A non-Markovian model for cell population growth: speed of convergence and central limit theorem (Q1198603)

This paper is concerned with a non-Markovian model for cell population growth, in which two types of cells \(A\) and \(B\) are distinguished, with \(A\) cells being \(A^ 1\) or \(A^ 0\) depending on whether they have been stimulated or not before division. The authors examine the asymptotic behaviour of the cell populations when the initial cell numbers tend to infinity. If the total cell number is \(N_ n(t)\) at time \(t\geq 0\), where this is a non-Markovian counting process with \(N_ n(0)=n\), it is shown that \(n^{-1}N_ n(t)\) converges a.s. uniformly on the real line to a certain non-random function. The rate of convergence is also derived, and a Central Limit Theorem is proved. Some computer simulations are used to illustrate the process, and the model is compared graphically with some experimental data. The paper contains several interesting mathematical results, and appears to provide a reasonably realistic model for cell population growth.