Estimation of Dormant Cell Population in Cancer Patients: A New Approach
Kouadio Jean Claude Kouaho *
Laboratory of Applied Mathematics and Computer Science, Universite Felix Houphouet-Boigny, 22 BP 582 Abidjan 22, C^ote d'Ivoire.
Koffi Yao Modeste N'zi
Laboratory of Applied Mathematics and Computer Science, Universite Felix Houphouet-Boigny, 22 BP 582 Abidjan 22, C^ote d'Ivoire.
Innocent Adoubi
Director of the Department of Immuno Hematocancerology, Universite Felix Houphouet-Boigny, 22 BP 582 Abidjan 22, C^ote d'Ivoire.
*Author to whom correspondence should be addressed.
Abstract
The branching processes form a configuration for modeling tumor cells. Faced with unobserved data on dormant cells, inference based on the branching process is not easy to achieve. In large populations, we construct a new framework for estimating dormant cells and tumor dormancy rates. This inference uses of control theory is based on deterministic process statistics approximating branching process in large populations. Precisely, we use an auxiliary system called an observer whose solutions tend exponentially towards those of the limit deterministic model. This observer uses only available measurable data on tumor cells and provides estimates of the number of dormant cells. In addition, the constructed observer does not use the parameter of the generally unknown tumor dormancy rate. We also derive a method to estimate it using the estimated states. We apply this estimation method using simulated data from the branching process.
Keywords: Branching process, cancer, dormant cell, estimation, observers, resistant cells, susceptible cells