  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.
