Reaction Systems for Modeling and Validation of Biological Signaling Pathways: G1/S Checkpoint of the Cell Cycle

Stability analysis of the singular points and Hopf bifurcations of a tumor growth control model

“…V(x) = 0} does not contain any orbit except the trivial one x ≡ 0, then the origin of system (A4) is asymptotically stable. It is obvious that conditions (2) and (3) are satisfied for the function (A2); however, verifying condition (1) becomes a difficult problem, so employing the approach based on formula (16), which we used in Section 4, is preferable. mma.9885.…”

“…The state of the first compartment $$$ {x}_3 $$$ is the drug level in the central compartment (the blood), and the state of the second compartment is the drug level in the peripheral compartment $$$ {x}_4 $$$. The model was created with an analogy to formal reaction kinetics [14–16, 24], which improves communication and validation with medical experts.…”

“…In our analysis, we use a tumor model describing the tumor growth with linear dynamics, using nonlinear pharmacodynamics and linear pharmacokinetics [14], discussed in Section 2. The model is formulated using formal reaction kinetics [15,16]. We chose this model because it describes all the fundamental physiological phenomena in a compact model, and it has been successfully used for therapy optimization in mice experiments [17,18].…”