Habitat choice of multiple pollinators in almond trees and its potential effect on pollen movement and productivity: A theoretical approach using the Shigesada–Kawasaki–Teramoto model

From Bee Species Aggregation to Models of Disease Avoidance: The Ben-Hur effect

“…4 The effects of a high cross-diffusion effect of solitary bees on honey bees (α 1 = α 2 = β 11 = β 21 = β 22 = 1, γ 1 = γ 2 = 5, β 12 = 10). Honey bees (u 1 ) are in low densities in areas where solitary bees (u 2 ) are in high densities and honey bees are found in high densities in areas where solitary bees are in low densities, thus demonstrating the avoidance effects of cross-diffusion [41].…”

“…The dynamics of solitary and honey bees and their role in enhancing cross-pollination in California almond tree farms was studied via a cross-diffusion model in [41]. The model for the interaction of honey bees, u 1 (x, y,t), and solitary bees, u 2 (x, y,t) at time t and position (x, y) ∈ Ω , proposed in [41], is given by the system:…”

“…Following the approach in [41], the role of density-dependent cross-diffusion in the aggregation of individuals according to epidemiological states during a nefarious disease outbreak is carried out below. We expand on the type of cross-diffusion model in [6] via the use only of a population of S-individuals (susceptible) and I-individuals (infectives), that is, symptomatic infectious individuals.…”

“…Most recently, the role of density-dependent crossdiffusion in epidemiology has been explored numerically by Berres and Ruiz-Baier [5] via the model where K is the carrying capacity, r is the intrinsic birth rate, β is the transmission rate, γ is the recovery rate, D S and D I are the susceptible and infective diffusion coefficients, respectively, and c is the cross-diffusion coefficient. Following the approach in [41], the role of density-dependent cross-diffusion in the aggregation of individuals according to epidemiological states during a nefarious disease outbreak is carried out below. We expand on the type of cross-diffusion model in [6] via the use only of a population of S-individuals (susceptible) and I-individuals (infectives), that is, symptomatic infectious individuals.…”

A variable nonlinear splitting algorithm for reaction diffusion systems with self‐ and cross‐ diffusion

“…The inclusion of self-and cross-diffusion terms allow for realistic responses to predator and prey movement and are often incorporated into mathematical models in population biology [8][9][10][11]. Our current efforts consider only a two species model, yet the methods developed herein can by readily extended to more general systems.…”