A mathematical model for chemoimmunotherapy of chronic lymphocytic leukemia

TL;DR

This paper develops a mathematical model to analyze chemoimmunotherapy strategies for chronic lymphocytic leukemia, demonstrating potential effectiveness when chemotherapy does not hinder immunotherapy success.

Contribution

It introduces a simple ODE model for chemoimmunotherapy of CLL based on existing ideas and pharmacokinetics, filling a gap in mathematical studies of this treatment.

Findings

Chemoimmunotherapy can be effective if chemotherapy does not limit immunotherapy.

The model confirms positivity and stability of the system variables.

Numerical simulations support the potential success of combined treatments.

Abstract

Immunotherapy is currently regarded as the most promising treatment to fight against cancer. This is particularly true in the treatment of chronic lymphocytic leukemia, an indolent neoplastic disease of B-lymphocytes which eventually causes the immune system's failure. In this and other areas of cancer research, mathematical modeling is pointed out as a prominent tool to analyze theoretical and practical issues. Its lack in studies of chemoimmunotherapy of chronic lymphocytic leukemia is what motivates us to come up with a simple ordinary differential equation model. It is based on ideas of de Pillis & Radunskaya and on standard pharmacokinetics-pharmacodynamics assumptions. In order to check the positivity of the state variables, we first establish an invariant region where these time-dependent variables remain positive. Afterwards, the action of the immune system, as well as the chemoimmunotherapeutic role in promoting cancer cure are investigated by means of numerical simulations and the classical linear stability analysis. The role of adoptive cellular immunotherapy is also addressed. Our overall conclusion is that chemoimmunotherapeutic protocols can be effective in treating chronic lymphocytic leukemia provided that chemotherapy is not a limiting factor to the immunotherapy efficacy.