
Mathematical Biosciences and Engineering, 2019, 16(4): 17981814. doi: 10.3934/mbe.2019087
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Global stability of multigroup SIR epidemic model with group mixing and human movement
School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, P.R. China
Received: , Accepted: , Published:
Special Issues: Modeling and Complex Dynamics of Populations
References
1. M. Kermark and A. Mckendrick, Contributions to the mathematical theory of epidemics, Proc. Roy. Soc. A, 115 (1927), 700–721.
2. H. Shu, D. Fan and J.Wei, Global stability of multigroup SEIR epidemic models with distributed delays and nonlinear transmission, Nonlinear Anal. Real World Appl., 13 (2012), 1581–1592.
3. H. Guo, M. Li and Z. Shuai, Global stability of the endemic equilibrium of multigroup SIR epidemic models, Canadian Appl. Math. Quart., 14 (2006), 259–284.
4. H. Guo, M. Y. Li and Z. Shuai, A graphtheoretic approach to the method of global Lyapunov functions, Proc. Amer. Math. Soc., 136 (2008), 2793–2802.
5. T. Kuniya, Y. Murya and Y. Enatsu, Threshold dynamics of an SIR epidemic model with hybird of nultigroup and patch structures, Math. Biosci. Eng., 11 (2014), 1357–1393.
6. T. Kuniya and Y. Muroya, Global stability of a multigroup SIS epidemic model with varying total population size, Appl. Math. Comput., 265 (2015), 785–798.
7. A. Lajmanovich and J. A. York, A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci., 28 (1976), 221–236.
8. M. Y. Li and Z. Shuai, Global stability of an epidemic model in a patchy environment, Canadian Appl. Math. Quart., 17 (2009), 175–187.
9. M. Y. Li and Z. Shuai, Globalstability problem for coupled systems of differential equations on networks, J. Differ. Eqn., 248 (2010), 1–20.
10. Y. Muroya, Y. Enatsu and T. Kuniya, Global stability for a multigroup SIRS epidemic model with varying population sizes, Nonlinear Anal. Real World Appl, 14 (2013), 1693–1704.
11. H. L. Smith, P. Waltman, The Theory of the Chemostat, Cambridge University, 1995.
12. R. Sun and J. Shi, Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates, Appl. Math. Comput., 218 (2011), 280–286.
13. W. Wang and X. Zhao, An epidemic model with population dispersal and infection period, SIAM J. Appl. Math., 66 (2006), 1454–1472.
14. L.Wang andW. Yang, Global dynamics of a twopatch SIS model with infection during transport, Appl. Math. Comput., 217 (2011), 84588467.
15. How Many Ebola Patients Have Been Treated Outside of Africa?, Source of New York Times, 2014. Available from: https://ritholtz.com/2014/10/ howmanyebolapatientshavebeentreatedoutsideafrica/.
16. J. Arino, J. R. Davis, D. Hartley, et al., A multispecies epidemic model with spatial dynamics, Math. Med. Biol., 22 (2005), 129–142.
17. X. Liu and Y. Takeuchi, Spread of disease with transportrelated infection and entry screening, J Theor. Biol., 242 (2006), 517–528.
18. T. Chen, Z. Sun and B. Wu, Stability of multigroup models with crossdispersal based on graph theory, Appl. Math. Model., 47 (2017), 745–754.
19. H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599–653.
20. T. Kuniya and Y. Muroya, Global stability of a multigroup SIS epidemic model for population migration, Discrete Continuous Dynam. Systems  B, 19 (2014), 1105–1118.
21. Y. Muroya, Y. Enatsu and T. Kuniya, Global stability of extended multigroup SIR epidemic models with patches through migration and cross patch infection, Acta Math. Sci., 33 (2013), 341–361.
22. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
23. N. P. Bhatia and G. P. Szegö, Dynamical Systems: Stability Theory and Applications, Springer, Berlin, 2006.
24. C. CastilloChavez and H. Thieme, Asymptotically autonomous epidemic models, in Mathematical Population Dynamics: Analysis of Heterogeneity (eds. O. Arino, D. Axelrod, M. Kimmel and M. Langlais), Springer, Berlin, 1995, 33–50.
25. P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transimission, Math. Biosci., 180 (2002), 29–48.
26. M. C. Eisenberg, Z. Shuai, J. H. Tien, et al., A cholera model in a patchy environment with water and human movement, Math. Biosci., 246 (2013), 105–112.
27. H. I. Freedman, S. Ruan and M. Tang, Uniform persistence and flows near a closed positively invariant set, J. Dyn. Differ. Equ., 6 (1994), 583–600.
28. K. Mischaikow, H. L. Smith and H. R. Thieme, Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions, Trans. Am. Math. Soc., 347 (1995), 1669–1685.
29. J. P. LaSalle and S. Kefscgetz, Stability by Liapunovs Direct Method with Applications, Academic Press, New York, 1961.
30. M. Y. Li, J. R. Graef, L. Wang, et al., Global dynamics of a SEIR model with varying total population size, Math. Biosci., 160 (1999), 191–213.
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