scholarly journals Virus-host interactions shape viral dispersal giving rise to distinct classes of travelling waves in spatial expansions

2020 ◽  
Author(s):  
Michael Hunter ◽  
Tongfei Liu ◽  
Wolfram Möbius ◽  
Diana Fusco
Keyword(s):  
Cooperative Behavior ◽  
Test Organism ◽  
Host Density ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Effective Density ◽  
Density Dependent ◽  
Phage T7 ◽  
The Impact ◽  
Density Dependent Dispersal

Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the front and stochastic fluctuations are high, or pushed, where cooperation in growth or dispersal results in a bulk-driven wave in which fluctuations are suppressed. These concepts have been well studied experimentally in populations where the cooperation leads to a density-dependent growth rate. By contrast, relatively little is known about experimental populations that exhibit a density-dependent dispersal rate.Using bacteriophage T7 as a test organism, we present novel experimental measurements that demonstrate that the diffusion of phage T7, in a lawn of host E. coli, is hindered by steric interactions with host bacteria cells. The coupling between host density, phage dispersal and cell lysis caused by viral infection results in an effective density-dependent diffusion rate akin to cooperative behavior. Using a system of reaction-diffusion equations, we show that this effect can result in a transition from a pulled to pushed expansion. Moreover, we find that a second, independent density-dependent effect on phage dispersal spontaneously emerges as a result of the viral incubation period, during which phage is trapped inside the host unable to disperse. Our results indicate both that bacteriophage can be used as a controllable laboratory population to investigate the impact of density-dependent dispersal on evolution, and that the genetic diversity and adaptability of expanding viral populations could be much greater than is currently assumed.

Reflood Oxidation Model Based on Reaction-Diffusion Equations

2010 ◽  
Author(s):  
Xiaoqiang He ◽  
Hongxing Yu ◽  
Guangming Jiang
Keyword(s):  
Metal Layer ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Severe Accident ◽  
Model Based ◽  
Oxidation Model ◽  
The Impact ◽  
Relap5 Code ◽  
Good Agreement

An important accident management measure in PWRs is the injection of water to cool the degrading core, in which process the temperature and hydrogen production will significantly increase due to enhanced oxidation after shattering of zircaloy fuel rod. This phenomenon can be described by Zr oxidation model and shattering model. The process of Zr oxidation is usually represented by parabolic rate correlations. But, after consumption of primary β-Zr, or in steam starvation conditions, the correlation approach is restricted. Besides, using this approach, it is impossible to obtain detailed oxygen distribution in the cladding which impacts the detailed mechanical behavior, such as shattering of cladding. The shattering of cladding is mainly contributed by deep cracks penetrating the oxide layer as well as the adjacent metallic. In SCDAP/RELAP5, the shattering criterion is relevant to the thickness of β-Zr, the cladding temperature, and the cooldown rate. After shattering of cladding, the oxide scale is simply removed. This shattering criterion deviates from the experiment of Chung and Kassner when the maximum cladding temperature exceeds 1560 K, and the model can’t reveal the impact of the cladding surface temperature before cooldown on cladding conditions after shattered. An oxidation model based on reaction-diffusion equations at the temperature range from 923K to 2098K is developed in this study. By comparison with experimental data, the model shows reasonable results. Based on the oxidation model, the advanced shattering criterion is adopted, and a new empirical model to describe the cladding conditions after shattered is proposed. In present shattering model, R(T, m), which is the ratio between the area of new crack surfaces in the metal layer and the area of outer cladding surface, is the function of T (the temperature of the cladding surface before cooldown) and m (the thickness of the metal layer). With the help of single-rod QUENCH experiment, the preliminary expression of R(T, m) is obtained, and the results are in a good agreement qualitatively with the observation in this experiment. Further activities should focus on the impact of m and T on R(T, m), which needs more detailed single-rod experiments. Those developed models can be implemented into the SCDAP/RELAP5 code easily and used in the severe accident analysis in the future.

scholarly journals When higher carrying capacities lead to faster propagation

2018 ◽  
Author(s):  
Marjorie Haond ◽  
Thibaut Morel-Journel ◽  
Eric Lombaert ◽  
Elodie Vercken ◽  
Ludovic Mailleret ◽  
...  
Keyword(s):  
Carrying Capacity ◽  
Invasion Biology ◽  
Reaction Diffusion Equations ◽  
Positive Density ◽  
Allee Effects ◽  
Demographic Stochasticity ◽  
Positive Dependence ◽  
Density Dependent ◽  
Temporal Models ◽  
Density Dependent Dispersal

