Modelling the effects of combined immunotherapy treatments on the dynamics of cancerous tumor cells

Abstract

In this dissertation, a mathematical model is formulated and analyzed to measure the effects of combined immunotherapy on the dynamics of cancerous tumor cells. In modeling these dynamics, the compartmental model is divided into five classes namely, cancerous tumor cells, immune cells, immune activators molecules, immuno-suppressors, and combined treatment. The model is analyzed based on the existence of equilibria points both in the absence and presence of cancerous tumor cells. Sensitivity analysis of embedded parameters is discussed by using the partial rank correlation co-efficient so as to see their relative importance in controlling the cancerous tumor cells. Also, numerical simulations to show the behavior of cancerous tumor cells, immune cells, immune activators, and immunosuppresses in both the presence and absence of combined treatment are presented. The results show that the presence of combined immunotherapy facilitates the control of cancerous tumor cells.