Abstract
The effect of tumor microenvironmental factors on tumor growth dynamics modeled by multiplicative colored noise is investigated. Using the Novikov theorem and Fox approach, an approximate Fokker--Planck equation for the non-Markovian stochastic equation is obtained and an analytic expression for the steady-state probability distribution \(P_{st} (x)\) is derived. We found that the strength of the microenvironmental factors \(\theta\) have a negative effect on the stability of tumor growth at weak correlation time \(\tau\) and at strong correlation time, the effect of \(\theta\) is opposed and instead a positive growth stability is noticed for the tumor growth dynamics which in other words corresponds to growth effect. The result indicated that the growth effect exerted by the non-immunogenic components of tumor microenvironmental depend on the strength of the correlation time \(\tau\).
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Acknowledgments
One of the Authors (Ibrahim Mu’awiyya Idris) acknowledges financial support from Umaru Musa Yar’adua University Katsina Nigeria.
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Idris, I.M., Bakar, M.R.A. (2017). Effect of Tumor Microenvironmental Factors on the Stability of Tumor Growth Dynamics with Nonzero Correlation Time. In: Ahmad, AR., Kor, L., Ahmad, I., Idrus, Z. (eds) Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015). Springer, Singapore. https://doi.org/10.1007/978-981-10-2772-7_14
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DOI: https://doi.org/10.1007/978-981-10-2772-7_14
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