Abstract
We use a system biology approach to translate the interaction of Bacillus Calmette-Gurin (BCG) + interleukin 2 (IL-2) for the treatment of bladder cancer into a mathematical model. The main goal of this research is to predict the outcome of BCG + IL-2 treatment combinations. We examined whether the delay effect caused by the proliferation of tumor antigen-specific effector cells after the immune system destroys BCG-infected urothelium cells after BCG and IL-2 immunotherapy influences success in bladder cancer treatment. To do this, we introduce a system of differential equations where the variables are the main participants in the immune response after BCG installations to fight cancer: the number of tumor cells, BCG cells, immune cells, and cytokines involved in the tumor-immune response. The relevant parameters describing the dynamics of the system are taken from a variety of biological, clinical literature and estimated using the mathematical models. We examine the local stability analysis of non-negative equilibrium states of the model. In theory, treatment could improve system stability, and we analyze the stability of all equilibria using the method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). Our results prove that the period for the proliferation of tumor antigen-specific effector cells does not influence to the success of the non-responsive patients after an intensified combined BCG + IL-2 treatment.
Highlights
Bladder cancer (BC) is the fourth most common cancer in males [1] and the 11th most common cancer in women [2]
The concept of equilibrium refers to the theory of dynamical systems, that is, systems developing in time
In this work we present the improved model of combined therapy Bacillus Calmette-Gurin (BCG) + interleukin 2 (IL-2) immunotherapy for BC
Summary
Bladder cancer (BC) is the fourth most common cancer in males [1] and the 11th most common cancer in women [2]. After TURBT, in malignant case, the treatment is either chemotherapy or immunotherapy for eradication of any residual cancer cells. Chemotherapeutic agents such as mitomycin C, doxorubicin, and epirubicin have long been used as intravesical therapies for BC [3,4]. This research is based on the model of BC immunotherapy [10], focusing on the clinical use of BCG and IL-2. During this treatment, the malignant cells are attacked by the patient’s own immune system rather than through external chemical or surgical intervention. Standard definitions of stability are used (see, for instance [21])
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