Analysis of an SVEIR model with age-dependence vaccination, latency and relapse
-
2128
Downloads
-
3561
Views
Authors
Jinliang Wang
- School of Mathematical Science, Heilongjiang University, Harbin 150080, China.
Xiu Dong
- School of Mathematical Science, Heilongjiang University, Harbin 150080, China.
Hongquan Sun
- School of Mathematical Science, Heilongjiang University, Harbin 150080, China.
Abstract
In this paper, we propose an epidemic model with age-dependence vaccination, latency and relapse. We derive the positivity
and boundedness of solutions and find the basic reproduction number. Asymptotic smoothness, the existence of global compact
attractor and uniform persistence of the model are investigated. By constructing Lyapunov functionals, we establish global
stability of the equilibria in a threshold type.
Share and Cite
ISRP Style
Jinliang Wang, Xiu Dong, Hongquan Sun, Analysis of an SVEIR model with age-dependence vaccination, latency and relapse, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3755--3776
AMA Style
Wang Jinliang, Dong Xiu, Sun Hongquan, Analysis of an SVEIR model with age-dependence vaccination, latency and relapse. J. Nonlinear Sci. Appl. (2017); 10(7):3755--3776
Chicago/Turabian Style
Wang, Jinliang, Dong, Xiu, Sun, Hongquan. "Analysis of an SVEIR model with age-dependence vaccination, latency and relapse." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3755--3776
Keywords
- Vaccination age
- latency age
- relapse age
- global stability
- Lyapunov function.
MSC
References
-
[1]
C. J. Browne, S. S. Pilyugin, Global analysis of age-structured within-host virus model , Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999–2017.
-
[2]
Y.-M. Chen, S.-F. Zou, J.-Y. Yang, Global analysis of an SIR epidemic model with infection age and saturated incidence, Nonlinear Anal. Real World Appl., 30 (2016), 16–31.
-
[3]
R. D. Demasse, A. Ducrot, An age-structured within-host model for multistrain malaria infections, SIAM J. Appl. Math., 73 (2013), 572–593.
-
[4]
X.-C. Duan, S.-L. Yuan, X.-Z. Li, Global stability of an SVIR model with age of vaccination, Appl. Math. Comput., 226 (2014), 528–540.
-
[5]
W. J. Edmunds, G. F. Medley, D. J. Nokes, A. J. Hall, H. C. Whittle, The influence of age on the development of the hepatitis B carrier state, Proc. R. Soc. Lond. B Biol. Sci., 253 (1993), 197–201.
-
[6]
D. Ganem, A. M. Prince, Hepatitis B virus infection—natural history and clinical consequences, N. Engl. J. Med., 350 (2004), 1118–1129.
-
[7]
J. K. Hale, Functional differential equations, Applied Mathematical Sciences, Springer-Verlag New York, New York- Heidelberg (1971)
-
[8]
J. K. Hale, Asymptotic behavior of dissipative systems, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI (1988)
-
[9]
J. K. Hale, P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989), 388–395.
-
[10]
M. Iannelli , Mathematical theory of age-structured population dynamics, Appl. Math. Monogr. C.N.R., Giardini Editori e Stampatori in Pisa (1995)
-
[11]
L.-L. Liu, J.-L. Wang, X.-N. Liu, Global stability of an SEIR epidemic model with age-dependent latency and relapse, Nonlinear Anal. Real World Appl., 24 (2015), 18–35.
-
[12]
P. Magal, Compact attractors for time-periodic age-structured population models, Electron. J. Differential Equations, 2001 (2001), 35 pages.
-
[13]
P. Magal, C. C. McCluskey, Two-group infection age model including an application to nosocomial infection, SIAM J. Appl. Math., 73 (2013), 1058–1095.
-
[14]
P. Magal, C. C. McCluskey, G. F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Appl. Anal., 89 (2010), 1109–1140.
-
[15]
P. Magal, X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251–275.
-
[16]
C. C. McCluskey, Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes, Math. Biosci. Eng., 9 (2012), 819–841.
-
[17]
L.-L. Rong, Z.-L. Feng, A. S. Perelson, Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy, SIAM J. Appl. Math., 67 (2007), 731–756.
-
[18]
H. R. Thieme, Semiflows generated by Lipschitz perturbations of non-densely defined operators, Differential Integral Equations, 3 (1990), 1035–1066.
-
[19]
H. R. Thieme, Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators, J. Differential Equations, 250 (2011), 3772–3801.
-
[20]
P. van den Driessche, L. Wang, X.-F. Zou, Modeling diseases with latency and relapse, Math. Biosci. Eng., 4 (2007), 205–219.
-
[21]
P. van den Driessche, X.-F. Zou, Modeling relapse in infectious diseases, Math. Biosci., 207 (2007), 89–103.
-
[22]
J. A. Walker, Dynamical systems and evolution equations, Theory and applications, Mathematical Concepts and Methods in Science and Engineering, Plenum Press, New York-London (1980)
-
[23]
J.-L. Wang, R. Zhang, T. Kuniya, Global dynamics for a class of age-infection HIV models with nonlinear infection rate, J. Math. Anal. Appl., 432 (2015), 289–313.
-
[24]
J.-L. Wang, R. Zhang, T. Kuniya, The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes, J. Biol. Dyn., 9 (2015), 73–101.
-
[25]
J.-L. Wang, R. Zhang, T. Kuniya, A note on dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 13 (2016), 227–247.
-
[26]
J.-L. Wang, R. Zhang, T. Kuniya, The dynamics of an SVIR epidemiological model with infection age, IMA J. Appl. Math., 81 (2016), 321–343.
-
[27]
G. F. Webb, Theory of nonlinear age-dependent population dynamics, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York (1985)
-
[28]
J.-X. Yang, Z.-P. Qiu, X.-Z. Li, Global stability of an age-structured cholera model, Math. Biosci. Eng., 11 (2014), 641–665.