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We show that disease transmission models in a spatially heterogeneous environment can have a large number of coexisting endemic equilibria. A general compartmental model is considered to describe the spread of an infectious disease in a…
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…
The objective of the present study is twofold. First, the last developments and validation results of a hybrid model designed to simulate fire patterns in heterogeneous landscapes are presented. The model combines the features of a…
The Amazon rainforest is considered one of the core tipping elements in the climate system with a potential tipping point from rainforest to savannah between 2 and 6 {\deg}C of global warming. However, ongoing deforestation constitutes an…
In this work, we study the dynamics of a spatially heterogeneous single population model with the memory effect and nonlinear boundary condition. By virtue of the implicit function theorem and Lyapunov-Schmidt reduction, spatially…
The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics,…
Smooth cordgrass Spartina alterniflora is a grass species commonly found in tidal marshes. It is an ecosystem engineer, capable of modifying the structure of its surrounding environment through various feedbacks. The scale-dependent…
We investigate the long-time behavior of phenotype-structured models describing evolutionary dynamics of asexual populations, and analyze the joint effects of nonlocal interactions and spatial resource distributions on the global dynamics…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
We present a spatially-extended system of chemical reactions exhibiting adaptation to time-dependent influxes of reactants. Here adaptation is defined as improved reproductive success, namely the ability of one of the many locally stable…
In this paper, we consider a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture; that was derived in [Frierson, D.M.W.; Majda, A.J.; Pauluis, O.M.: Dynamics of…
We consider $\mathbb Z$-valued $p$-SOS-models with nearest neighbor interactions of the form $|\omega_v-\omega_w|^p$, and finite-spin ferromagnetic models on regular trees. This includes the classical SOS-model, the discrete Gaussian model…
Despite the advanced stage of epidemic modeling, there is a major demand for methods to incorporate behavioral responses to the spread of a disease such as social distancing and adoption of prevention methods. Mobility plays an important…
Due to climate change, overgrazing, and deforestation, arid ecosystems are vulnerable to desertification and land degradation. As aridity increases, vegetation cover loses spatial homogeneity and self-organizes into heterogeneous vegetation…
UK woodlands, forests, and urban treescapes are under threat from invasive species, exacerbated by climate change, trade, and transport. Invasive tree pests debilitate their host and disrupt forest ecosystems, thus it is imperative to…
We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bistable cases, we prove the first sharp quantitative estimate…
Investigation of species abundance has become a vital component of many ecological monitoring studies. The primary objective of these studies is to understand how specific species are distributed across the study domain, as well as…
The diffusion in the comb structures is a popular model of geometrically induced anomalous diffusion. In the present work we concentrate on the diffusion along the backbone in a system where sidebranches are planes, and the diffusion…
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of…