The role of initial tumor biomass size in a mathematical model of periodically pulsed chemotherapy

Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer

“…Bifurcation analysis is a powerful tool to study the changes in dynamics as parameter values vary. Recently, numerical methods for bifurcation analysis have been constructed for ODE systems with periodically pulsed therapies [38,39,40]. In this paper, we propose the numerical method developed in [38] for one-parameter bifurcation analysis, which is an efficient technique to approximate the initial tumor size as a function of the dosage and to predict the outcome of a treatment over a range of parameter values.…”

PULSED CHEMOTHERAPY MODEL Vol. 2(1) Jan 2014, No. 12, pp. 127-148 AH. LAKMECHE, M. HELAL AND AEK. LAKMECHE

“…In this section we consider the following system ẋ1 (t) = F 1 (x 1 (t), x 2 (t), x 3 (t)), (7) ẋ2 (t) = F 2 (x 1 (t), x 2 (t), x 3 (t)), (8) ẋ3 (t) = F 3 (x 1 (t), x 2 (t), x 3 (t)), (9) x 1 (t + i ) = Θ 1 (x 1 (t i ), x 2 (t i ), x 3 (t i )), (10) x 2 (t + i ) = Θ 2 (x 1 (t i ), x 2 (t i ), x 3 (t i )), (11)…”

“…can be determined using a fixed point method with some additional conditions on F and Θ assumed smooth enough ( [3]). If x 2 = x 3 = 0 the problem ( 7), (10) has a τ 0 -periodic solution denoted x s , it is assumed stable, i.e…”

“…The mathematical model obtained is a system of impulsive differential equations. Numerical analysis of the Panetta model [8] is considered in [10], where the role of the initial tumor biomass on the evolution of the tumor is studied. In Panetta [8] two cancer models with resistant tumor cells are discussed, the first one with acquired resistance and the second one with reduced resistance.…”