Related papers: Survival and invasion dynamics in cell populations…
Capturing the structure of a population and characterising contacts within the population are key to reliable projections of infectious disease. Two main elements of population structure -- contact heterogeneity and age -- have been…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
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…
Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not…
Cell migration in confining physiological environments relies on the concerted dynamics of several cellular components, including protrusions, adhesions with the environment, and the cell nucleus. However, it remains poorly understood how…
Biological aging is characterized by an age-dependent increase in the probability of death and by a decrease in the reproductive capacity. Individual age-dependent rates of survival and reproduction have a strong impact on population…
Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur,…
We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to…
This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…
We consider a multiscale stochastic compartmental model with three types of cells (stem cells, immature cells and mature cells) which combines cell proliferation and cell differentiation. We derive a hydrodynamic limit when the number of…
Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment…
Here we propose and implement a generalized mathematical model to find the time evolution of population in infectious diseases and apply the model to study the recent COVID-19 pandemic. Our model at the core is a non-local generalization of…
We explore the role of cellular life cycles for viruses and host cells in an infection process. For this purpose, we derive a generalized version of the basic model of virus dynamics (Nowak, M.A., Bangham, C.R.M., 1996. Population dynamics…
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…
We study the dynamics of the Fisher-KPP equation on the infinite homogeneous tree and Erd\H{o}s-R\'eyni random graphs. We assume initial data that is zero everywhere except at a single node. For the case of the homogeneous tree, the…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological…
The time distribution of relaxation events in an aging system is investigated via molecular dynamics simulations. The focus is on the distribution functions of the first passage time, $p_1(\Delta t)$, and the persistence time, $p(\tau)$. In…
Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick-von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in [1,2]. Here we develop…
We study the effect of correlations in generation times on the dynamics of population growth of microorganisms. We show that any non-zero correlation that is due to cell-size regulation, no matter how small, induces long-term oscillations…