AbstractThis preprint has been reviewed and recommended by Peer Community In Ecology (https://dx.doi.org/10.24072/pci.ecology.100004). Finding general patterns in the expansion of natural populations is a major challenge in ecology and invasion biology. Classical spatio-temporal models predict that the carrying capacity (K) of the environment should have no influence on the speed (v) of an expanding population. We tested the generality of this statement with reaction-diffusion equations, stochastic individual-based models, and microcosms experiments with Trichogramma chilonis wasps. We investigated the dependence between K and v under different assumptions: null model (Fisher-KPP-like assumptions), strong Allee effects, and positive density-dependent dispersal. These approaches led to similar and complementary results. Strong Allee effects, positive density-dependent dispersal and demographic stochasticity in small populations lead to a positive dependence between K and v. A positive correlation between carrying capacity and propagation speed might be more frequent than previously expected, and be the rule when individuals at the edge of a population range are not able to fully drive the expansion.

scholarly journals On the Spatial Diffusion of Cooperation with Endogenous Matching Institutions

Games ◽  
2018 ◽  
Vol 9 (3) ◽  
pp. 58
Author(s):  
Emanuela Migliaccio ◽  
Thierry Verdier
Keyword(s):  
Local Community ◽  
Low Cost ◽  
Cooperative Behavior ◽  
Local Population ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Assortative Matching ◽  
Endogenous Matching ◽  
Asymptotic Speed ◽  
Mathematical Techniques

This paper studies the spatial joint evolution of cooperative behavior and a partially assortative matching institution that protects cooperators. We consider cooperation as characterized by a cultural trait transmitted via an endogenous socialization mechanism and we assume that such trait can diffuse randomly in space due to some spatial noise in the socialization mechanism. Using mathematical techniques from reaction-diffusion equations theory, we show that, under some conditions, an initially localized domain of preferences for cooperation can invade the whole population and characterize the asymptotic speed of diffusion. We consider first the case with exogenous assortativeness, and then endogeneize the degree of social segmentation in matching, assuming that it is collectively set at each point of time and space by the local community. We show how relatively low cost segmenting institutions can appear in new places thanks to the spatial random diffusion of cooperation, helping a localized cultural cluster of cooperation to invade the whole population. The endogenous assortative matching institution follows a life cycle process: appearing, growing and then disappearing once a culture of cooperation is sufficiently established in the local population.

Effects of Catastrophic Anemia in an Intra-Host Model of Malaria

2014 ◽  
Vol 24 (07) ◽  
pp. 1450105
Author(s):  
Eddy Takoutsing ◽  
Samuel Bowong ◽  
David Yemele ◽  
Jurgen Kurths
Keyword(s):  
Blood Cells ◽  
Malaria Parasite ◽  
Reaction Diffusion ◽  
The Body ◽  
Reaction Diffusion Equations ◽  
Reproduction Rate ◽  
Spatiotemporal Model ◽  
Cell Reproduction ◽  
Temporal Model ◽  
The Impact

In this paper, we develop a mathematical model to assess the strength of the effects of catastrophic anemia level on the dynamical transmission of malaria parasite within the body of a host. We first consider a temporal model. The important mathematical features of the model are thoroughly investigated. We found that the model exhibits forward bifurcation. We also consider a spatiotemporal model using reaction–diffusion equations. The model is numerically analyzed to assess the impact of anemia on the dynamical transmission of malaria parasite within the body of a host. Through numerical simulation, we found that malaria can lead to a catastrophic anemia level even if the parasite is nonpersistent within the body of a host. Numerical results also suggest that to reduce or control the anemia level, the strategy should be to accelerate innate cell reproduction rate or should have the ability to clean parasitized red blood cells (PRBCs) with a high mortality rate.

scholarly journals On the Spatial Diffusion of Cooperation with Endogenous Matching Institutions

2018 ◽  
Author(s):  
Emanuela Migliaccio ◽  
Thierry Verdier
Keyword(s):  
Local Community ◽  
Low Cost ◽  
Cooperative Behavior ◽  
Local Population ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Assortative Matching ◽  
Endogenous Matching ◽  
Asymptotic Speed ◽  
Mathematical Techniques

This paper studies the spatial joint evolution of cooperative behavior and a partially assortative matching institution that protects cooperators. We consider cooperation as characterized by a cultural trait transmitted via an endogenous socialization mechanism a la Bisin and Verdier (2001) and we assume that such trait can diffuse randomly in space due to some spatial noise in the socialization mechanism. Using mathematical techniques from reaction-diffusion equations theory, we show that, under some conditions, an initially localized domain of preferences for cooperation can invade the whole population and characterize the asymptotic speed of diffusion. We consider first thecase with exogenous assortativeness, and then endogeneize the degree of social segmentation in matching, assuming that it is collectively set at each point of time and space by the local community. We show how relatively low cost segmenting institutions can appear in new places thanks to the spatial random diffusion of cooperation, helping a localized cultural cluster of cooperation to invade the whole population. The endogenous assortative matching institution follows a life cycle process : appearing, growing and then disappearing once a culture of cooperation is suffciently established in the local population.

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