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This paper deals with a control strategy through impulsive drug treatment to study the effect of Chemotherapy and CTL activator drug to eradicate the cervical cancer. CTL kills the HPV infected cells and helps to prevent cervical cancer. Dendritic cell (DC) plays a crucial role in this disease dynamics in enhancing the activity of CTL. To explore these effects, we have formulated a mathematical model consisting of six compartments to describe the interactions between HPV and three classes of cervical cells (susceptible, infected, cancerous), with DC and CTL. Calculating the basic reproduction ratio, we find that there exists a disease-free equilibrium point and an endemic equilibrium point. In our study, we have shown that though DC enhances the activity of CTL, it is not sufficient to eradicate the disease totally. How we could restrict the cancer development by using double drug in an impulsive way with particular drug doses is being reflected in the results. To illustrate our results, numerical simulations are also presented. [ABSTRACT FROM AUTHOR]

In this paper, a new mathematical model of the interactions between a growing tumor and an immune system is presented by incorporating the danger model. The populations involved are tumor cells, CD8+ T-cells, natural killer cells (NK-cells), dendritic cells (DCs) and cytokine interleukin-12 (IL-12). A key feature of this work is the inclusion of the danger model into the dynamics of the immune system, which is rarely considered by previous works. Regarding the constructed mathematical model, both the location of equilibria and their stability properties are discussed, which are useful not only to gain a broad understanding of the specific system dynamics, but also to help guide the development of therapies. Moreover, numerical simulations of the system with chemotherapy and immunotherapy by using specific parameters are presented to illustrate that proper therapy is able to eliminate the entire tumor. In addition, we illustrate cases for which neither chemotherapy nor immunotherapy alone are able to control tumor growth, but a combination treatment is sufficient to eliminate the tumor cells. [ABSTRACT FROM AUTHOR]