Math. Model. Nat. Phenom.
Volume 14, Number 5, 2019
Nonlocal and delay equations
Article Number 505
Number of page(s) 22
Published online 05 December 2019
  1. M. Adimy, A. Chekroun and B. Kazmierczak, Traveling waves in a coupled reaction-diffusion and difference model of hematopoiesis. J. Differ. Equ. 262 (2017) 4085–4128. [Google Scholar]
  2. M. Adimy, A. Chekroun and T. Kuniya, Delayed nonlocal reaction-diffusion model for hematopoietic stem cell dynamics with Dirichlet boundary conditions. MMNP 12 (2017) 1–22. [Google Scholar]
  3. H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976) 620–709. [CrossRef] [MathSciNet] [Google Scholar]
  4. M.S. Bartlett, Deterministic and stochastic models for recurrent epidemics, in Proc. of Third Berkeley Symp. Math. Statist. Prob., edited by J. Neyman. Univ. of Calif. Press, Berkeley (1956) 81–109. [Google Scholar]
  5. C.J. Browne and S.S. Pilyugin, Global analysis of age-structured within-host virus model. Disc. Cont. Dyn. Syst. Series B 18 (2013) 1999–2017. [CrossRef] [Google Scholar]
  6. V. Capasso and D. Fortunato, Stability results for semilinear evolution equations and their application to some reaction-diffusion problems. SIAM J. Appl. Math. 39 (1980) 37–47. [Google Scholar]
  7. F. Chatelin, The spectral approximation of linear operators with applications to the computation of eigenelements of differential and integral operators. SIAM Rev. 23 (1981) 495–522. [CrossRef] [Google Scholar]
  8. A. Chekroun and T. Kuniya, An infection age-space structured SIR epidemic model with Neumann boundary condition. Appl. Anal. (2018) 1–14. [Google Scholar]
  9. A. Chekroun, M.N. Frioui, T. Kuniya and T.M. Touaoula, Global stability of an age-structured epidemic model with general Lyapunov functional. Math. Biosci. Eng. 16 (2019) 1525–1553. [CrossRef] [PubMed] [Google Scholar]
  10. Y. Chen, J. Yang and F. Zhang, The global stability of an SIRS model with infection age. Math. Biosci. Eng. 11 (2014) 449–469. [CrossRef] [PubMed] [Google Scholar]
  11. E.M.C. D’Agata, P. Magal, S. Ruan and G. Webb, Asymptotic behavior in nosocomial epidemic models with antibiotic resistance. Diff. Int. Eq. 19 (2006) 573–600. [Google Scholar]
  12. O. Diekmann, J.A.P. Heesterbeek and J.A.J. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990) 365–382. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  13. W. Ding, W. Huang and S. Kansakar, Traveling wave solutions for a diffusive SIS epidemic model. Disc. Cont. Dyn. Syst. Series B 18 (2013) 1291–1304. [CrossRef] [Google Scholar]
  14. A. Ducrot and P. Magal, Travelling wave solutions for an infection-age structured epidemic model with external supplies. Nonlinearity 24 (2011) 2891–2911. [Google Scholar]
  15. A. Ducrot, P. Magal and S. Ruan, Travelling wave solutions in multigroup age-structured epidemic models. Arch. Rational Mech. Anal. 195 (2010) 311–331. [CrossRef] [Google Scholar]
  16. Y. Enatsu, Y. Nakata and Y. Muroya, Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays. Disc. Cont. Dyn. Syst. Series B 15 (2011) 61–74. [CrossRef] [Google Scholar]
  17. W.E. Fitzgibbon, M.E. Parrott and G.F. Webb, Diffusion epidemic models with incubation and crisscross dynamics. Math. Biosci. 128 (1995) 131–155. [Google Scholar]
  18. Z. Guo, Z.-C. Yang and X. Zou, Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition – a non-monotone case. Comm. Pure Appl. Anal. 11 (2012) 1825–1838. [CrossRef] [Google Scholar]
  19. Y. Hosono and B. Ilyas, Traveling waves for a simple diffusive epidemic model. Math. Model. Meth. Appl. Sci. 5 (1995) 935–966. [CrossRef] [Google Scholar]
