# American Institute of Mathematical Sciences

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October  2016, 21(8): 2473-2489. doi: 10.3934/dcdsb.2016056

## Moment stability for nonlinear stochastic growth kinetics of breast cancer stem cells with time-delays

 1 School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China 2 Center of Clinical Pharmacology, The Third Xiangya Hospital, Central South University, Changsha 410083, China 3 Department of Mathematics, University of South Carolina, Columbia, SC 29208, United States

Received  November 2015 Revised  February 2016 Published  September 2016

Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are a highly tumorigenic cell type found in developmentally diverse tumors that are believed to be resistant to standard chemotherapeutic drugs and responsible for tumor recurrence. Thus understanding the tumor growth kinetics is critical for development of novel strategies for cancer treatment. In this paper, the moment stability of nonlinear stochastic systems of breast cancer stem cells with time-delays has been investigated. First, based on the technique of the variation- of-constants formula, we obtain the second order moment equations for the nonlinear stochastic systems of breast cancer stem cells with time-delays. By the comparison principle along with the established moment equations, we can get the comparative systems of the nonlinear stochastic systems of breast cancer stem cells with time-delays. Then moment stability theorems have been established for the systems with the stability properties for the comparative systems. Based on the linear matrix inequality (LMI) technique, we next obtain a criteria for the exponential stability in mean square of the nonlinear stochastic systems for the dynamics of breast cancer stem cells with time-delays. Finally, some numerical examples are presented to illustrate the efficiency of the results.
Citation: Chengjun Guo, Chengxian Guo, Sameed Ahmed, Xinfeng Liu. Moment stability for nonlinear stochastic growth kinetics of breast cancer stem cells with time-delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2473-2489. doi: 10.3934/dcdsb.2016056
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