A mixed therapy minimal model: Some strategies for eradication or minimization of cancer

BACKGROUND AND OBJECTIVE In most of the cancer therapeutic models separate equations for consumption of drugs are used, we however use parameters m and s to see the effect of chemotherapy and immunotherapy respectively. The main objective of this theoretical study is to develop strategies for eradication or minimization of cancer. METHODS Linearization method to study the local stability of model equilibria. RESULTS The results obtained in this study provide thresholds on m-fraction of cancer cells killed by chemotherapy and s-fraction of immune cells stimulated by immunotherapy. CONCLUSION The model considered relates to immune-cancer-normal cell interactions in post vascularization process. The study aims to develop strategies for complete eradication or minimization of cancer in terms of model parameters. This paper presents a minimal immuno-chemotherapeutic cancer model by describing interacting dynamics of cancer, immune and normal cells in a system of three ordinary differential equations. The source of the immune cells is considered outside the sytem given by a constant influx rate, s. The minimality of the model lies in not considering a separate equation for the dynamics of the drug but its overall killing effect on the cancer cells represented by a parameter, m. Thus the parameter m relates to chemotherapy and s to immunotherapy. The analysis of the model yields thresholds on these parameters for therapeutic strategies which guarantee either eradication or minimization of cancer from a patient's body.