showing 4 related works from this author
Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response.
2006
We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization of a Brownian dynamics for which the model reaction kinetics takes on the form of a stochastic differential equation. After eliminating a fast kinetics, the model can be rephrased into a form of a one-dimensional overdamped Langevin equation. We discuss physical aspects of environmental noises acting in such a reduced system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena …
Cancer growth dynamics: stochastic models and noise induced effects
2009
In the framework of the Michaelis‐Menten (MM) reaction kinetics, we analyze the cancer growth dynamics in the presence of the immune response. We found the coexistence of noise enhanced stability (NES) and resonant activation (RA) phenomena which act in an opposite way with respect to the extinction of the tumor. The role of the stochastic resonance (SR) in the case of weak cancer therapy has been analyzed. The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a Monte Carlo approach. We analyzed the effects of a targeted therapy on the evolutionary dynamics of normal, first‐mutant and cancerous cell populations. We show how …
Monitoring noise-resonant effects in cancer growth influenced by external fluctuations and periodic treatment
2007
In the paper we investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells is based on the generic Michaelis-Menten kinetics depicting interaction and competition between the tumor and the immune system. The appropriate phenomenological equation modeling cell-mediated immune surveillance against cancer is of the predator-prey form and exhibits bistability within a given choice of the immune response-related parameters. Under the influence of weak external fluctuations, the model may be analyzed in terms of a stochastic differential equation bearing the form of an overdamped Langevin-like dynam…
Coexistence of resonant activation and noise enhanced stability in a model of tumor-host interaction: Statistics of extinction times
2006
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 phen…