scholarly journals Demographic feedbacks can hamper the spatial spread of a gene drive

2021 ◽  
Author(s):  
Florence Debarre ◽  
Leo Girardin
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Gene Drive ◽  
Analytical Challenge ◽  
Spatial Spread ◽  
Bistable Systems ◽  
Negative Effect ◽  
Previous Reaction

This paper is concerned with a reactionddiffusion system modeling the fixation and the invasion in a population of a gene drive (an allele biasing inheritance, increasing its own transmission to offspring). In our model, the gene drive has a negative effect on the fitness of individuals carrying it, and is therefore susceptible of decreasing the total carrying capacity of the population locally in space. This tends to generate an opposing demographic advection that the gene drive has to overcome in order to invade. While previous reaction-diffusion models neglected this aspect, here we focus on it and try to predict the sign of the traveling wave speed. It turns out to be an analytical challenge, only partial results being within reach, and we complete our theoretical analysis by numerical simulations. Our results indicate that taking into account the interplay between population dynamics and population genetics might actually be crucial, as it can effectively reverse the direction of the invasion and lead to failure. Our findings can be extended to other bistable systems, such as the spread of cytoplasmic incompatibilities caused by Wolbachia.

scholarly journals Existence of Traveling Wave Solutions for Cholera Model

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Tianran Zhang ◽  
Qingming Gou ◽  
Xiaoli Wang
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Shooting Method ◽  
Reproduction Number ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Reaction Diffusion Model ◽  
Minimal Wave Speed ◽  
The Basic Reproduction Number

To investigate the spreading speed of cholera, Codeço’s cholera model (2001) is developed by a reaction-diffusion model that incorporates both indirect environment-to-human and direct human-to-human transmissions and the pathogen diffusion. The two transmission incidences are supposed to be saturated with infective density and pathogen density. The basic reproduction numberR0is defined and the formula for minimal wave speedc*is given. It is proved by shooting method that there exists a traveling wave solution with speedcfor cholera model if and only ifc≥c*.

scholarly journals Spatial gene drives and pushed genetic waves

2017 ◽  
Author(s):  
Hidenori Tanaka ◽  
Howard A. Stone ◽  
David R. Nelson
Keyword(s):  
Reaction Diffusion ◽  
Two Dimensions ◽  
Wild Type Allele ◽  
Gene Drive ◽  
Wild Type ◽  
Wave Regime ◽  
Spatial Spread ◽  
Type Allele ◽  
Reaction Diffusion Model ◽  
Gene Drives

Gene drives have the potential to rapidly replace a harmful wild-type allele with a gene drive allele engineered to have desired functionalities. However, an accidental or premature release of a gene drive construct to the natural environment could damage an ecosystem irreversibly. Thus, it is important to understand the spatiotemporal consequences of the super-Mendelian population genetics prior to potential applications. Here, we employ a reaction-diffusion model for sexually reproducing diploid organisms to study how a locally introduced gene drive allele spreads to replace the wild-type allele, even though it posses a selective disadvantages> 0. Using methods developed by N. Barton and collaborators, we show that socially responsible gene drives require 0.5 <s< 0.697, a rather narrow range. In this “pushed wave” regime, the spatial spreading of gene drives will be initiated only when the initial frequency distribution is above a threshold profile called “critical propagule”, which acts as a safeguard against accidental release. We also study how the spatial spread of the pushed wave can be stopped by making gene drives uniquely vulnerable (“sensitizing drive”) in a way that is harmless for a wild-type allele. Finally, we show that appropriately sensitized drives in two dimensions can be stopped even by imperfect barriers perforated by a series of gaps.

scholarly journals Spatial gene drives and pushed genetic waves

2017 ◽  
Vol 114 (32) ◽  
pp. 8452-8457 ◽  
Author(s):  
Hidenori Tanaka ◽  
Howard A. Stone ◽  
David R. Nelson
Keyword(s):  
Reaction Diffusion ◽  
Two Dimensions ◽  
Wild Type Allele ◽  
Gene Drive ◽  
Wild Type ◽  
Wave Regime ◽  
Spatial Spread ◽  
Type Allele ◽  
Reaction Diffusion Model ◽  
Gene Drives

