Mathematical modeling, interpretation, and simulation of tumor dynamics in the presence of CD4 + cells with chemotherapeutic drug intervention

A tumor is a condition of uncontrolled cell division in solid tissues such as an organ, bone, or muscle. After a sequence of mutations (changes in the genetic sequence), tumor cells normally develop and become progressively abnormal. These mutations in our environment are either hereditary or, more commonly, caused by carcinogens (cancer-causing substances). This abnormal condition of tumor growth evolves a series of mechanisms that can caricature the peripheral immune forbearance and hence escaping the tumoricidal attack by the immune cells. In the present research, we contemplate mocking the roles of various immune cells in tumor attack using the mathematical model formulated. Also, we study the constitution of these various cell densities, involved under our study, by employing drug interventions through diverse therapy techniques. The mathematical model formulated for our study prevails to be unique due to the exemplary composition: tumor cells, natural killers, dendritic cells, CD8+ cells, CD4+ cells, interleukin 2 cytokines (IL-2 cytokines), and drug interference term. The model established is analyzed mathematically for its stability using standard methods. The system of differential equations is solved using an ordinary differential equation solver, with the values of the parameters taken from pathologically tested sources. The cases of with and without drug interference have been analyzed using the graphical results obtained. Also, we intend to study the tumor cell density by changing the frequency of therapy employed. The results followed a hysteresis loop, adding uniqueness to our present work.