A generalised prey-predator type model of immunogenic cancer with the effect of immunotherapy

Abstract

This paper deals with the qualitative analysis of the system of nonlinear ordinary differential equations describing the interaction between cancer and immune cells during immunotherapy. Mathematical analysis of the model equation with regard to boundedness of solutions, nature of equilibria and their local and global study is done. Numerical analysis is performed to support analytical findings. It is observed that cancer cell population decrease considerably due to proliferation of lymphocytes mediated by immunotherapy. It is found from our analysis that cancer population can be controlled easily if cancer is immunogenic that is, cancer cells possess distinctive surface markers called tumor-specific antigens. Further, time delay in production of immuno-agents due to the presence of antigenic cancer cells is studied and critical value of delay for which stability switch occurs is determined.

Keywords: Cancer cells, Immune Response, Hunting cells, Resting cells, Antigenicity