A mixed therapy minimal model: Some strategies for eradication or minimization of cancer. (August 2020) - Younus Baba, M.; Saleem, M.; Noman, M.; Raheem, Abdur
Highlights: The model we considered refers to a situation of immune-cancer-normal cell interactions after the vascularization process is complete. Further, the model is valid for non-cycle specific mixed therapy treatment procedures. It has been formulated under the simplified assumption with chemotherapy regimen such that the anti-cancer drug or the combination of drugs kills only the cancer cells. This assumption can be relaxed and the effect of the drug on all cell types can be considered. The novelty of this study lies in the fact that it provides specific thresholds on the two parameters: parameter s related to immunotherapy and parameter m with chemotherapy. These thresholds can help regulate immunotherapy modules and select a specific anti-cancer drug or a combination of drugs either for eradication of the cancer or survival of the patient with cancer. Abstract: 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.