References
- Huang G, Liu X, Takeuchi Y. Lyapunov functions and global stability for age-structured HIV infection model. SIAM J Appl Math. 2012;72:25–38. doi: https://doi.org/10.1137/110826588
- Nelson PW, Gilchrist MA, Coombs D, et al. An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells. Math Biosci Eng. 2004;1:267–288. doi: https://doi.org/10.3934/mbe.2004.1.267
- Allen LJS, Schwartz EJ. Free-virus and cell-to-cell transmission in models of equine infectious anemia virus infection. Math Biosci. 2015;270:237–248. doi: https://doi.org/10.1016/j.mbs.2015.04.001
- De Leenheer P, Smith HL. Virus dynamics: a global analysis. SIAM J Appl Math. 2003;63:1313–1327. doi: https://doi.org/10.1137/S0036139902406905
- Li B, Chen Y, Lu X, Liu S. A delayed HIV-1 model with virus waning term. Math Biosci. 2016;13:135–157. doi: https://doi.org/10.3934/mbe.2016.13.135
- Pourbashash H, Pilyugin SS, De Leenheer P, et al. Global analysis of within host virus models with cell-to-cell viral transmission. Discrete Contin Dyn Syst Ser B. 2014;19:3341–3357.
- Wang Y, Zhou Y, Brauer F, et al. Viral dynamics model with CTL immune response incorporating antiretroviral therapy. J Math Biol. 2013;67:901–934. doi: https://doi.org/10.1007/s00285-012-0580-3
- Regoes RR, Ebert D, Bonhoeffer S. Dose-dependent infection rates of parasites produce the Allee effect in epidemiology. Proc R Soc Lond Ser B. 2002;269:271–279. doi: https://doi.org/10.1098/rspb.2001.1816
- Huang G, Ma W, Takeuchi Y. Global properties for virus dynamics model with Beddington–DeAngelis functional response. Appl Math Lett. 2009;22:1690–1693. doi: https://doi.org/10.1016/j.aml.2009.06.004
- McCluskey CC, Yang Y. Global stability of a diffusive virus dynamics model with general incidence function and time delay. Nonlinear Anal Real World Appl. 2015;25:64–78. doi: https://doi.org/10.1016/j.nonrwa.2015.03.002
- Shu H, Chen Y, Wang L. Impacts of the cell-free and cell-to-cell infection modes on viral dynamics. J Dynam Differ Equ. 2018;30:1817–1836. doi: https://doi.org/10.1007/s10884-017-9622-2
- Frioui MN, Miri SE, Touaoula TM. Unified Lyapunov functional for an age-structured virus model with very general nonlinear infection response. J Appl Math Comput. 2018;58:47–73. doi: https://doi.org/10.1007/s12190-017-1133-0
- Wang J, Zhang R, Kuniya T. Global dynamics for a class of age-infection HIV models with nonlinear infection rate. J Math Anal Appl. 2015;432:289–313. doi: https://doi.org/10.1016/j.jmaa.2015.06.040
- Xu J, Geng Y, Zhou Y. Global dynamics for an age-structured HIV virus infection model with cellular infection and antiretroviral therapy. Appl Math Comput. 2017;305:62–83.
- Yang Y, Ruan S, Xiao D. Global stability of an age-structured virus dynamics model with Beddington–DeAngelis infection function. Math Biosci Eng. 2015;12:859–877. doi: https://doi.org/10.3934/mbe.2015.12.859
- Browne CJ. A multi-strain virus model with infected cell age structure: application to HIV. Nonlinear Anal Real World Appl. 2015;22:354–372. doi: https://doi.org/10.1016/j.nonrwa.2014.10.004
- Fan D, Hao P, Sun D. Global stability of multi-group viral models with general incidence functions. J Math Biol. 2018;76:1301–1326. doi: https://doi.org/10.1007/s00285-017-1178-6
- Guo H, Li MY, Shuai Z. A graph-theoretic approach to the method of global Lyapunov functions. Proc Amer Math Soc. 2008;136:2793–2802. doi: https://doi.org/10.1090/S0002-9939-08-09341-6
- Guo H, Li MY, Shuai Z. Global dynamics of a general class of multistage models for infectious diseases. SIAM J Appl Math. 2012;72:261–279. doi: https://doi.org/10.1137/110827028
- Kuniya T. Global stability of a multi-group SVIR epidemic model. Nonlinear Anal Real World Appl. 2013;14:1135–1143. doi: https://doi.org/10.1016/j.nonrwa.2012.09.004
- Kuniya T, Wang J, Inaba H. A multi-group SIR epidemic model with age structure. Discrete Contin Dyn Syst Ser B. 2016;21:3515–3550. doi: https://doi.org/10.3934/dcdsb.2016109
- Lajmanovich A, Yorke JA. A deterministic model for gonorrhea in a nonhomogeneous population. Math Biosci. 1976;28:221–236. doi: https://doi.org/10.1016/0025-5564(76)90125-5
- Li M, Jin Z, Sun G, Zhang J. Modeling direct and indirect disease transmission using multi-group model. J Math Anal Appl. 2017;446:1292–1309. doi: https://doi.org/10.1016/j.jmaa.2016.09.043
- Li MY, Shuai Z, Wang C. Global stability of multi-group epidemic models with distributed delays. J Math Anal Appl. 2010;361:38–47. doi: https://doi.org/10.1016/j.jmaa.2009.09.017
- Shu H, Fan D, Wei J. Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission. Nonlinear Anal Real World Appl. 2012;13:1581–1592. doi: https://doi.org/10.1016/j.nonrwa.2011.11.016
- Sun R, Shi J. Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates. Appl Math Comput. 2011;218:280–286.
