongly adherent patient can miss before resistance 
emerges. Conversely, it is shown that if this threshold is 
crossed, even for 24 hours, then resistance levels are 
extremely high and will not dissipate for weeks. After this 
therapy interruption, the minimum number of successive doses 
that should be taken is also determined. Estimates are 
provided for all protease-sparing drugs approved by the U.S. 
Food and Drug Administration.