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Xiao-qiang Zhao - One of the best experts on this subject based on the ideXlab platform.
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A Reaction–Diffusion Model of Vector-Borne Disease with Periodic Delays
Journal of Nonlinear Science, 2019Co-Authors: Xiao-qiang ZhaoAbstract:A vector-borne disease is caused by a range of pathogens and transmitted to hosts through vectors. To investigate the multiple effects of the spatial heterogeneity, the temperature sensitivity of extrinsic incubation period and intrinsic incubation period, and the seasonality on disease transmission, we propose a nonlocal reaction–diffusion Model of vector-borne disease with periodic delays. We introduce the basic reproduction number $$\mathfrak {R}_0$$ R 0 for this Model and then establish a threshold-type result on its global dynamics in terms of $$\mathfrak {R}_0$$ R 0 . In the case where all the coefficients are constants, we also prove the global attractivity of the positive constant steady state when $$\mathfrak {R}_0>1$$ R 0 > 1 . Numerically, we study the malaria transmission in Maputo Province, Mozambique.
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A Reaction-Diffusion Model of Vector-Borne Disease with Periodic Delays
Journal of Nonlinear Science, 2018Co-Authors: Xiao-qiang ZhaoAbstract:A vector-borne disease is caused by a range of pathogens and transmitted to hosts through vectors. To investigate the multiple effects of the spatial heterogeneity, the temperature sensitivity of extrinsic incubation period and intrinsic incubation period, and the seasonality on disease transmission, we propose a nonlocal reaction–diffusion Model of vector-borne disease with periodic delays. We introduce the basic reproduction number $$\mathfrak {R}_0$$ for this Model and then establish a threshold-type result on its global dynamics in terms of $$\mathfrak {R}_0$$ . In the case where all the coefficients are constants, we also prove the global attractivity of the positive constant steady state when $$\mathfrak {R}_0>1$$ . Numerically, we study the malaria transmission in Maputo Province, Mozambique.
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Monostable waves and spreading speed for a Reaction-Diffusion Model with seasonal succession
Discrete and Continuous Dynamical Systems - Series B, 2015Co-Authors: Xiao-qiang ZhaoAbstract:This paper is devoted to the study of propagation phenomena for a two-species competitive Reaction-Diffusion Model with seasonal succession in the monostable case. By appealing to theory of traveling waves and spreading speeds for monotone semiflows, we establish the existence of the minimal wave speed for rightward traveling waves and its coincidence with the rightward spreading speed. We also obtain a set of sufficient conditions for the spreading speed to be linearly determinate.
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spatiotemporal patterns in a reaction diffusion Model with the degn harrison reaction scheme
Journal of Differential Equations, 2013Co-Authors: Rui Peng, Xiao-qiang ZhaoAbstract:Abstract Spatial and temporal patterns generated in ecological and chemical systems have become a central object of research in recent decades. In this work, we are concerned with a reaction–diffusion Model with the Degn–Harrison reaction scheme, which accounts for the qualitative feature of the respiratory process in a Klebsiella aerogenes bacterial culture. We study the global stability of the constant steady state, existence and nonexistence of nonconstant steady states as well as the Hopf and steady state bifurcations. In particular, our results show the existence of Turing patterns and inhomogeneous periodic oscillatory patterns while the system parameters are all spatially homogeneous. These results also exhibit the critical role of the system parameters in leading to the formation of spatiotemporal patterns.
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Spatiotemporal patterns in a reaction–diffusion Model with the Degn–Harrison reaction scheme☆
Journal of Differential Equations, 2013Co-Authors: Rui Peng, Xiao-qiang ZhaoAbstract:Abstract Spatial and temporal patterns generated in ecological and chemical systems have become a central object of research in recent decades. In this work, we are concerned with a reaction–diffusion Model with the Degn–Harrison reaction scheme, which accounts for the qualitative feature of the respiratory process in a Klebsiella aerogenes bacterial culture. We study the global stability of the constant steady state, existence and nonexistence of nonconstant steady states as well as the Hopf and steady state bifurcations. In particular, our results show the existence of Turing patterns and inhomogeneous periodic oscillatory patterns while the system parameters are all spatially homogeneous. These results also exhibit the critical role of the system parameters in leading to the formation of spatiotemporal patterns.