  20. G. Huang, X. Liu and Y. Takeuchi, Lyapunov functions and global stability for age-structured HIV infection model. SIAM J. Appl. Math. 72 (2012) 25–38. [Google Scholar]
  21. M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics. Giardini editori e stampatori, Pisa (1995). [Google Scholar]
  22. H. Inaba, Age-Structured Population Dynamics in Demography and Epidemiology. Springer, Singapore (2017). [CrossRef] [Google Scholar]
  23. T. Kajiwara, T. Sasaki and Y. Otani, Global stability of an age-structured model for pathogen-immune interaction. J. Appl. Math. Comput. 59 (2019) 631–660. [Google Scholar]
  24. D.G. Kendall, Mathematical models of the spread of infection, in Mathematics and Computer Science in Biology and Medicine. Medical Research Council, London (1965) 213–225. [Google Scholar]
  25. W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics-I. Proc. Roy. Soc. 115 (1927) 700–721. [CrossRef] [Google Scholar]
  26. E.M. Lotfi, M. Maziane, K. Hattaf and N. Yousfi, Partial differential equations of an epidemic model with spatial diffusion. Int. J. Part. Diff. Equ. 2014 (2014) 186437. [Google Scholar]
  27. W. Ma, M. Song and Y. Takeuchi, Global stability of an SIR epidemic model with time delay. Appl. Math. Lett. 17 (2004) 1141–1145. [Google Scholar]
  28. P. Magal, C.C. McCluskey and G.F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model. Appl. Anal. 89 (2010) 1109–1140. [Google Scholar]
  29. C.C. McCluskey, Complete global stability for an SIR epidemic model with delay - distributed or discrete. Nonlinear Anal. RWA 11 (2010) 55–59. [CrossRef] [Google Scholar]
  30. F.A. Milner and R. Zhao, S-I-R model with directed spatial diffusion. Math. Popul. Stud. 15 (2008) 160–181. [Google Scholar]
  31. P. de Mottoni, E. Orlandi and A. Tesei, Asymptotic behavior for a system describing epidemics with migration and spatial spread of infection. Nonlinear Anal. RWA 3 (1979) 663–675. [CrossRef] [Google Scholar]
  32. G. Mulone and B. Straughan, Nonlinear stability for diffusion models in biology. SIAM J. Appl. Math. 69 (2009) 1739–1758. [Google Scholar]
  33. B. Soufiane and T.M. Touaoula, Global analysis of an infection age model with a class of nonlinear incidence rates. J. Math. Anal. Appl. 434 (2016) 1211–1239. [Google Scholar]
  34. H.R. Thieme and C. Castillo-Chavez, On the role of variable infectivity in the dynamics of the human immunodeficiency virus epidemic,in Mathematical and Statistical Approaches to AIDS Epidemiology, edited by C. Castillo-Chavez. Springer, Berlin (1989) 157–176. [Google Scholar]
  35. H.R. Thieme and C. Castillo-Chavez, How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS? SIAM J. Appl. Math. 53 (1993) 1447–1479. [Google Scholar]
  36. C. Vargas-De-León, L. Esteva and A. Korobeinikov, Age-dependency in host-vector models: the global analysis. Appl. Math. Comput. 243 (2014) 969–981. [Google Scholar]
  37. J.A. Walker, Dynamical Systems and Evolution Equations: Theory and Applications. Plenum Press (1980). [CrossRef] [Google Scholar]
  38. T. Wang, Dynamics of an epidemic model with spatial diffusion. Phys. A: Stat. Mech. Appl. 409 (2014) 119–129. [CrossRef] [Google Scholar]
  39. G.F. Webb, An age-dependent epidemic model with spatial diffusion. Arch. Ratl. Mech. Anal. 75 (1980) 91–102. [CrossRef] [Google Scholar]
  40. K. Yamazaki and X. Wang, Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model. Disc. Cont. Dyn. Syst. Series B 21 (2016) 1297–1316. [CrossRef] [Google Scholar]

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