Keeping Viruses Under Control

We introduce a probability model for populations of conflicting agents such as computer software (cells) and computer viruses that interact in the presence of an anti-viral agent. Cells can be infected by viruses, and their longevity and ability to avoid infection is modified if they survive successive attacks by viruses. Viruses that survive the effect of the anti-viral agent may find that their ability to survive a future encounter with molecules of the anti-viral agent is modified, as is their ability to infect a uninfected cell. Additionally, we assume that the anti-viral agent can be a cocktail with different proportions of agents that target different strains of the virus. In this paper, we give the state equations for the model and prove its analytical solution in steady state. The solution then provides insight into the approriate mix or “cocktail” of anti-viral agents that are designed to deal with the virus’ ability to mutate. In particular, the analysis shows that the concentration of anti-viral agent by itself does not suffice to ultimately control the infection, and that it is important to dose a mix of anti-viral agents so as to target each strain of virus in a specific manner, taking into account the ability of each virus strain to survive in the presence of the anti-viral agent.