- Yuan Z, Zou X. Global threshold property in an epidemic model for disease with latency spreading in a heterogeneous host population. Nonlinear Anal Real World Appl. 2010;11:3479–3490. doi: https://doi.org/10.1016/j.nonrwa.2009.12.008
- Yang J, Li X, Martcheva M. Global stability of a DS–DI epidemic model with age of infection. J Math Anal Appl. 2012;385:655–671. doi: https://doi.org/10.1016/j.jmaa.2011.06.087
- Demasse RD, Ducrot A. An age-structured within-host model for multistrain malaria infections. SIAM J Appl Math. 2013;73:572–593. doi: https://doi.org/10.1137/120890351
- Wang J, Liu X, Kuniya T, Pang J. Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility. Discrete Contin Dyn Syst Ser B. 2017;22:2795–2812.
- Xu J, Zhou Y. Global stability of a multi-group model with generalized nonlinear incidence and vaccination age. Discrete Contin Dyn Syst Ser B. 2016;21:977–996. doi: https://doi.org/10.3934/dcdsb.2016.21.977
- Koenig S, Gendelman HE, Orenstein JM, et al. Detection of AIDS virus in macrophages in brain tissue from AIDS patients with encephalopathy. Science. 1986;233:1089–1093. doi: https://doi.org/10.1126/science.3016903
- Pope M, Betjes MGH, Romani N, et al. Conjugates of dendritic cells and memory T lymphocytes from skin facilitate productive infection with HIV-1. Cell. 1994;78:389–398. doi: https://doi.org/10.1016/0092-8674(94)90418-9
- Wang S, Wu J, Rong L. A note on the global properties of an age-structured viral dynamic model with multiple target cell populations. Math Biosci Eng. 2017;14:805–820. doi: https://doi.org/10.3934/mbe.2017044
- Wang X, Lou Y, Song X. Age-structured within-host HIV dynamics with multiple target cells. Stud Appl Math. 2017;138:43–76. doi: https://doi.org/10.1111/sapm.12135
- Heffernan JM, Wahl LM. Monte Carlo estimates of natural variation in HIV infection. J Theor Biol. 2005;236:137–153. doi: https://doi.org/10.1016/j.jtbi.2005.03.002
- Kepler TB, Perelson AS. Drug concentration heterogeneity facilitates the evolution of drug resistance. Proc Natl Acad Sci USA. 1998;95:11514–11519. doi: https://doi.org/10.1073/pnas.95.20.11514
- Qesmi R, Wu J, Wu J, et al. Influence of backward bifurcation in a model of hepatitis B and C viruses. Math Biosci. 2010;224:118–125. doi: https://doi.org/10.1016/j.mbs.2010.01.002
- Shu H, Wang L. Global stability and backward bifurcation of a general viral infection model with virus-driven proliferation of target cells. Discrete Contin Dyn Syst Ser B. 2014;19:1749–1768.
- Yang Y, Zou L, Ruan S. Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions. Math Biosci. 2015;270:183–191. doi: https://doi.org/10.1016/j.mbs.2015.05.001
- Xu R. Global stability of an HIV-1 infection model with saturation infection and intracellular delay. J Math Anal Appl. 2011;375:75–81. doi: https://doi.org/10.1016/j.jmaa.2010.08.055
- Webb GF. Theory of nonlinear age-dependent population dynamics. New York (NY): Marcel Dekker; 1985.
- Hale JK. Asymptotic behavior of dissipative systems. Providence (RI): American Mathematical Society; 1988. (Mathematical Surveys and Monographs; 25).
- Magal P. Compact attractors for time-periodic age-structured population models. Electron J Differ Equ. 2001;65:1–35.
- Magal P, Thieme HR. Eventual compactness for semiflows generated by nonlinear age-structured models. Commun Pure Appl Anal. 2004;3:695–727. doi: https://doi.org/10.3934/cpaa.2004.3.695
- Pang J, Chen J, Liu Z, et al. Local and global stabilities of a viral dynamics model with infection-age and immune response. J Dynam Differ Equ. 2019;31:793–813. doi: https://doi.org/10.1007/s10884-018-9663-1
- Hale JK, Waltman P. Persistence in infinite-dimensional systems. SIAM J Math Anal. 1989;20:388–395. doi: https://doi.org/10.1137/0520025
- Sigdel RP, McCluskey CC. Global stability for an SEI model of infectious disease with immigration. Appl Math Comput. 2014;243:684–689.
- Li MY, Muldowney JS. A geometric approach to the global-stability problems. SIAM J Math Anal. 1996;27:1070–1083. doi: https://doi.org/10.1137/S0036141094266449