Des E. Conlong - One of the best experts on this subject based on the ideXlab platform.
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a reaction diffusion Model for the control of eldana saccharina walker in sugarcane using the sterile insect technique
Ecological Modelling, 2013Co-Authors: L. Potgieter, Jh Van Vuuren, Des E. ConlongAbstract:Abstract A reaction–diffusion Model is formulated for the population dynamics of an Eldana saccharina Walker infestation of sugarcane under the influence of partially sterile released insects. The Model describes the population growth of and interaction between normal and sterile E. saccharina moths in a temporally variable and spatially heterogeneous environment. It consists of a discretized reaction–diffusion system with variable diffusion coefficients, subject to strictly positive initial data and zero-flux Neumann boundary conditions on a bounded spatial domain. The primary objectives are to establish a Model which may be used within an area-wide integrated pest management programme for E. saccharina in order to investigate the efficiency of different sterile moth release strategies without having to conduct formal field experiments, and to present guidelines according to which release ratios, release frequencies and spatial distributions of releases may be estimated which are expected to lead to suppression of the pest. Although many reaction–diffusion Models have been formulated in the literature describing the sterile insect technique, few of these Models describe the technique for Lepidopteran species with more than one life stage and where F1-sterility is relevant. In addition, none of these Models consider the technique when fully sterile females and partially sterile males are released. The Model formulated here is also the first reaction–diffusion Model formulated describing E. saccharina growth and migration, and the sterile insect technique applied specifically to E. saccharina .
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A reaction–diffusion Model for the control of Eldana saccharina Walker in sugarcane using the sterile insect technique
Ecological Modelling, 2013Co-Authors: L. Potgieter, Jh Van Vuuren, Des E. ConlongAbstract:Abstract A reaction–diffusion Model is formulated for the population dynamics of an Eldana saccharina Walker infestation of sugarcane under the influence of partially sterile released insects. The Model describes the population growth of and interaction between normal and sterile E. saccharina moths in a temporally variable and spatially heterogeneous environment. It consists of a discretized reaction–diffusion system with variable diffusion coefficients, subject to strictly positive initial data and zero-flux Neumann boundary conditions on a bounded spatial domain. The primary objectives are to establish a Model which may be used within an area-wide integrated pest management programme for E. saccharina in order to investigate the efficiency of different sterile moth release strategies without having to conduct formal field experiments, and to present guidelines according to which release ratios, release frequencies and spatial distributions of releases may be estimated which are expected to lead to suppression of the pest. Although many reaction–diffusion Models have been formulated in the literature describing the sterile insect technique, few of these Models describe the technique for Lepidopteran species with more than one life stage and where F1-sterility is relevant. In addition, none of these Models consider the technique when fully sterile females and partially sterile males are released. The Model formulated here is also the first reaction–diffusion Model formulated describing E. saccharina growth and migration, and the sterile insect technique applied specifically to E. saccharina .
Rui Peng - One of the best experts on this subject based on the ideXlab platform.
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the role of protection zone on species spreading governed by a reaction diffusion Model with strong allee effect
Journal of Differential Equations, 2019Co-Authors: Kai Du, Rui PengAbstract:Abstract It is known that a species dies out in the long run for small initial data if its evolution obeys a reaction of bistable nonlinearity. Such a phenomenon, which is termed as the strong Allee effect, is well supported by numerous evidence from ecosystems, mainly due to the environmental pollution as well as unregulated harvesting and hunting. To save an endangered species, in this paper we introduce a protection zone that is governed by a Fisher–KPP nonlinearity, and examine the dynamics of a reaction–diffusion Model with strong Allee effect and protection zone. We show the existence of two critical values 0 L ⁎ ≤ L ⁎ , and prove that a vanishing-transition-spreading trichotomy result holds when the length of protection zone is smaller than L ⁎ ; a transition-spreading dichotomy result holds when the length of protection zone is between L ⁎ and L ⁎ ; only spreading happens when the length of protection zone is larger than L ⁎ . This suggests that the protection zone works when its length is larger than the critical value L ⁎ . Furthermore, we compare two types of protection zone with the same length: a connected one and a separate one, and our results reveal that the former is better for species spreading than the latter.
