Abstract
We present a revised mathematical model of the immune response to Bacillus Calmette-Guérin (BCG) treatment of bladder cancer, optimized according to biological and clinical data accumulated during the last decade. The improved model accounts for cytotoxic T lymphocyte differentiation as an integral element of the delayed immune response, as well as the logistic growth terms for cancer cell proliferation. Three equilibria are demonstrated for the proposed model, which is assumed to be influenced by white noise stochastic perturbations that are directly proportional to the system state deviation from an equilibrium. Stability conditions for all equilibria are analyzed using the Kolmanovskii-Shaikhet general method of Lyapunov functionals construction.
Highlights
Bladder cancer (BC) is 7th most common cancer with approximately 356,000 new cases each year and more than 145,000 deaths per year
In this work we present the improved model of Bacillus Calmette-Guerin (BCG) immunotherapy in superficial bladder cancer
This study investigates stability of new treatment model with constant instillations of BCG under stochastic perturbations
Summary
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. A. Computational and Mathematical Methods in Medicine system of ordinary differential equations (ODE) was used for effective description of BCG treatment dynamics. Computational and Mathematical Methods in Medicine system of ordinary differential equations (ODE) was used for effective description of BCG treatment dynamics In this manuscript, we present an improved BCG model based upon that of B-M et al [9] which describes the tumor-immune system interactions in the bladder in response to BCG therapy, updated according to newly published biological and clinical data. Obtained asymptotic mean square stability conditions of the linear system zero solution at the same time are sufficient conditions for stability in probability of a corresponding equilibrium of the initial nonlinear system This method can be applied to a system of arbitrary nonlinear differential equations with the order of nonlinearity higher than one.
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