Theory of the Spread of Epidemics and Movement Ecology of Animals

Kenkre, V. M.; Giuggioli, Luca

doi:10.1017/9781108882279

Cited by 22 publications

(12 citation statements)

References 391 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, permeable barriers are found at the ecological level where, e.g. animal dispersal is affected by the presence of roads and fences within a heterogeneous landscape [8–10].…”

Section: Introductionmentioning

confidence: 99%

A probabilistic model of diffusion through a semi-permeable barrier

Bressloff

2022

Proc. R. Soc. A.

View full text Add to dashboard Cite

Diffusion through semi-permeable structures arises in a wide range of processes in the physical and life sciences. Examples at the microscopic level range from artificial membranes for reverse osmosis to lipid bilayers regulating molecular transport in biological cells to chemical and electrical gap junctions. There are also macroscopic analogues such as animal migration in heterogeneous landscapes. It has recently been shown that one-dimensional diffusion through a barrier with constant permeability κ 0 is equivalent to snapping out Brownian motion (BM). The latter sews together successive rounds of partially reflecting BMs that are restricted to either the left or the right of the barrier. Each round is killed when its Brownian local time exceeds an exponential random variable parameterized by κ 0 . A new round is then immediately started in either direction with equal probability. In this article, we use a combination of renewal theory, Laplace transforms and Green’s function methods to show how an extended version of snapping out BM provides a general probabilistic framework for modelling diffusion through a semi-permeable barrier. This includes modifications of the diffusion process away from the barrier (e.g. stochastic resetting) and non-Markovian models of membrane absorption that kill each round of partially reflected BM. The latter leads to time-dependent permeabilities.

show abstract

“…Finally, permeable barriers are found at the ecological level where, e.g. animal dispersal is affected by the presence of roads and fences within a heterogeneous landscape [8–10].…”

Section: Introductionmentioning

confidence: 99%

A probabilistic model of diffusion through a semi-permeable barrier

Bressloff

2022

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…It should enable users to address a variety of questions related to invasion risks and spatio‐temporal demo‐genetic structures of populations, as well as to handle different spatial and temporal scales and varying numbers of network nodes, as exemplified by the scenarios explored in this article. However, it is important to note that other modeling approaches may be more suitable for describing and predicting the transport of plant pathogens and pests at specific scales, for particular organisms and to test particular hypotheses (Clobert et al., 2012; Jeger et al., 2007; Kenkre & Giuggioli, 2021; Nathan et al., 2011; Schmale & Ross, 2015). The aforementioned examples concern plant pests and diseases, but our approach can be used to generate connectivity data for diverse application domains: for example, the dispersal from identified sources of pollen, dust, radioactive elements, smokes, and other pollutants; see references in the introduction.…”

Section: Discussionmentioning

confidence: 99%

Computing Geographical Networks Generated by Air‐Mass Movement

Richard,

Martinetti,

Lercier

et al. 2023

GeoHealth

View full text Add to dashboard Cite

As air masses move within the troposphere, they transport a multitude of components including gases and particles such as pollen and microorganisms. These movements generate atmospheric highways that connect geographic areas at distant, local, and global scales that particles can ride depending on their aerodynamic properties and their reaction to environmental conditions. In this article we present an approach and an accompanying web application called tropolink for measuring the extent to which distant locations are potentially connected by air‐mass movement. This approach is based on the computation of trajectories of air masses with the HYSPLIT atmospheric transport and dispersion model, and on the computation of connection frequencies, called connectivities, in the purpose of building trajectory‐based geographical networks. It is illustrated for different spatial and temporal scales with three case studies related to plant epidemiology. The web application that we designed allows the user to easily perform intensive computation and mobilize massive archived gridded meteorological data to build weighted directed networks. The analysis of such networks allowed us for example, to describe the potential of invasion of a migratory pest beyond its actual distribution. Our approach could also be used to compute geographical networks generated by air‐mass movement for diverse application domains, for example, to assess long‐term risk of spread from persistent or recurrent sources of pollutants, including wildfire smoke.

show abstract

“…As an instance, even if a quadratic term is absent in the dynamical equations for liquid crystals in two dimensions due to the traceless condition of its tensor order parameter, other systems may admit such a term. The spatially-dependent Nagumo equation contains such nonlinear dependence [3]:…”

Section: Discussionmentioning

confidence: 99%

“…When nonlinear dynamical systems take into account spatial dependencies, they often are modeled in a continuum fashion with partial differential equations. Among the diversity of such systems, the Newell-Whitehead equation (1) finds application diverse fields such as population growth and epidemics in ecology [3], pattern formation in cloud fields [4], mechanical and chemical engineering [5], and the dynamics of phase transitions [6]:…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Nanoparticle Self-Assembly by Liquid Crystal Sorting in Two Dimensions

et al. 2021

View full text Add to dashboard Cite

We study nonlinear dynamical equations for coupled conserved and non-conserved fields describing nanoparticle concentration and liquid crystal order parameter, respectively, and solve them numerically over bidimensional domains. These equations model the rapid segregation of nanoparticles away from nematic domains, which has been observed experimentally in a suspension of gold nanoparticles in 5CB below the isotropic-nematic transition temperature. We contrast the different behaviors obtained when the LC order parameter is treated as a scalar or a tensor, as well as the different rates of evolution observed with each of these. We find, after an instantaneous quench lowering the temperature below the transition one, an initial linear regime where the ordering of the nematic phase proceeds exponentially with time. Only after a lag period the nanoparticle material couples effectively to the LC order parameter and segregates to regions that are less orientationally ordered (extended domain walls for a scalar order parameter, but point disclinations for a tensor one). The lag period is followed by the onset of nonlinear dynamics and saturation of the order parameter. The choice of a scalar or tensor LC order parameter does not change this sequence but results in a clear overshooting of the nonlinear saturation level for the tensor order parameter case. These results are found to be insensitive to weak anchoring due to coupling of gradients of the conserved and non-conserved variables, for the nanoparticle concentrations and anchoring parameters studied. Our modeling approach can be extended in a straightforward manner to cases where the cooling rate is finite and to other systems where a locally conserved concentration is coupled to a orientation field, such as active Langmuir monolayers, and possibly to other examples of nonlinear dynamics in ecological or excitable media problems.

show abstract

Theory of the Spread of Epidemics and Movement Ecology of Animals

Cited by 22 publications

References 391 publications

A probabilistic model of diffusion through a semi-permeable barrier

A probabilistic model of diffusion through a semi-permeable barrier

Computing Geographical Networks Generated by Air‐Mass Movement

Dynamics of Nanoparticle Self-Assembly by Liquid Crystal Sorting in Two Dimensions

Contact Info

Product

Resources

About