×

The global dynamics in a wild-type and drug-resistant HIV infection model with saturated incidence. (English) Zbl 1487.92037


MSC:

92D30 Epidemiology
92C60 Medical epidemiology
37N25 Dynamical systems in biology

References:

[1] Rong, L.; Gilchrist, M. A.; Feng, Z., Modeling within-host HIV-1 dynamics and the the evolution of drug resistance: trade-offs between viral enzyme function and drug susceptibility, J. Theor. Biol., 247, 804-818 (2007) · Zbl 1455.92087 · doi:10.1016/j.jtbi.2007.04.014
[2] Feng, Z.; Velasco-Hernandez, J.; Tapia-Santons, B., A mathematical model for coupling within-host and between-host dynamics in an environmentally-driven infectious disease, Math. Biosci., 241, 49-55 (2013) · Zbl 1309.92066 · doi:10.1016/j.mbs.2012.09.004
[3] Feng, Z.; Velasco-Hernandez, J.; Tapia-Santons, B., A model for coupling within-host and between-host dynamics in an infectious disease, Nonlinear Dyn., 68, 401-411 (2012) · Zbl 1254.92077 · doi:10.1007/s11071-011-0291-0
[4] Bonhoeffer, S.; Nowak, M. A., Pre-existence and emergence of drug resistance in HIV-1 infection, Proc. R. Soc. Lond. B, 264, 631-637 (1997) · doi:10.1098/rspb.1997.0089
[5] Huang, G.; Ma, W.; Takeuchi, Y., Global analysis for delay virus dynamics model with Beddington-DeAngelis functional response, Appl. Math. Lett., 24, 1199-1203 (2011) · Zbl 1217.34128 · doi:10.1016/j.aml.2011.02.007
[6] Cen, X.; Feng, Z.; Zhao, Y., Coupled within-host and between-host dynamics and evolution of virulence, Math. Biosci., 270, 204-212 (2015) · Zbl 1364.92042 · doi:10.1016/j.mbs.2015.02.012
[7] Perelson, A. S.; Neumann, A. U.; Markowitz, M., HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Science, 271, 1582-1586 (1996) · doi:10.1126/science.271.5255.1582
[8] Ribeiro, R. M.; Bonhoeffer, S., Production of resistant HIV mutants during antiretroviral therapy, Proc. Natl. Acad. Sci., 97, 7681-7686 (2000) · Zbl 0956.92022 · doi:10.1073/pnas.97.14.7681
[9] Rong, L.; Feng, Z.; Perelson, A. S., Emergence of HIV-1 drug resistance during antiretroviral treatment, Bull. Math. Biol., 69, 2027-2060 (2007) · Zbl 1298.92053 · doi:10.1007/s11538-007-9203-3
[10] Huang, G.; Ma, W.; Takeuchi, Y., Global properties for virus dynamics model with Beddington-DeAngelis functional response, Appl. Math. Lett., 22, 1690-1693 (2009) · Zbl 1178.37125 · doi:10.1016/j.aml.2009.06.004
[11] Beddington, J. R., Mutual interference between parasites or predators and its effect on searching efficiency, J. Anim. Ecol., 44, 331-340 (1975) · doi:10.2307/3866
[12] Deangelis, D. L.; Goldstein, R. A.; O’Neill, R. V., A model for trophic interaction, Ecology, 56, 881-892 (1975) · doi:10.2307/1936298
[13] Bonhoeffer, S.; May, R. M.; Shaw, G. M., Virus dynamics and drug therapy, Proc. Natl. Acad. Sci., 94, 6971-6976 (1997) · doi:10.1073/pnas.94.13.6971
[14] Shiri, T.; Garira, W.; Musekwa, S. D., A two-strain HIV-1 mathematical model to assess the effects of chemotherapy on disease parameters, Math. Biosci. Eng., 2, 811-832 (2005) · Zbl 1097.92031 · doi:10.3934/mbe.2005.2.811
[15] Miao, H.; Teng, Z.; Li, Z., Global stability of delayed viral infection models with nonlinear antibody and CTL immune responses and general incidence rate, Comput. Math. Methods Med. (2016) · Zbl 1368.92103 · doi:10.1155/2016/3903726
[16] Van Den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, 29-48 (2002) · Zbl 1015.92036 · doi:10.1016/S0025-5564(02)00108-6
[17] Kuang, Y., Delay Differential Equations with Application in Population Dynamics (1993), Boston: Academic Press, Boston · Zbl 0777.34002
[18] Butler, G.; Freedman, H. I.; Waltman, P., Uniformly persistent systems, Proc. Am. Math. Soc., 96, 425-430 (1986) · Zbl 0603.34043 · doi:10.1090/S0002-9939-1986-0822433-4
[19] Ngina, P.; Mbogo, R. W.; Luboobi, L. S., HIV drug resistance: insights from mathematical modelling, Appl. Math. Model., 75, 141-161 (2019) · Zbl 1481.92066 · doi:10.1016/j.apm.2019.04.040
[20] Kaddar, A., On the dynamics of a delayed SIR epidemic model with a modified saturated incidence rate, Electron. J. Differ. Equ., 2009 (2009) · Zbl 1183.37092
[21] Elaiw, A. M.; Raezah, A. A.; Hattaf, K., Stability of HIV-1 infection with saturated virus-target and infected-target incidences and CTL immune response, Int. J. Biomath. (2017) · Zbl 1367.34098 · doi:10.1142/S179352451750070X
[22] Duan, X.; Yin, J.; Li, X., Competitive exclusion in a multi-strain virus model with spatial diffusion and age of infection, J. Math. Anal. Appl., 459, 717-742 (2018) · Zbl 1381.92076 · doi:10.1016/j.jmaa.2017.10.074
[23] Yang, Y.; Ruan, S.; Xiao, D., Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function, Math. Biosci. Eng., 12, 859-877 (2015) · Zbl 1330.35480 · doi:10.3934/mbe.2015.12.859
[24] Shen, M.; Xiao, Y.; Rong, L., Global stability of an infection-age structured HIV-1 model linking within-host and between-host dynamics, Math. Biosci., 263, 37-50 (2015) · Zbl 1371.92130 · doi:10.1016/j.mbs.2015.02.003
[25] Wang, J.; Zhang, R.; Kuniya, T., Mathematical analysis for an age-structured HIV infection model with saturation infection rate, Electron. J. Differ. Equ., 2015 (2015) · Zbl 1350.34003 · doi:10.1186/s13662-015-0379-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.