  We study a Langevin equation derived from the Michaelis-Menten (MM)
phenomenological scheme for catalysis accompanying a spontaneous replication of
molecules, which may serve as a simple model of cell-mediated immune
surveillance against cancer. We examine how two different and statistically
independent sources of noise - dichotomous multiplicative noise and additive
Gaussian white noise - influence the population's extinction time. This
quantity is identified as the mean first passage time of the system across the
zero population state. We observe the effects of resonant activation (RA) and
noise-enhanced stability (NES) and we report the evidence for competitive
co-occurrence of both phenomena in a given regime of noise parameters. We
discuss the statistics of first passage times in this regime and the role of
different pseudo-potential profiles on the RA and NES phenomena. The RA/NES
coexistence region brings an interesting interpretation for the growth kinetics
of cancer cells population, as the NES effect enhancing the stability of the
tumoral state becomes strongly reduced by the RA phenomenon.
