TY - JOUR AU - Wang, Yanmei AU - Liu, Guirong AU - Zhao, Aimin PY - 2018 TI - Traveling waves for a diffusive SIR model with delay and nonlinear incidence JO - Journal of Nonlinear Sciences and Applications SP - 1313--1330 VL - 11 IS - 12 AB - This paper is concerned with the existence and non-existence of traveling wave solutions for a diffusive SIR model with delay and nonlinear incidence. First, we construct a pair of upper and lower solutions and a bounded cone. Then we prove the existence of traveling wave by using Schauder's fixed point theorem and constructing a suitable Lyapunov functional. The nonexistence of traveling wave is obtained by two-sided Laplace transform. Moreover, numerical simulations support the theoretical results. Finally, we also obtain that the minimal wave speed is decreasing with respect to the latent period and increasing with respect to the diffusion rate of infected individuals. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.011.12.03 DO - 10.22436/jnsa.011.12.03 ID - Wang2018 ER - TY - JOUR TI - Traveling waves in a delayed SIR epidemic model with nonlinear incidence AU - Z. G. Bai AU - S.-L. Wu JO - Appl. Math. Comput. PY - 2015 DA - 2015// VL - 263 ID - Bai2015 ER - TY - JOUR TI - Global asymptotic stability of an SIR epidemic model with distributed time delay AU - E. Beretta AU - T. Hara AU - W. Ma AU - Y. Takeuchi JO - Nonlinear Anal. PY - 2001 DA - 2001// VL - 47 ID - Beretta2001 ER - TY - JOUR TI - Spatial dynamics of a nonlocal and time-delayed reaction diffusion system AU - J. Fang AU - J. J. Wei AU - X.-Q. Zhao JO - J. Differential Equations PY - 2008 DA - 2008// VL - 245 ID - Fang2008 ER - TY - JOUR TI - Traveling waves for a diffusive SIR model with delay AU - S.-C. Fu JO - J. Math. Anal. Appl. PY - 2016 DA - 2016// VL - 435 ID - Fu 2016 ER - TY - JOUR TI - Traveling waves for a simple diffusive epidemic model AU - Y. Hosono AU - B. Ilyas JO - Math. Models Methods Appl. Sci. PY - 1995 DA - 1995// VL - 5 ID - Hosono1995 ER - TY - JOUR TI - Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate AU - G. Huang AU - Y. Takeuchi AU - W. Ma AU - D. Wei JO - Bull. Math. Biol. PY - 2010 DA - 2010// VL - 72 ID - Huang2010 ER - TY - JOUR TI - A contribution to the mathematical theory of epidemics AU - W. O. Kermack AU - A. G. Mckendrick JO - Proc. Roy. Soc. London Ser. A PY - 1927 DA - 1927// VL - 115 ID - Kermack1927 ER - TY - JOUR TI - Global properties of infectious disease models with nonlinear incidence AU - A. Korobeinikov JO - Bull. Math. Biol. PY - 2007 DA - 2007// VL - 69 ID - Korobeinikov 2007 ER - TY - JOUR TI - Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission AU - A. Korobeinikov JO - Bull. Math. Biol. PY - 2006 DA - 2006// VL - 68 ID - Korobeinikov 2006 ER - TY - JOUR TI - Non-linear incidence and stability of infectious disease models AU - A. Korobeinikov AU - P. K. Maini JO - Math. Med. Biol. PY - 2005 DA - 2005// VL - 22 ID - Korobeinikov2005 ER - TY - JOUR TI - Permanence of an SIR epidemic model with distributed time delays AU - W. Ma AU - Y. Takeuchi AU - T. Hara AU - E. Beretta JO - Tohoku Math. J. PY - 2002 DA - 2002// VL - 54 ID - Ma2002 ER - TY - JOUR TI - Dynamical behavior of an epidemic model with a nonlinear incidence rate AU - S. G. Ruan AU - W. D. Wang JO - J. Differential Equations PY - 2003 DA - 2003// VL - 188 ID - Ruan2003 ER - TY - JOUR TI - The effect of incidence functions on the dynamics of a quarantine/isolation model with time delay AU - M. A. Safi AU - A. B. Gumel JO - Nonlinear Anal. Real World Appl. PY - 2011 DA - 2011// VL - 12 ID - Safi2011 ER - TY - JOUR TI - Global asymptotic properties of a delay SIR epidemic model with finite incubation times AU - Y. Takeuchi AU - W. Ma AU - E. Beretta JO - Nonlinear Anal. Ser. A: Theory Methods PY - 2000 DA - 2000// VL - 42 ID - Takeuchi2000 ER - TY - JOUR TI - Spreading speed and traveling waves for a multi-type SIS epidemic model AU - P. X. Weng AU - X.-Q. Zhao JO - J. Differential Equations PY - 2006 DA - 2006// VL - 229 ID - Weng2006 ER - TY - JOUR TI - Asymptotic speed of propagation and traveling wavefronts for a SIR epidemic model AU - C. F. Wu AU - P. X. Weng JO - Discrete Contin. Dyn. Syst. Ser. B PY - 2011 DA - 2011// VL - 15 ID - Wu2011 ER - TY - JOUR TI - Traveling waves in a Kermack-Mckendrick epidemic model with diffusion and latent period AU - Z. Xu JO - Nonlinear Anal. PY - 2014 DA - 2014// VL - 111 ID - Xu2014 ER - TY - JOUR TI - Global stability of a SIR epidemic model with nonlinear incidence rate and time delay AU - R. Xu AU - Z. Ma JO - Nonlinear Anal. Real World Appl. PY - 2009 DA - 2009// VL - 10 ID - Xu2009 ER -