Related papers: Linking discrete and continuous models of cell bir…
Two types of population models are well known -- the continuous and the discrete types.The two have very different characteristics and methods of solutions and analysis.In this note, we point out that an iterative technique when applied to…
The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in…
We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring…
We review a body of recent work by the author and collaborators on controlling the spatial organisation of large agent populations across multiple scales. A central theme is the systematic bridging of microscopic agent-level dynamics and…
In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker…
Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue…
Cell-cell adhesion is widely hypothesised to maintain cohesion within the long streams of follower cells that trail leader subpopulations during collective migration, including in neural crest cell migration, angiogenesis, and cancer cell…
Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour…
Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven,…
Artificial ants are "small" units, moving autonomously on a shared, dynamically changing "space", directly or indirectly exchanging some kind of information. Artificial ants are frequently conceived as a paradigm for collective adaptive…
Coupled natural systems are generally modeled at multiple abstraction levels. Both structural scale and behavioral complexity of these models are determinants in the kinds of questions that can be posed and answered. As scale and complexity…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
Advances in synthetic biology allow us to engineer bacterial collectives with pre-specified characteristics. However, the behavior of these collectives is difficult to understand, as cellular growth and division as well as extra-cellular…
This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
Migratory and tissue resident cells exhibit highly branched morphologies to perform their function and to adapt to the microenvironment. Immune cells, for example, display transient branched shapes while exploring the surrounding tissues.…