Journal of Obesity & Weight Loss Therapy
Open Access

Abstract

The method of stability investigation under stochastic perturbations of mathematical models of various types of epidemics, in particular, of the model of social obesity epidemic, was successfully used for investigation of cancer models. In this work the model of bladder cancer is investigated. Bladder cancer (BC) is 7th most common cancer (the 4th most common for men) with approximately 356,000 new cases each year and more than 145,000 deaths per year. Our model describes the treatment effects of the Bacillus Calmette-Guérin (BCG) bacteria. Based on previous study, we have developed a new model with adding delay in the immune response to BCG injection and special adaptation to new knowledge about the BCG immunotherapy. The model characterizes the dynamics of the interactions between the four different biological components (BCG bacteria within the bladder (B), effector T-lymphocytes, mostly CTLs that react to BCG and to tumor antigens (E), tumor cells infected with BCG (Ti) and tumor cells that are not infected by BCG (Tu)) and is described by the system of four non-linear differential equations with a variable delay and stochastic perturbations of the type of white noise. The stability investigation of the considered model is based on the general method of Lyapunov functionals construction that was proposed and developed by V. Kolmanovskii and L. Shaikhet during last two decades.

Biography

Email: leonid.shaikhet@usa.net