Wave propagation in a nonlocal diffusion epidemic model with nonlocal delayed effects

Abstract A nonlocal diffusion epidemic model with nonlocal delayed effects is investigated. The existence and non-existence of the non-trivial and non-negative traveling wave solutions for the model are obtained, respectively. It is found that the threshold dynamics of the model is determined by the basic reproduction number of the corresponding reaction system and minimal wave speed.

[1]  Zhenguo Bai,et al.  Traveling waves of a diffusive SIR epidemic model with a class of nonlinear incidence rates and distributed delay , 2015 .

[2]  Wan-Tong Li,et al.  Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays , 2006 .

[3]  Guo-Bao Zhang,et al.  Global stability of wavefronts with minimal speeds for nonlocal dispersal equations with degenerate , 2011 .

[4]  Shuxia Pan.  Traveling Wave Fronts in an Epidemic Model with Nonlocal Diffusion and Time Delay , 2008 .

[5]  Shangbing Ai,et al.  Traveling wave fronts for generalized Fisher equations with spatio-temporal delays , 2007 .

[6]  Wan-Tong Li,et al.  Traveling waves in a nonlocal dispersal SIR epidemic model , 2015 .

[7]  L. Tian,et al.  Existence, uniqueness and asymptotic behavior of traveling wave fronts for a generalized Fisher equation with nonlocal delay , 2017 .

[8]  Rong Yuan,et al.  Traveling waves for a diffusive SEIR epidemic model with non-local reaction and with standard incidences , 2017 .

[9]  Linghai Zhang,et al.  Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks , 2004 .

[10]  Bilal Ilyas,et al.  TRAVELING WAVES FOR A SIMPLE DIFFUSIVE EPIDEMIC MODEL , 1995 .

[11]  Xingfu Zou,et al.  Traveling Wave Fronts of Reaction-Diffusion Systems with Delay , 2001 .

[12]  Zhi-Cheng Wang,et al.  Entire solutions in nonlocal dispersal equations with bistable nonlinearity , 2011 .

[13]  Jerome Coville,et al.  Nonlocal anisotropic dispersal with monostable nonlinearity , 2008, 1106.4531.

[14]  Peter W. Bates,et al.  Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen-Cahn equation , 2002 .

[15]  Jerome Coville,et al.  Pulsating fronts for nonlocal dispersion and KPP nonlinearity , 2013, 1302.1053.

[16]  Wan-Tong Li,et al.  Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity , 2012 .

[17]  Wan-Tong Li,et al.  Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay , 2007 .

[18]  Jianhong Wu,et al.  Travelling waves of a diffusive Kermack–McKendrick epidemic model with non-local delayed transmission , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[19]  J. Xu,et al.  Existence and non-existence of traveling wave solutions for a nonlocal dispersal SIR epidemic model with nonlinear incidence rate , 2018, Nonlinear Analysis: Real World Applications.

[20]  Fengxin Chen.  Stability and uniqueness of traveling waves for system of nonlocal evolution equations with bistable nonlinearity , 2009 .

[21]  Wan-Tong Li,et al.  Entire solutions in the Fisher-KPP equation with nonlocal dispersal , 2010 .

[22]  Wan-Tong Li,et al.  Traveling wave solutions of a nonlocal delayed SIR model without outbreak threshold , 2014 .

[23]  Omar Abu Arqub,et al.  Solution of the fractional epidemic model by homotopy analysis method , 2013 .

[24]  Yu Yang,et al.  Traveling waves for a nonlocal dispersal SIR model with general nonlinear incidence rate and spatio-temporal delay , 2017 .

[25]  Dongmei Xiao,et al.  Travelling wave solutions in a non-local and time-delayed reaction–diffusion model , 2013 .

[26]  Xiang-Sheng Wang,et al.  Traveling Wave Phenomena in a Kermack–McKendrick SIR Model , 2015, Journal of Dynamics and Differential Equations.

[27]  Wan-Tong Li,et al.  TRAVELING WAVES OF A DELAYED DIFFUSIVE SIR EPIDEMIC MODEL , 2015 .

[28]  L. Tian,et al.  Existence and asymptotic behavior of traveling wave fronts for a food-limited population model with spatio-temporal delay , 2017 .

[29]  Xuefeng Wang,et al.  Metastability and Stability of Patterns in a Convolution Model for Phase Transitions , 2002 .

[30]  P. Bates,et al.  Traveling Waves in a Convolution Model for Phase Transitions , 1997 .

[31]  Zhiting Xu,et al.  Traveling waves in a Kermack–Mckendrick epidemic model with diffusion and latent period☆ , 2014 .

[32]  Y. Kuang.  Delay Differential Equations: With Applications in Population Dynamics , 2012 .

[33]  Hiroki Yagisita,et al.  Existence and nonexistence of traveling waves for a nonlocal monostable equation , 2008, 0810.3317.

[34]  Hiroki Yagisita.  Existence of traveling wave solutions for a nonlocal bistable equation: an abstract approach , 2008 .

[35]  Shigui Ruan,et al.  Spatial-Temporal Dynamics in Nonlocal Epidemiological Models , 2007 .

[36]  Shi-Liang Wu,et al.  Traveling waves in a delayed SIR epidemic model with nonlinear incidence , 2015, Appl. Math. Comput..

[37]  Chunhua Ou,et al.  Persistence of wavefronts in delayed nonlocal reaction-diffusion equations , 2007 .