`a`
Mathematical Biosciences and Engineering (MBE)
 

The global stability of an SIRS model with infection age
Pages: 449 - 469, Issue 3, June 2014

doi:10.3934/mbe.2014.11.449      Abstract        References        Full text (482.8K)           Related Articles

Yuming Chen - Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, China (email)
Junyuan Yang - Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, China (email)
Fengqin Zhang - Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, China (email)

1 À. Calsina, J. M. Palmada and J. Ripoll, Optimal latent period in a bacteriophage population model structured by infection-age, Math. Models Methods Appl. Sci., 21 (2011), 693-718.       
2 C. Castillo-Chavez et al., Epidemiological models with age structure, proportionate mixing, and cross-immunity, J. Math. Bioi., 27 (1989), 233-258.       
3 B. Buonomo and S. Rionero, On the Lyapunov stability for SIRS epidemic models with generalized nonlinear incidence rate, Appl. Math. Comput., 217 (2010), 4010-4016.       
4 A. Ducrot and P. Magal, Travelling wave solutions for an infection-age structured epidemic model with external supplies, Nonlineaity, 24 (2011), 2891-2911.       
5 Z. Feng, M. Iannelli and F. A. Milner, A two-strain tuberculosis model with age of infection, SIAM. J. Appl. Math., 62 (2002), 1634-1656.       
6 D. F. Francis et al., Infection of chimpanzees with lymphadenopathy-associated virus, Lancet, 2 (1984), 1276-1277.
7 H. W. Hethcote and J. A. Yorke, Gonorrhea Transmission Dynamics and Control, Springer-Verlag, Berlin, 1984.       
8 W. M. Hirsch, H. Hanisch and J.-P. Gabriel, Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior, Comm. Pure Appl. Math., 38 (1985), 733-753.       
9 J. M. Hyman and J. Li, Infection-age structured epidemic models with behavior change or treatment, J. Biol. Dyn., 1 (2007), 109-131.       
10 H. Inaba and H. Sekine, A mathematical model for Chagas disease with infection-age-dependent infectivity, Math. Biosci., 190 (2004), 39-69.       
11 A. Lahrouz et al., Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination, Appl. Math. Comput., 218 (2012), 6519-6525.       
12 J. M. A. Lange et al., Persistent HIV antigenaemia and decline of HIV core antibodies associated with transition to AIDS, British Medical J., 293 (1986), 1459-1462.
13 J. Liu and Y. Zhou, Global stability of an SIRS epidemic model with trasport-related infection, Chaos Solitons Fractals, 40 (2009), 145-158.       
14 Z. Liu, P. Magal and S. Ruan, Hopf bifurcation for non-densely defined Cauchy problems, Z. Angew. Math. Phys., 62 (2011), 191-222.       
15 P. Magal, Compact attrators for time-periodic age-structured population models, Electron. J. Differntial Equations, 2001 (2001), 35 pp.       
16 P. Magal, C. C. McCluskey and G. F. Webb, Lyapunov fucntional and global asymptoticalc stability for an infection-age model, Appl. Anal., 89 (2010), 1109-1140.       
17 P. Magal and X.-Q. Zhao, Global attractors in uniformly persistent dynamical systems, SIAM J. Mah. Anal., 37 (2005), 251-275.       
18 M. Martcheva and S. S. Pilyugin, The role of coinfection in multidisease dynamics, SIAM J. Appl. Math., 66 (2006), 843-872.       
19 C. C. McCluskey, Global stability for an SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. Eng., 6 (2009), 603-610.       
20 C. Pedersen et al., Temporal relation of antigenaemia and loss of antibodies to core core antigens to development of clinical disease in HIV infection, British Medical J., 295 (1987), 567-569.
21 S. Z. Salahuddin et al., HLTV-III in symptom-free seronegative persons, Lancet, 2 (1984), 1418-1420.
22 H. R. Thieme, Semiflows generated by Lipschitz pertrubations of non-densely defined operators, Differential Integral Equations, 3 (1990), 1035-1066.       
23 H. R. Thieme, Quasi-compact semigroups via bounded perturbation, in Advances in Mathematical Population Dynamics-Molecules, Cells and Man (eds. O. Arino, D. Axelrod and M. Kimmel), World Sci. Publ., (1997), 691-711.       
24 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.       
25 J.-Y. Yang, X.-Z. Li and M. Martcheva, Global stability of a DS-DI epidemic model with age of infection, J. Math. Anal. Appl., 385 (2012), 655-671.       
26 J.-Y. Yang et al., Intrinsic transmission global dynamics of tuberculosis with age structure, Int. J. Biomath., 4 (2011), 329-346.       
27 Z. Zhang and J. Peng, A SIRS epiemic model with infection-age dependence, J. Math. Anal. Appl., 331 (2007), 1396-1414.       
28 Y. Zhou et al., Modeling and prediction of HIV in China: Transmission rates structured by infection ages, Math. Biosci. Eng., 5 (2008), 403-418.       

Go to top