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Review of Stochastic Stability and Analysis Tumor-Immune Systems

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In this paper we review and at the same time investigate some stochastic models for tumor-immune systems. To describe these models, we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability around the equilibrium points, by constructing the Lyapunov exponent, depending on the parameters that describe the model. Stochastic stability was also proved by constructing a Lyapunov function and the second order moments. We have studied and analyzed a Kuznetsov-Taylor like stochastic model and a Bell stochastic model for tumor-immune systems. These stochastic models are studied from stability point of view and they were graphically represented using the second order Euler scheme and Maple 12 software.
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Keywords: Lyapunov exponent; lyapunov function; stochastic models; stochastic stability; wiener process

Document Type: Research Article

Publication date: September 1, 2013

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  • Current Bioinformatics aims to publish all the latest and outstanding developments in bioinformatics. Each issue contains a series of timely, in-depth reviews written by leaders in the field, covering a wide range of the integration of biology with computer and information science.

    The journal focuses on reviews on advances in computational molecular/structural biology, encompassing areas such as computing in biomedicine and genomics, computational proteomics and systems biology, and metabolic pathway engineering. Developments in these fields have direct implications on key issues related to health care, medicine, genetic disorders, development of agricultural products, renewable energy, environmental protection, etc.

    Current Bioinformatics is an essential journal for all academic and industrial researchers who want expert knowledge on all major advances in bioinformatics.
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