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The Speed of Spatial Spread
When a population can persist in a certain environment, we expect that it will spread through that environment if it is initially spatially confined...
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Origin and persistence of polymorphism in loci targeted by disassortative preference: a general model
The emergence and persistence of polymorphism within populations generally requires specific regimes of natural or sexual selection. Here, we develop...
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Dating and localizing an invasion from post-introduction data and a coupled reaction–diffusion–absorption model
Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical...
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Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation
Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate...
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Invasion Dynamics in an Intraguild Predation System with Predator-Induced Defense
Intraguild predation systems describe food webs in which an omnivorous predator competes with an intermediate prey for a basal resource. The...
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Propagation of Epidemics Along Lines with Fast Diffusion
It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed...
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Spatio-temporal solutions of a diffusive directed dynamics model with harvesting
The study considers a directed dynamics reaction-diffusion competition model to study the density of evolution for a single species population with...
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Pushing the Boundaries: Models for the Spatial Spread of Ecosystem Engineers
Ecosystems engineers are species that can substantially alter their abiotic environment and thereby enhance their population growth. The net growth...
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Range Expansion Theories Could Shed Light on the Spatial Structure of Intra-tumour Heterogeneity
Many theoretical studies of range expansions focus on the dynamics of species’ ranges or on causes and consequences of biological invasions. The...
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The Interplay Between Dispersal and Allee Effects in a Two-Patch Discrete-Time Model
We consider a discrete-time two-patch model with dispersal and a nonlinear non-monotone growth rate suggesting that the population in a patch may...
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A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations
We study traveling waves in a non-local cross-diffusion-type model, where organisms move along gradients in population densities. Such models are...
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Explicit and Approximate Solutions for the Conformable-Caputo Time-Fractional Diffusive Predator–Prey Model
The aim of this work is twofold. First, we seek functional explicit solutions to the conformable-time fractional predator–prey model by adapting the...
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Spreading in Homogeneous and Shifting Environments
In this chapter, we discuss the Fisher–KPP model in R1. First, we introduce the notion of spreading speed, and establish the classical result for...
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A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives
In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of...
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Accurate Recognition of Spatial Patterns Arising in Spatio-Temporal Dynamics of Invasive Species
Accurate identification of spatial patterns remains a challenging problem in many ecological applications. One example is a problem of biological...
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The persistence of solutions in a nonlocal predator-prey system with a shifting habitat
In this paper, we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment. It is known that...
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Heterogeneity in Behaviour and Movement can Influence the Stability of Predator–Prey Periodic Travelling Waves
Cyclic predator–prey systems are often observed in nature. In a spatial setting, these can manifest as periodic traveling waves (PTW). Environmental...
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Construction of a New Model to Investigate Breast Cancer Data
Modelling is a way to describe the elements of the network/system, their states and their interactions with other elements in order to understand the...
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Seed predation-induced Allee effects, seed dispersal and masting jointly drive the diversity of seed sources during population expansion
The environmental factors affecting plant reproduction and effective dispersal, in particular biotic interactions, have a strong influence on plant...
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Structured Populations
So far, we have treated populations as homogeneous: all individuals were assumed to be identical with respect to reproduction and dispersal. We only...