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the role of protection zone on species spreading governed by a reaction diffusion Model with strong allee effect
arXiv: Analysis of PDEs, 2018Co-Authors: Kai Du, Rui PengAbstract:It is known that a species dies out in the long run for small initial data if its evolution obeys a reaction of bistable nonlinearity. Such a phenomenon, which is termed as the strong Allee effect, is well supported by numerous evidence from ecosystems, mainly due to the environmental pollution as well as unregulated harvesting and hunting. To save an endangered species, in this paper we introduce a protection zone that is governed by a Fisher-KPP nonlinearity, and examine the dynamics of a Reaction-Diffusion Model with strong Allee effect and protection zone. We show the existence of two critical values $0
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asymptotic profile of the positive steady state for an sis epidemic reaction diffusion Model effects of epidemic risk and population movement
Physica D: Nonlinear Phenomena, 2013Co-Authors: Rui PengAbstract:Abstract Identifying the epidemic risk for infectious disease is crucial in order to effectively perform control measures. In a series of our work, from an analytical aspect we study the effects of epidemic risk and population movement on the spatiotemporal transmission of infectious disease via an SIS epidemic reaction–diffusion Model proposed by Allen et al. (2008) in [36] . In Allen et al. (2008) [36] , Peng (2009) [37] , it was assumed that the habitat of the populations consists of only the low and high risk areas. The present paper concerns a more complicated heterogeneous environment where the moderate risk area occurs, and deals with two cases: (i) only the moderate and high risk areas exist; (ii) the low, moderate and high risk areas coexist. In each case, we rigorously determine the asymptotic profile of the positive steady state (i.e., the endemic equilibrium) as the migration rate of either the susceptible or infected population tends to zero. Our results show how epidemic risk and population movement affect the spatial distribution of infectious disease and thereby suggest important implications for predicting the patterns of disease occurrence and designing optimal control strategies. Numerical simulations are carried out to support the theoretical results.
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spatiotemporal patterns in a reaction diffusion Model with the degn harrison reaction scheme
Journal of Differential Equations, 2013Co-Authors: Rui Peng, Xiao-qiang ZhaoAbstract:Abstract Spatial and temporal patterns generated in ecological and chemical systems have become a central object of research in recent decades. In this work, we are concerned with a reaction–diffusion Model with the Degn–Harrison reaction scheme, which accounts for the qualitative feature of the respiratory process in a Klebsiella aerogenes bacterial culture. We study the global stability of the constant steady state, existence and nonexistence of nonconstant steady states as well as the Hopf and steady state bifurcations. In particular, our results show the existence of Turing patterns and inhomogeneous periodic oscillatory patterns while the system parameters are all spatially homogeneous. These results also exhibit the critical role of the system parameters in leading to the formation of spatiotemporal patterns.
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Spatiotemporal patterns in a reaction–diffusion Model with the Degn–Harrison reaction scheme☆
Journal of Differential Equations, 2013Co-Authors: Rui Peng, Xiao-qiang ZhaoAbstract:Abstract Spatial and temporal patterns generated in ecological and chemical systems have become a central object of research in recent decades. In this work, we are concerned with a reaction–diffusion Model with the Degn–Harrison reaction scheme, which accounts for the qualitative feature of the respiratory process in a Klebsiella aerogenes bacterial culture. We study the global stability of the constant steady state, existence and nonexistence of nonconstant steady states as well as the Hopf and steady state bifurcations. In particular, our results show the existence of Turing patterns and inhomogeneous periodic oscillatory patterns while the system parameters are all spatially homogeneous. These results also exhibit the critical role of the system parameters in leading to the formation of spatiotemporal patterns.
