Dynamic of Lotka-Volterra model for tumor-host systems under constant or periodic perturbation: implications for the therapy of cancer

Abstract

In this paper, the interaction tumor-host is described by a Lotka-Volterra model. The critical parameters that define the possible dynamical regimes are determined using linear stability analysis. The effects of constant and periodic perturbations are discussed, as well as their implications in clinics. The treatment dose required to lead the system to a desired state is obtained. It is also shown that aggressive tumors evolve to a limit cycle when the host is under the action of treatment applied periodically with a low frequency. A transition to a non-chaotic attractor occurs for higher frequencies. This transition tends to contract with the increment of the frequency of this external periodic perturbation. It is not detected chaotic behavior, even for higher values of both the strength and the frequency of the perturbation because the maximum Lyapunov exponent remains negative. These results may suggest that although aggressive tumors cannot be completely eliminated by conventional anticancer therapies, they might be controlled using external periodic therapies when only the host is perturbed.