Escaping stochastic extinction of mutant virus: Temporal pattern of emergence of drug resistance within a host.

After infecting a host, a viral strain may increase rapidly within the body and produce mutants with a faster proliferation rate than the virus itself. However, most of the mutants become extinct because of the stochasticity caused by the small number of infected cells. In addition, the mean growth rate of a mutant strain decreases with time because the number of susceptible target cells is reduced by the original strain. In this study, we calculated the fraction of mutants that can escape stochastic extinction, based on a continuous-time branching process with a time-dependent growth rate. We analyzed two cases differing in the mode of viral transmission: (1) an infected cell transmits the virus through cell-to-cell contact with a susceptible target cell; (2) an infected cell releases numerous free viral particles that subsequently infect susceptible target cells. The chance for a mutant strain to be established decreases with time after infection of the original type, and it may oscillate before convergence at the stationary value. We then calculated the probability of escaping stochastic extinction for a drug-resistant mutant when a patient received an antiviral drug that suppressed the original strain. Combining the rate of mutant production from the original strain and the chance of escaping stochastic extinction, the number of emerging drug-resistant mutations may have two peaks: one soon after the infection of the original type and the second at the start of antiviral drug administration.