Combinatorial Optimization in Rapidly Mutating Drug-Resistant Viruses

Resistance to chemicals is a common current problem in many pests and pathogens that formerly were controlled by chemicals. An extreme case occurs in rapidly mutating viruses such as Human Immunodeficiency Virus (HIV), where the emergence of selective drug resistance within an individual patient may become an important factor in treatment choice. The HIV patient subpopulation that already has experienced at least one treatment failure due to drug resistance is considered more challenging to treat because the treatment options have been reduced. A triply nested combinatorial optimization problem occurs in computational attempts to optimize HIV patient treatment protocol (drug regimen) with respect to drug resistance, given a set of HIV genetic sequences from the patient. In this paper the optimization problem is characterized, and the objects involved are represented computationally. An implemented branch-and-bound algorithm that computes a solution to the problem is described and proved correct. Data shown includes empirical timing results on representative patient data, example clinical output, and summary statistics from an initial small-scale human clinical trial.