Examination of logistic mathematical models and providing an appropriate response for treatment of cancerous tumors

 In this research, we examined the different mathematical models of cancerous tumor growth and compared several models to calculate and evaluate the response of the growth logistic model to the specific growth rate conditions. The growth rate was simulated by considering it as a function of time (linear, exponential growth, and linear growth-decay). Responses were obtained by using Range-Kutta's numerical solution method. The general response is the logistic growth curve, but the external factors in the treatment can be controlled to optimally respond of model.The optimal conditions for controlling the growth of the tumor obtained by the linear growth rate-decay for the constants k1=0.1 and k2=1. Solid tumor structure is associated with a decrease in the stage of growth of the cells prior to angiogenesis. Increasing lagging agents such as accelerating immunological response during exponential growth functions can control tumor growth. The numerical results obtained in this study can provide an optimal therapeutic strategy by reducing the volume of primary cancer by calculating angiogenic inhibitors. Also, by analyzing pathology, mechanical properties of tumor growth, cellular adaptation and therapeutic resistance, we can overcome some of the previous constraints in the general growth model.
Key Words: Treatment, Tumor growth, Cancer, logistic mathematical models, Control