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Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…
Heterogeneity in the size distribution of cancer cell populations has been recently linked to drug resistance and invasiveness. However, despite many progresses have been made in understanding how such heterogeneous size distributions arise…
In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell…
Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…
The aim of this study is to compare the growth speed of different cell populations measured by their Malthus parameter. We focus on both the age-structured and size-structured equations. A first population (of reference) is composed of…
The main purpose of this paper is to analyze the dynamics of the system of time-delay differential equations (DDEs) \begin{equation*} \begin{split} \dot{T}(t)&=T(t) f(t,T(t))-\gamma E(t)T(t),\\ \dot{E}(t)&=\sigma+…
In this paper we propose a systematic approach to construct mathematical models describing populations of cancer-cells at different stages of disease development. The methodology we propose is based on stochastic Concurrent Constraint…
A ubiquitous feature of living cells is their growth over time followed by division into daughter cells. How isogenic cell populations maintain size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
Microbial growth and division are fundamental processes relevant to many areas of life science. Of particular interest are homeostasis mechanisms, which buffer growth and division from accumulating fluctuations over multiple cycles. These…
Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…
Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. Methods: In this paper, we propose a…
Cellular phenotype is characterized by different components such as cell size, protein content and cell cycle time. These are global variables that are the outcome of multiple internal microscopic processes. Accordingly, they display some…
The mitotic cell cycle governs DNA replication and cell division. The effectiveness of radiotherapy and chemotherapy depends on cell-cycle position, with increased resistance during DNA replication and mitosis. Thus, accurate mathematical…
In this paper, we conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution…
Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically interplay with other kind of cells, e.g. endothelial cells or immune system effectors,…
In this paper, we consider an age-structured mechanical model for tumor growth. This model takes into account the life-cycle of tumor cells by including an age variable. The underlying process for tumor growth is the same as classical tumor…
The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential-difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory…
We present a model for the interaction dynamics of lymphocytes-tumor cells population. This model reproduces all known states for the tumor. Futherly,we develop it taking into account periodical immunotheraphy treatment with cytokines…
Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by…