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Prey predator population dynamics has been frequently studied in literature to model many robust but contrastive biological populations. In this paper, based on prey predator population dynamics, a nonlinear model to predict the behavior of virus treatment of cancer cells is suggested. Based on the goals of virus curing and consideration of some practical issues, the suggested model has the capability to cover these following cases: both cancer cells and viruses vanish, one is eliminated by the other, or both survive in a robust periodically convergent manner or both become divergent. Relative to the values of some parameters such as the virus intrinsic growth rate, carrying capacity, capturing rate, half saturation constant, maximal tumor cells growth rate, and tumor cells mortality rate, and the initial population values of both tumor cells and viruses, some examples are solved. These examples exhibit logical and feasible behavior for the system. They show under which conditions the virus therapy fails or succeeds; as well when the bifurcation occurs or when the trajectories converge to a limit cycle.
Solids and Structures – Science and Engineering Publishing Company
Published: Jun 1, 2013
Keywords: Cancer Tumours; Virus Therapy; Limit Cycle; Bifurcation; Predator Prey Model
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