Delays do not cause oscillations in a corrected model of humoral mediated immune response

In the paper we focus on modelling immune system–cancer cells interactions with time delays included into the model. The first model we consider, is the (Feyissa and Banerjee, 2013) model of humoral immune response, for which we show that the non-negativity property is not preserved. This is the reason we propose a modification, which under the assumption that the tumour is non-immunogenic can be simplified into the system of three equations without delays, that is the second model we consider. For the simplified model we have made mathematical analysis, including asymptotic stability, as well as numerical analysis, showing wide spectrum of possible model dynamics, including globally stable steady state, bistability and oscillatory behaviour. The dynamics of the simplified model is numerically compared with the dynamics of the full model with time delays for the parameter values from the literature. It occurs that if tumour immunogenicity is low time delays have no significant influence on the full system and both systems behave similarly.