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The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
Constraints on changes in expression levels across all cell components imposed by the steady growth of cells have recently been discussed both experimentally and theoretically. By assuming a small environmental perturbation and considering…
We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the…
Inspired by Carrillo-Li-Wang's work [Proc. London Math. Soc., 2021] on stationary solutions to the singular Keller-Segel system, this paper presents a novel family of explicit steady-state solutions for the same model on a bounded interval,…
Unraveling bacterial strategies for spatial exploration is crucial for understanding the complexity in the organization of life. Bacterial motility determines the spatio-temporal structure of microbial communities, controls infection…
Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in…
A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…
We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many…
From the formation of animal flocks to the emergence of coordinate motion in bacterial swarms, at all scales populations of motile organisms display coherent collective motion. This consistent behavior strongly contrasts with the difference…
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…
A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are…
In a letter published in Molecular Biology Evolution [10], Chen and Zhang argue that the variation of the mutation rate along the Escherichia coli genome that we recently reported [3] cannot be evolutionarily optimised. To support this…
The existence of phenotypic heterogeneity in single-species bacterial biofilms is well-established in the published literature. However, the modeling of population dynamics in biofilms from the viewpoint of social interactions, i.e.…
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…
This paper is concerned with the kinetic model of Othmer-Dunbar-Alt for bacterial motion. Following a previous work, we apply the dispersion and Strichartz estimates to prove global existence under several borderline growth assumptions on…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
Motile bacteria can migrate along chemical gradients in a process known as chemotaxis. When exposed to uniform environmental stress, Escherichia coli cells coordinate their chemotactic responses to form millimeter-sized condensates…
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathematical theory for the emergence of these localised cellular…
We consider motility of keratocyte cells driven by myosin contraction and introduce a 2D free boundary model for such motion. This model generalizes a 1D model from [12] by combining a 2D Keller-Segel model and a Hele-Shaw type boundary…
The accumulation of adaptive mutations is essential for survival in novel environments. However, in clonal populations with a high mutational supply, the power of natural selection is expected to be limited. This is due to clonal…