Related papers: On a reaction-diffusion system modeling strong com…
Spatial segregation occurs in population dynamics when $k$ species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competition-diffusion system of $k$ differential equations \[ -\Delta…
We consider a two-species reaction-diffusion system in one space dimension that is derived from an epidemiological model in a spatially periodic environment with two types of pathogens: the wild type and the mutant. The system is of a…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
The relationship between division of labor and individuals' spatial behavior in social insect colonies provides a useful context to study how social interactions influence the spreading of agent (which could be information or virus) across…
Habitat fragmentation, often driven by human activities, alters ecological landscapes by disrupting connectivity and reshaping species interactions. In such fragmented environments, habitats can be modeled as networks, where individuals…
Over 50% of the world population is at risk of mosquito-borne diseases. Female Ae. aegypti mosquito species transmit Zika, Dengue, and Chikungunya. The spread of these diseases correlate positively with the vector population, and this…
We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one of the effects…
Interactions among multiple infectious agents are increasingly recognized as a fundamental issue in the understanding of key questions in public health, regarding pathogen emergence, maintenance, and evolution. The full description of…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under…
We introduce a multitype contact process with temporal heterogeneity involving two species competing for space on the $d$-dimensional integer lattice. Time is divided into seasons called alternately season 1 and season 2. We prove that…
We consider a simple information-theoretic model of communication, in which two species of bacteria have the option of exchanging information about their environment, thereby improving their chances of survival. For this purpose, we model a…
We study a system of PDEs modeling the population dynamics of two competitive species whose spatial movements are governed by both diffusion and mutually repulsive chemotaxis effects. We prove that solutions to this system are globally…
Different pathogens spreading in the same host population often generate complex co-circulation dynamics because of the many possible interactions between the pathogens and the host immune system, the host life cycle, and the space…
We study the dynamic properties of a model for wetting with two competing adsorbates on a planar substrate. The two species of particles have identical properties and repel each other. Starting with a flat interface one observes the…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…