References
- E. Beretta and Y. Takeuchi, Convergence results in SIR epidemic models with varying population sizes, Nonlinear Anal. 28 (1997), no. 12, 1909–1921. https://doi.org/10.1016/S0362-546X(96)00035-1
- R. Bhattacharyya and B. Mukhopadhyay, Spatial dynamics of nonlinear prey- predator models with prey migration and predator switching, Ecological Complexity 3 (2006), 160–169. https://doi.org/10.1016/j.ecocom.2006.01.001
- F. D. Chen and X. D. Xie, Permanence and extinction in nonlinear single and multiple species system with diffusion, Appl. Math. Comput. 177 (2006), no. 1, 410–426. https://doi.org/10.1016/j.amc.2005.11.019
- J. A. Cui and L. S. Chen, The effect of diffusion on the time varying logistic population growth, Comput. Math. Appl. 36 (1998), no. 3, 1–9. https://doi.org/10.1016/S0898-1221(98)00124-2
- S. J. Gao, L. S. Chen, and Z. D. Teng, Hopf bifurcation and global stability for a delayed predator-prey system with stage structure for predator, Appl. Math. Comput. 202 (2008), no. 2, 721–729. https://doi.org/10.1016/j.amc.2008.03.011
- J. Hale, Theory of Functional Differential Equation, Springer-Verlag, 1977.
- J. Hale and S. Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
- B. Hassard, D. Kazarino, and Y. Wan, Theory and applications of Hopf bifurcation, Cambridge University Press, Cambridge, 1981.
- H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev. 42 (2000), no. 4, 599–653. https://doi.org/10.1137/S0036144500371907
- Y. Kuang and Y. Takeuchi, Predator-prey dynamics in models of prey dispersal in two-patch environments, Math. Biosci. 120 (1994), no. 1, 77–98. https://doi.org/10.1016/0025-5564(94)90038-8
- G. H. Li and Z. Jin, Global stability of an SEI epidemic model, Chaos Solitons Fractals 21 (2004), no. 4, 925–931. https://doi.org/10.1016/j.chaos.2003.12.031
- G. H. Li and Z. Jin, Global stability of an SEI epidemic model with general contact rate, Chaos, Solitons and Fractals 23 (2005), no. 3, 997–1004.
- Z. Lu and Y. Takeuchi, Global asymptotic behavior in single-species discrete diffusion systems, J. Math. Biol. 32 (1993), no. 1, 67–77. https://doi.org/10.1007/BF00160375
- Prajneshu and P. Holgate, A prey-predator model with switching effect, J. Theoret. Biol. 125 (1987), no. 1, 61–66. https://doi.org/10.1016/S0022-5193(87)80179-0
- S. G. Ruan and J. J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 10 (2003), no. 6, 863–874.
- B. Shulgin, L. Stone, and Z. Agur, Pulse vaccination strategy in the SIR epidemic model, Bull. Math. Bio. 60 (1998), 1–26. https://doi.org/10.1006/bulm.1997.0010
- X. Y. Song and L. S. Chen, Persistence and global stability for nonautonomous predatorprey system with diffusion and time delay, Comput. Math. Appl. 35 (1998), no. 6, 33–40. https://doi.org/10.1016/S0898-1221(98)00015-7
- C. J. Sun, Y. P. Lin, and M. A. Han, Stability and Hopf bifurcation for an epidemic disease model with delay, Chaos, Solitons and Fractals 30 (2006), no. 1, 204–216. https://doi.org/10.1016/j.chaos.2005.08.167
- Y. Takeuchi, J. A. Cui, R. Miyazaki, and Y. Satio, Permanence of dispersal population model with time delays, J. Comput. Appl. Math. 192 (2006), no. 2, 417–430. https://doi.org/10.1016/j.cam.2005.06.002
- M. Tansky, Switching effect in prey-predator system, J. Theoret. Biol. 70 (1978), no. 3, 263–271. https://doi.org/10.1016/0022-5193(78)90376-4
- E. I. Teramoto, K. Kawasaki, and N. Shigesada, Switching effect of predation on competitive prey species, J. Theoret. Biol. 79 (1979), no. 3, 303–315. https://doi.org/10.1016/0022-5193(79)90348-5
- R. Xu and Z. E. Ma, Stability and Hopf bifurcation in a ratio-dependent predator-prey system with stage structure, Chaos, Solitons and Fractals 38 (2008), no. 3, 669-684. https://doi.org/10.1016/j.chaos.2007.01.019
- K. Yang, Delay Differential Equations With Applications in Population Dynamics, Academic Press, INC, 1993.
- S. L. Zhang and H. Q. Fang, The dispersal properties of a class of epidemic models, J. Biomath. 14 (1999), no. 3, 264–268.
- T. Zhao, Y. Kuang, and H. L. Simith, Global existence of periodic solutions in a class of delayed Gause-type predator-prey systems, Nonlinear Anal. 28 (1997), no. 8, 1373–1394. https://doi.org/10.1016/0362-546X(95)00230-S
- X. Y. Zhou, X. Y. Shi, and X. Y. Song, Analysis of nonautonomous predator-prey model with nonlinear diffusion and time delay, Appl. Math. Comput. 196 (2008), no. 1, 129–136. https://doi.org/10.1016/j.amc.2007.05.041