Gene drives have the potential to rapidly replace a harmful wild-type allele with a gene drive allele engineered to have desired functionalities. However, an accidental or premature release of a gene drive construct to the natural environment could damage an ecosystem irreversibly. Thus, it is important to understand the spatiotemporal consequences of the super-Mendelian population genetics before potential applications. Here, we use a reaction–diffusion model for sexually reproducing diploid organisms to study how a locally introduced gene drive allele spreads to replace the wild-type allele, although it possesses a selective disadvantages> 0. Using methods developed by Barton and collaborators, we show that socially responsible gene drives require 0.5 <s< 0.697, a rather narrow range. In this “pushed wave” regime, the spatial spreading of gene drives will be initiated only when the initial frequency distribution is above a threshold profile called “critical propagule,” which acts as a safeguard against accidental release. We also study how the spatial spread of the pushed wave can be stopped by making gene drives uniquely vulnerable (“sensitizing drive”) in a way that is harmless for a wild-type allele. Finally, we show that appropriately sensitized drives in two dimensions can be stopped, even by imperfect barriers perforated by a series of gaps.

TRAVELING WAVES FOR A SIMPLE DIFFUSIVE EPIDEMIC MODEL

1995 ◽  
Vol 05 (07) ◽  
pp. 935-966 ◽  
Author(s):  
YUZO HOSONO ◽  
BILAL ILYAS
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Shooting Argument ◽  
Wave Solutions ◽  
Minimal Wave Speed ◽  
Manifold Theory

We investigate the existence of traveling wave solutions for the infective-susceptible two-component epidemic model. The model system is described by reaction-diffusion equations with the nonlinear reaction term of the classical Kermack-McKendric type. The diffusion coefficients of infectives and susceptibles are assumed to be positive constants d1 and d2 respectively. By the shooting argument with the aid of the invariant manifold theory, we prove that there exists a positive constant c* such that the traveling wave solutions exist for any c≥c*. The minimal wave speed c* is shown to be independent of d2 and to have the same value as that for d2=0.

scholarly journals Traveling Wave Solutions in a Reaction-Diffusion Epidemic Model

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Sheng Wang ◽  
Wenbin Liu ◽  
Zhengguang Guo ◽  
Weiming Wang
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Monotone Iteration ◽  
Wave Solutions ◽  
Minimal Wave Speed

We investigate the traveling wave solutions in a reaction-diffusion epidemic model. The existence of the wave solutions is derived through monotone iteration of a pair of classical upper and lower solutions. The traveling wave solutions are shown to be unique and strictly monotonic. Furthermore, we determine the critical minimal wave speed.

scholarly journals Drift perturbation’s influence on traveling wave speed in KPP-Fisher system

2016 ◽  
Vol 24 (1) ◽  
pp. 189-200
Author(s):  
Fathi Dkhil ◽  
Bechir Mannoubi
Keyword(s):  
Asymptotic Expansion ◽  
Small Parameter ◽  
Traveling Wave ◽  
Wave Speed ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Fisher Equation ◽  
Front Solution ◽  
Traveling Front

AbstractThis paper dressed the drift perturbation effects on the traveling wave speed in a reaction-diffusion system. We prove the existence of a traveling front solution of a KPP-Fisher equation and we show an asymptotic expansion of her speed. Finally, we discuss according all parameters of our system regions of the plane in which the traveling wave speed increases or decreases as a function of a small parameter ε.

scholarly journals Continuous Dependence in Front Propagation for Convective Reaction-Diffusion Models with Aggregative Movements

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Luisa Malaguti ◽  
Cristina Marcelli ◽  
Serena Matucci
Keyword(s):  
Traveling Wave ◽  
Continuous Dependence ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Front Propagation ◽  
Real Parameter ◽  
Reaction Diffusion Equation ◽  
Qualitative Properties ◽  
Wave Profiles

The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.

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