T model of growth and its application in systems of tumor-immunedynamics
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1.
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505
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2.
School of Medicine, University of Alabama at Birmingham, Birmingham AL 35294
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Received:
01 May 2012
Accepted:
29 June 2018
Published:
01 April 2013
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MSC :
91B62, 62P10.
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In this paper we introduce a new growth model called Tgrowth model. This model is capable of representing sigmoidal growth as wellas biphasic growth. This dual capability is achieved without introducingadditional parameters. The T model is useful in modeling cellularproliferation or regression of cancer cells, stem cells, bacterial growth anddrug dose-response relationships. We recommend usage of the T growth model forthe growth of tumors as part of any system of differential equations. Use ofthis model within a system will allow more flexibility in representing thenatural rate of tumor growth. For illustration, we examine some systems oftumor-immune interaction in which the T growth rate is applied. We also applythe model to a set of tumor growth data.
Citation: Mohammad A. Tabatabai, Wayne M. Eby, Karan P. Singh, Sejong Bae. T model of growth and its application in systems of tumor-immunedynamics[J]. Mathematical Biosciences and Engineering, 2013, 10(3): 925-938. doi: 10.3934/mbe.2013.10.925
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Abstract
In this paper we introduce a new growth model called Tgrowth model. This model is capable of representing sigmoidal growth as wellas biphasic growth. This dual capability is achieved without introducingadditional parameters. The T model is useful in modeling cellularproliferation or regression of cancer cells, stem cells, bacterial growth anddrug dose-response relationships. We recommend usage of the T growth model forthe growth of tumors as part of any system of differential equations. Use ofthis model within a system will allow more flexibility in representing thenatural rate of tumor growth. For illustration, we examine some systems oftumor-immune interaction in which the T growth rate is applied. We also applythe model to a set of tumor growth data.
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