L. Potgieter - One of the best experts on this subject based on the ideXlab platform.
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a reaction diffusion Model for the control of eldana saccharina walker in sugarcane using the sterile insect technique
Ecological Modelling, 2013Co-Authors: L. Potgieter, Jh Van Vuuren, Des E. ConlongAbstract:Abstract A reaction–diffusion Model is formulated for the population dynamics of an Eldana saccharina Walker infestation of sugarcane under the influence of partially sterile released insects. The Model describes the population growth of and interaction between normal and sterile E. saccharina moths in a temporally variable and spatially heterogeneous environment. It consists of a discretized reaction–diffusion system with variable diffusion coefficients, subject to strictly positive initial data and zero-flux Neumann boundary conditions on a bounded spatial domain. The primary objectives are to establish a Model which may be used within an area-wide integrated pest management programme for E. saccharina in order to investigate the efficiency of different sterile moth release strategies without having to conduct formal field experiments, and to present guidelines according to which release ratios, release frequencies and spatial distributions of releases may be estimated which are expected to lead to suppression of the pest. Although many reaction–diffusion Models have been formulated in the literature describing the sterile insect technique, few of these Models describe the technique for Lepidopteran species with more than one life stage and where F1-sterility is relevant. In addition, none of these Models consider the technique when fully sterile females and partially sterile males are released. The Model formulated here is also the first reaction–diffusion Model formulated describing E. saccharina growth and migration, and the sterile insect technique applied specifically to E. saccharina .
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A reaction–diffusion Model for the control of Eldana saccharina Walker in sugarcane using the sterile insect technique
Ecological Modelling, 2013Co-Authors: L. Potgieter, Jh Van Vuuren, Des E. ConlongAbstract:Abstract A reaction–diffusion Model is formulated for the population dynamics of an Eldana saccharina Walker infestation of sugarcane under the influence of partially sterile released insects. The Model describes the population growth of and interaction between normal and sterile E. saccharina moths in a temporally variable and spatially heterogeneous environment. It consists of a discretized reaction–diffusion system with variable diffusion coefficients, subject to strictly positive initial data and zero-flux Neumann boundary conditions on a bounded spatial domain. The primary objectives are to establish a Model which may be used within an area-wide integrated pest management programme for E. saccharina in order to investigate the efficiency of different sterile moth release strategies without having to conduct formal field experiments, and to present guidelines according to which release ratios, release frequencies and spatial distributions of releases may be estimated which are expected to lead to suppression of the pest. Although many reaction–diffusion Models have been formulated in the literature describing the sterile insect technique, few of these Models describe the technique for Lepidopteran species with more than one life stage and where F1-sterility is relevant. In addition, none of these Models consider the technique when fully sterile females and partially sterile males are released. The Model formulated here is also the first reaction–diffusion Model formulated describing E. saccharina growth and migration, and the sterile insect technique applied specifically to E. saccharina .
M.b.a. Mansour - One of the best experts on this subject based on the ideXlab platform.
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Traveling wave solutions for an autocatalytic reaction–diffusion Model
Communications in Nonlinear Science and Numerical Simulation, 2013Co-Authors: M.b.a. MansourAbstract:Abstract In this paper we consider an autocatalytic reaction–diffusion Model which has many applications. We extend previous results using qualitative analysis and show the existence of an exponentially decaying traveling wave front for a minimum speed and algebraically decaying wave fronts for large speeds. Further, the wave front profiles are calculated and the minimum speed is accurately determined using different numerical methods.
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Traveling wave solutions of a reaction–diffusion Model for bacterial growth
Physica A: Statistical Mechanics and its Applications, 2007Co-Authors: M.b.a. MansourAbstract:Abstract In this paper, we consider a reaction–diffusion Model for the bacterial growth. Mathematical analysis on the traveling wave solutions of the Model is performed. This includes traveling wave analysis and numerical simulations of wave front propagation for a special case. Specifically, we show that such solutions exist only for wave speeds greater than some minimum speed giving wave with a sharp front. The minimum speed is estimated and the wave profile is calculated and compared with different numerical methods.
