Study of Nonlinear Dynamics and Chaos in Virotherapy and Radio Virotherapy

One of the medical science concerns is finding more effective treatments, especially for diseases with unpredictable behavior, such as tumors. By the advance in genetic engineering, new methods are developed for the therapy of cancer as virotherapy. To have the best treatment results, it is of main importance to model the dynamical behavior of these treatments mathematically and investigate the effect of different parameters on its efficiency. The mathematical model of virotherapy is based on the interactions between infected cells, uninfected cells, and free viruses. In the present paper, the dynamical behavior of treatment is analyzed numerically. Due to importance of sensitivity of system response to variation in initial conditions on treatment efficiency, the existence of chaotic response and the and the sensitivity of system behavior to initial condition is investigated by utilizing Lyapunov exponents and bifurcation diagram. Moreover, the effect of radiotherapy as the second phase of treatment is analyzed and the effect of parameters on therapy efficiency is discussed.

Keywords:

Lyapunov exponent , cancer , radio-virotherapy , virotherapy