Related papers: Spreading in a shifting environment modeled by the…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…
To better understand how populations respond to dynamic external pressure, we propose a new diffusion model in the moving half-line {z $\ge$ b(t)}, where the boundary position b(t) is a given nondecreasing function of time. A Robin boundary…
This paper investigates the spreading properties of globally defined bounded positive solutions of a chemotaxis system featuring a logistic source and consumption: \[ \left\{ \begin{aligned} &\partial_tu=\Delta u - \chi\nabla\cdot(u\nabla…
Numerous experimental studies have demonstrated that the microenvironment is a key regulator influencing the proliferative and migrative potentials of species. Spatial and temporal disturbances lead to adverse and hazardous…
Active particles often swim in confined environments. The transport mechanisms, especially the global one as reflected by the Taylor dispersion model, are of great practical interest to various applications. For active dispersion process in…
The system under study is a reaction-diffusion equation in a horizontal strip, coupled to a diffusion equation on its upper boundary via an exchange condition of the Robin type. This class of models was introduced by H. Berestycki, L. Rossi…
In this paper we consider diffusions on the half line (0, $\infty$) such that the expectation of the arrival time at the origin is uniformly bounded in the initial point. This implies that there is a well defined diffusion process starting…
Consider "Frozen Random Walk" on $\mathbb{Z}$: $n$ particles start at the origin. At any discrete time, the leftmost and rightmost $\lfloor{\frac{n}{4}}\rfloor$ particles are "frozen" and do not move. The rest of the particles in the "bulk"…
We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws…
We study a three-species cyclic model whose organisms are vulnerable to contamination with an infectious disease which propagates person-to-person. We consider that individuals of one species perform an evolutionary self-preservation…
In this paper, we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment. It is known that Choi et al. [J. Differ. Equ. 302 (2021), pp. 807-853] studied the persistence or extinction…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
Occupancy of new habitats through dispersion is a central process in nature. In particular, long range dispersal is involved in the spread of species and epidemics, although it has not been previously related with cancer invasion, a process…
We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $\beta$, separated by a distance $L$ and evenly spaced around the initial position of the particle.…
In Cao, Du, Li and Li [8], a nonlocal diffusion model with free boundaries extending the local diffusion model of Du and Lin [12] was introduced and studied. For Fisher-KPP type nonlinearities, its long-time dynamical behaviour is shown to…
We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…
We propose a spreading model in multilayer networks and study the nature of nonequilibrium phase transition in the model. The model integrates the susceptible-infected-susceptible (or susceptible-infected-recovered) spreading dynamics with…
This paper is a follow-up to a previous work where we considered populations with time-varying growth rates living in patches and irreducible migration matrix between the patches. Each population, when isolated, would become extinct.…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…