A Nonlinear Dynamical Model of Leukemia Progression with CAR T-cell Therapeutic Intervention

Leukemia is a hematological malignancy marked by uncontrolled proliferation of immature leukocytes, disrupting normal blood cells formation and limiting long-term therapeutic success. Despite advancements in treatment, achieving sustained remission remains a formidable challenge. To investigate therapeutic outcomes under chimeric antigen receptor (CAR) T-cell immunotherapy, a nonlinear ordinary differential equation model is developed that integrates susceptible, infected, cancer, and immune cell populations. The model incorporates immune-mediated cell clearance through a parameter γ, representing the elimination of infected cells by immune action. Analytical results establish positivity, boundedness, and the existence of biologically feasible equilibria. The basic reproduction number R_0 is derived using the next-generation matrix approach, serving as the threshold for disease persistence. Local and endemic equilibria are analyzed through Routh-Hurwitz and Lyapunov criteria to determine asymptotic stability conditions. Numerical simulations illustrate how CAR T-cell infusion and immune stimulation feedback influence leukemia suppression and immune persistence. Sensitivity analysis highlights β, γ, k_0 as dominant parameters shaping therapeutic outcomes. The proposed framework offers a compact, mechanistic description of immune-tumor dynamics and supports optimization of immunotherapeutic dosing strategies.