Drug-induced resistance is one the major obstacles that may lead to therapeutic failure during cancer treatment. Different genetic alterations occur when tumor cells divide. Among new generations of tumor cells, some may express intrinsic resistance to a specific chemotherapeutic agent. Also, some tumor cells may carry a gene that can develop resistance induced by the therapeutic drug. The methods by which the therapeutic approaches need to be revised in the occurrence of drug induced resistance is still being explored. Previously, we introduced a model that expresses only intrinsic drug resistance in a conjoint normal-tumor cell setting. The focus of this work is to expand our previously reported model to include terms that can express both intrinsic drug resistance and drug-induced resistance. Additionally, we assess the response of the cell population as a function of time under different treatment strategies and discuss the outcomes. The model introduced is expressed in the format of coupled differential equations which describe the growth pattern of the cells. The dynamic of the cell populations is simulated under different treatment cases. All computational simulations were executed using Mathematica v7.0. The outcome of the simulations clearly demonstrates that while some therapeutic strategies can overcome or control the intrinsic drug resistance, they may not be effective, and are even to some extent damaging, if the administered drug creates resistance by itself. In the present study, the evolution of the cells in a conjoint setting, when the system expresses both intrinsic and induced resistance, is mathematically modeled. Followed by a set of computer simulations, the different growing patterns that can be created based on choices of therapy were examined. The model can still be improved by considering other factors including, but not limited to, the nature of the cancer growth, the level of toxicity that the body can tolerate, or the strength of the patient’s immune system.

In this paper, we develop a theoretical contribution towards the understanding of the complex behavior of conjoint tumor-normal cell growth under the influence of immuno-chemotheraputic agents under simple immune system response. In particular, we consider a core model for the interaction of tumor cells with the surrounding normal cells. We then add the effects of a simple immune system, and both immune-suppression factors and immuno-chemotherapeutic agents as well. Through a series of numerical simulations, we illustrate that the interdependency of tumor-normal cells, together with choice of drug and the nature of the immunodeficiency, leads to a variety of interesting patterns in the evolution of both the tumor and the normal cell populations.

In this paper, we modify our previously developed conjoint tumor-normal cell model in order to make a distinction between tumor cells that are responsive to chemotherapy and those that may show resistance.