  We study minimal mean-field models of viral drug resistance development in
which the efficacy of a therapy is described by a one-dimensional stochastic
resetting process with mixed reflecting-absorbing boundary conditions. We
derive analytical expressions for the mean survival time for the virus to
develop complete resistance to the drug. We show that the optimal therapy
resetting rates that achieve a minimum and maximum mean survival times undergo
a second and first-order phase transition-like behaviour as a function of the
therapy efficacy drift. We illustrate our results with simulations of a
population-dynamics model of HIV-1 infection.
