Stability of a general delayed virus dynamics model with humoral immunity and cellular infection
Source abstract
Abstract
In this paper, we investigate the dynamical behavior of a general nonlinear model for virus dynamics with virus-target and infected-target incidences. The model incorporates humoral immune response and distributed time delays. The model is a four dimensional system of delay differential equations where the production and removal rates of the virus and cells are given by general nonlinear functions. We derive the basic reproduction parameter R̃0G and the humoral immune response activation number R̃1G and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. We use suitable Lyapunov functionals and apply LaSalle’s invariance principle to prove the global asymptotic stability of the all equilibria of the model. We confirm the theoretical results by numerical simulations.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Mathematical and Theoretical Epidemiology and Ecology Models · Evolution and Genetic Dynamics · Influenza Virus Research Studies
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, Faculty of Science, King Abdulaziz University 1 , P.O. Box 80203, Jeddah 21589, Saudi Arabia
Department of Mathematics, Faculty of Science, King Khalid University 2 , P.O. Box 25145, Abha 61466, Saudi Arabia
Funding
King Khalid University
References (49)
Show source-provided references
1. Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model10.1016/j.nonrwa.2012.10.021 ↗
2. Dynamical behavior of a general HIV-1 infection model with HAART and cellular reservoirs
3. Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy10.3934/mbe.2010.7.675 ↗
4. Global stability of HIV infection models with intracellular delays10.4134/jkms.2012.49.4.779 ↗
5. Global properties of a class of HIV infection models with Beddington-DeAngelis functional response10.1002/mma.2596 ↗
6. Global properties of a class of HIV models10.1016/j.nonrwa.2009.07.001 ↗
7. Global properties of delayed-HIV dynamics models with differential drug efficacy in co-circulating target cells10.1016/j.amc.2015.06.011 ↗
8. Global dynamics of delay-distributed HIV infection models with differential drug efficacy in cocirculating target cells10.1002/mma.3453 ↗
9. Backward bifurcation in a mathematical model for HIV infection in vivo with anti-retroviral treatment10.1016/j.nonrwa.2013.11.002 ↗
10. A delayed HIV-1 model with virus waning term10.3934/mbe.2016.13.135 ↗
11. Analysis of an HIV infection model with treatments and delayed immune response10.1016/j.apm.2015.10.003 ↗
12. Mathematical insights in evaluating state dependent effectiveness of HIV prevention interventions10.1007/s11538-013-9824-7 ↗
13. Analysis of stability and Hopf bifurcation for HIV-1 dynamics with PI and three intracellular delays10.1016/j.nonrwa.2015.07.014 ↗
14. Global properties of an improved hepatitis B virus model10.1016/j.nonrwa.2009.11.008 ↗
15. Stability analysis of a model for HBV infection with cure of infected cells and intracellular delay10.1016/j.amc.2012.06.029 ↗
16. The dynamics of a delay model of HBV infection with logistic hepatocyte growth10.3934/mbe.2009.6.283 ↗
17. Dynamical behaviors of an HBV infection model with logistic hepatocyte growth10.1016/j.mcm.2011.03.013 ↗
18. Dynamics of an HBV/HCV infection model with intracellular delay and cell proliferation10.1016/j.cnsns.2016.06.009 ↗
19. Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy10.1126/science.282.5386.103 ↗
20. Dynamic analysis and optimal control for a model of hepatitis C with treatment10.1016/j.cnsns.2016.10.017 ↗
21. Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression10.1016/s0025-5564(02)00103-7 ↗
22. Global stability of a delayed HTLV-I infection model with a class of nonlinear incidence rates and CTLs immune response10.1016/j.amc.2013.03.081 ↗
23. The complete classification for global dynamics of a model for the persistence of HTLV-I infection10.1016/j.amc.2014.03.138 ↗
24. Global dynamics of a mathematical model for HTLV-I infection of CD4+ T-cells10.1016/j.apm.2011.01.033 ↗
25. Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response10.1016/j.nonrwa.2011.02.026 ↗
26. Quantitative 3D video microscopy of HIV transfer across T cell virological synapses10.1126/science.1167525 ↗
27. A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay10.1007/s00285-002-0191-5 ↗
28. Global analysis of within host virus models with cell-to-cell viral transmission10.3934/dcdsb.2014.19.3341 ↗
29. Analysis of an age structured HIV infection model with virus-to-cell infection and cell-to-cell transmission10.1016/j.nonrwa.2016.08.001 ↗
30. Stability analysis in delayed within-host viral dynamics with both viral and cellular infections10.1016/j.jmaa.2016.05.003 ↗
31. Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay10.1016/j.amc.2016.06.032 ↗
32. Effect of humoral immunity on HIV-1 dynamics with virus-to-target and infected-to-target infections10.1063/1.4960987 ↗
33. Stability of general virus dynamics models with both cellular and viral infections10.22436/jnsa.010.04.21 ↗
34. Stability of delay-distributed virus dynamics model with cell-to-cell transmission and CTL immune response
35. Modeling cell-to-cell spread of HIV-1 with logistic target cell growth10.1016/j.jmaa.2014.10.086 ↗
36. Modelling HIV-1 virus dynamics with both virus-to-cell infection and cell-to-cell transmission10.1137/130930145 ↗
37. Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions10.1016/j.mbs.2015.05.001 ↗
38. Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity10.1016/j.matcom.2013.03.004 ↗
39. Global stability of in host viral models with humoral immunity and intracellular delays10.1016/j.apm.2011.07.086 ↗
40. Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal10.1016/j.nonrwa.2015.05.007 ↗
41. Stability of a general delay-distributed virus dynamics model with multi-staged infected progression and immune response10.1002/mma.4002 ↗
42. Delays do not cause oscillations in a corrected model of humoral mediated immune response10.1016/j.amc.2016.05.006 ↗
43. Lyapunov functionals for delay differential equations model of viral infections10.1137/090780821 ↗
44. Global stability for a virus dynamics model with nonlinear incidence of infection and removal10.1137/060654876 ↗
45. Dynamic modeling and dynamical analysis of pump-turbines in S-shaped regions during runaway operation10.1016/j.enconman.2017.01.053 ↗
46. Nonlinear modeling and dynamic analysis of hydro-turbine governing system in the process of load rejection transient10.1016/j.enconman.2014.11.020 ↗
47. The slow-fast dynamical behaviors of a hydro-turbine governing system under periodic excitations10.1007/s11071-016-3208-0 ↗
48. 1993
49. Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models10.1016/0898-1221(96)00129-0 ↗