Mathematical model of melanoma

The current article introduces a mathematical model of a growing four-stage surface melanoma. The model is represented by the Cauchy problem for a system of four ordinary differential equations. The stages of the disease are modeled by chambers of various capacities with the movement of malignant cells from chamber to chamber. The chemotherapy model takes into account the direct effect of drugs on tumor cells at a given time interval. Using a statistical approach, the authors develop a model for constructing the distribution of patients by the time of diagnosis, the duration of treatment, and the time of relapse. Also, the article provides an estimation of the drugs to be consumed for treatment to a given required level of survival. The model parameters are determined based on clinical data on the growth rate of the neoplasm, the time interval of treatment.