
Mathematical Biosciences and Engineering, 2020, 17(5): 60986127. doi: 10.3934/mbe.2020324
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Dynamics of an epidemic model with relapse over a twopatch environment
1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China
2 Department of Applied Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
Received: , Accepted: , Published:
Special Issues: Applications of delay differential equations in biology
References
1. S. W. Martin., Livestock Disease Eradication: Evaluation of the Cooperative StateFederal Bovine Tuberculosis Eradication Program, National Academy Press, Washington, 1994.
2. J. Chin., Control of Communicable Diseases Manual, American Public Health Association, Washington, 1999.
3. K. E. VanLandingham, H. B. Marsteller, G. W. Ross, F. G. Hayden, Relapse of herpes simplex encephalitis after conventional acyclovir therapy, JAMA, 259 (1988), 10511053.
4. P. van den Driessche, X. Zou, Modeling relapse in infectious diseases, Math. Biosci., 207 (2007), 89103.
5. J. Arino, P. van den Driessche, Disease spread in metapopulations, Fields Institute Communications, 48 (2006), 112.
6. T. Dhirasakdanon, H. R. Thieme, P. van Den Driessche, A sharp threshold for disease persistence in host metapopulations, J. Biol. Dyn., 1 (2007), 363378.
7. M. Salmani, P. van den Driessche, A model for disease transmission in a patchy environment, Discret. Cont. Dyn. Syst. Ser B, 6 (2006), C185C202.
8. W. Wang, X. Zhao, An epidemic model with population dispersal and infection period, SIAM J. Appl. Math., 66 (2006), 14541472.
9. Y. Xiao, X. Zou, Transmission dynamics for vectorborne diseases in a patchy environment, J. Math. Biol., 69 (2014), 113146.
10. R. M. Almarashi, C. C. McCluskey, The effect of immigration of infectives on diseasefree equilibria, J. Math. Biol., 79 (2020), 10151028.
11. S. Chen, J. Shi, Z. Shuai, Y. Wu, Asymptotic profiles of the steady states for an SIS epidemic patch model with asymmetric connectivity matrix, J. Math. Biol., 80 (2020), 23272361.
12. J. Li, X. Zou, Generalization of the KermackMcKendrick SIR model to patch environment for a disease with latency, Math. Model. Natl. Phenom., 4 (2009), 92118.
13. J. Li, X. Zou, Dynamics of an epidemic model with nonlocal infections for diseases with latency over a patch environment, J. Math. Biol., 60 (2010), 645686.
14. J. W. H. So, J. Wu, X. Zou, Structured population on two patches: modeling dispersal and delay, J. Math. Biol., 43 (2001), 3751.
15. J. Yang, H. R. Thieme, An endemic model with variable reinfection rate and application to influenza, Math. Biosci., 180 (2002), 207235.
16. M. V. Barbarossa, G. Röst, Immunoepidemiology of a population structured by immune status: a mathematical study of waning immunity and immune system boosting, J. Math. Biol., 71 (2015), 17371770.
17. A. Berman, R. J. Plemmons, Nonnegative matrices in the mathematical sciences, Academic Press, London 1979.
18. J. K. Hale, S. M. Verduyn Lunel, Introduction to functional differential equations, Spring, New York, 1993.
19. H. L. Smith, Monotone dynamical systems, An introduction to the theory of competitive and cooperative systems, Amer. Math. Soc., Providence, 1995.
20. H. L. Smith, P. Waltman, The theory of the chemostat, Cambridge University Press, Cambridge, 1995.
21. C. CastilloChaves, H. R. Thieme, Asymptotically autonomous epidemic models, In: Arino O et al (eds) Mathematical population dynamics: analysis of heterogeneity, I. Theory of epidemics. Wuerz, Winnipeg, 1995, 3350.
22. K. Mischaikow, H. Smith, H. R. Thieme, Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions, Trans. Amer. Math. Soc., 347 (1995), 16691685.
23. W. M. Hirsch, H. Hanisch, J. P. Gabriel, Differential equation models of some parasitic infections: methods for the study of asymptotic behavior, Commu. Pure Appl. Math., 38 (1985), 733753.
24. J. A. J. Metz, O. Diekmann, The Dynamics of Physiologically Structured Populations, SpringerVerlag, New York, 1986.
25. H. R. Thieme, Persistence under relaxed pointdissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993), 407435.
26. P. van den Driessche, L. Wang, X. Zou, Modeling diseases with latency and relapse, Math. Biosci. Eng., 4 (2007), 205219.
27. X. Zhao, Uniform persistence and periodic coexistence states in infinitedimensional periodic semiflows with applications, Can Appl Math Q, 3 (1995), 473495.
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