Fitting parameters and therapies of ODE tumor models with senescence and immune system

This work is devoted to introduce and study two quasispecies nonlinear ODE systems that model the behavior of tumor cell populations organized in different states. In the first model, replicative, senescent, extended lifespan, immortal and tumor cells are considered, while the second also includes immune cells. We fit the parameters regulating the transmission between states in order to approximate the outcomes of the models to a real progressive tumor invasion. After that, we study the identifiability of the fitted parameters, by using two sensitivity analysis methods. Then, we show that an adequate reduced fitting process (only accounting to the most identifiable parameters) gives similar results but saving computational cost. Three different therapies are introduced in the models to shrink (progressively in time) the tumor, while the replicative and senescent cells invade. Each therapy is identified to a dimensionless parameter. Then, we make a fitting process of the therapies' parameters, in various scenarios depending on the initial tumor according to the time when the therapies started. We conclude that, although the optimal combination of therapies depends on the size of initial tumor, the most efficient therapy is the reinforcement of the immune system. Finally, an identifiability analysis allows us to detect a limitation in the therapy outcomes. In fact, perturbing the optimal combination of therapies under an appropriate therapeutic vector produces virtually the same results.