Stability of a diffusive-delayed HCV infection model with general cell-to-cell incidence function incorporating immune response and cell proliferation.
Cell-to-cell transmission
Delayed reaction–diffusion
Logistic growth
Periodic solution
Spatially homogeneous equilibria
Journal
Theory in biosciences = Theorie in den Biowissenschaften
ISSN: 1611-7530
Titre abrégé: Theory Biosci
Pays: Germany
ID NLM: 9708216
Informations de publication
Date de publication:
Sep 2023
Sep 2023
Historique:
received:
02
02
2023
accepted:
16
06
2023
medline:
14
8
2023
pubmed:
12
7
2023
entrez:
12
7
2023
Statut:
ppublish
Résumé
In this work, we analyse the dynamics of a five-dimensional hepatitis C virus infection mathematical model including the spatial mobility of hepatitis C virus particles, the transmission of hepatitis C virus infection by mitosis process of infected hepatocytes with logistic growth, time delays, antibody response and cytotoxic T lymphocyte (CTL) immune response with general incidence functions for both modes of infection transmission, namely virus-to-cell as well as cell-to-cell. Firstly, we prove rigorously the existence, the uniqueness, the positivity and the boundedness of the solution of the initial value and boundary problem associated with the new constructed model. Secondly, we found that the basic reproductive number is the sum of the basic reproduction number determined by cell-free virus infection, determined by cell-to-cell infection and determined by proliferation of infected cells. It is proved the existence of five spatially homogeneous equilibria known as infection-free, immune-free, antibody response, CTL response and antibody and CTL responses. By using the linearization methods, the local stability of the latter is established under some rigorous conditions. Finally, we proved the existence of periodic solutions by highlighting the occurrence of a Hopf bifurcation for a certain threshold value of one delay.
Identifiants
pubmed: 37436586
doi: 10.1007/s12064-023-00395-z
pii: 10.1007/s12064-023-00395-z
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
235-258Informations de copyright
© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Références
Bakht S, Hattaf K, Fatmi NI (2020) Dynamics of a class of viral infection models with diffusion. Commun Math Biol Neurosci 2020:1
Bocharov G, Meyerhans A, Bessonov N, Trofimchuk S, Volpert V (2017) Modelling the dynamics of virus infection and immune response in space and time. Int J Parall Emergent Distrib Syst 1:1–15
Bocharov G, Meyerhans A, Bessonov N, Trofimchuk S, Volpert V (2018) Interplay between reaction and diffusion processes in governing the dynamics of virus infections. J Theoret Biol 457:221–236
doi: 10.1016/j.jtbi.2018.08.036
Brauner CM, Jolly D, Lorenzi L, Thiebaut R (2011) Heterogeneous viral environment in a HIV spatial model. Discret Contin Dyn Syst 15(3):545–572
Chen SS, Cheng CY, Takeuchi Y (2016) Stability analysis in delayed within-host viral dynamics with both viral and cellular infections. J Math Anal Appl 442(2):642–672
doi: 10.1016/j.jmaa.2016.05.003
Dahari H, Major M, Zhang X, Mihalik K, Rice CM, Perelson AS, Feinstone SM, Neumann AU (2005) Mathematical modeling of primary hepatitis C infection: noncytolytic clearance and early blockage of virion production. Gastroenterology 128(4):1056–1066
pubmed: 15825086
doi: 10.1053/j.gastro.2005.01.049
Dahari H, Lo A, Ribeiro RM, Perelson AS (2007) Modeling hepatitis C virus dynamics: liver regeneration and critical drug efficacy. J Theoret Biol 247(2):371–381
doi: 10.1016/j.jtbi.2007.03.006
Dahari H, Ribeiro RM, Perelson AS (2007) Triphasic decline of hepatitis C virus rna during antiviral therapy. Hepatology 46(1):16–21
pubmed: 17596864
doi: 10.1002/hep.21657
Dixit NM, Layden-Almer JE, Layden TJ, Perelson AS (2004) Modelling how ribavirin improves interferon response rates in hepatitis C virus infection. Nature 432(7019):922–924
pubmed: 15602565
doi: 10.1038/nature03153
Hattaf K (2019) Spatiotemporal dynamics of a generalized viral infection model with distributed delays and ctl immune response. Computation 7(2):21
doi: 10.3390/computation7020021
Hattaf K (2020) Global stability and hopf bifurcation of a generalized viral infection model with multi-delays and humoral immunity. Phys A 545:123689
doi: 10.1016/j.physa.2019.123689
Hattaf K, Noura Y (2013) Global stability for reaction–diffusion equations in biology. Comput Math Appl 66(8):1488–1497
doi: 10.1016/j.camwa.2013.08.023
Henry D (1981) Geometric theory of semilinear parabolic equations, vol 840. Lecture Notes in Mathematics. Springer, Berlin
Hui Miao, Zhidong Teng, Xamxinur Abdurahman, Zhiming Li (2018) Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response. Comput Appl Math 37(3):3780–3805
doi: 10.1007/s40314-017-0543-9
Li X, Wei J (2005) On the zeros of a fourth degree exponential polynomial with applicationss to an eural network model delay. Chaos Solition Fract 26:519–526
doi: 10.1016/j.chaos.2005.01.019
Li J, Men K, Yang Y, Li D (2015) Dynamical analysis on a chronic hepatitis C virus infection model with immune response. J Theoret Biol 365:337–346
doi: 10.1016/j.jtbi.2014.10.039
Li C, Zhang Y, Zhou Y (2020) Spatially antiviral dynamics determines HCV in vivo replication and evolution. J Theoret Biol 503:110378
doi: 10.1016/j.jtbi.2020.110378
Manna K, Chakrabarty SP (2015) Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids. J Differ Equ Appl 21(10):918–933
doi: 10.1080/10236198.2015.1056524
Mojaver A, Kheiri H (2016) Dynamical analysis of a class of hepatitis C virus infection models with application of optimal control. Int J Biomath 9(3):1650038
doi: 10.1142/S1793524516500388
Nangue A (2019) Global stability analysis of the original cellular model of hepatitis c virus infection under therapy. Am J Math Comput Model 4(3):58–65
doi: 10.11648/j.ajmcm.20190403.12
Nangue A, Tacteu Fokam WA (2022) A class of diffusive delayed viral infection models with general incidence function and cellular proliferation. Arab J Math 1:1–27. https://doi.org/10.1007/s40065-022-00412-x
doi: 10.1007/s40065-022-00412-x
Nangue A, Donfack T, Avava Ndode YD (2019) Global dynamics of an hepatitis c virus mathematical cellular model with a logistic term. Eur J Pure Appl Math 12(3):944–959
doi: 10.29020/nybg.ejpam.v12i3.3454
Nangue A, Fokoue C, Poumeni R (2019) The global stability analysis of a mathematical cellular model of hepatitis c virus infection with non-cytolytic process. J Appl Math Phys 7(7):1531–1546
doi: 10.4236/jamp.2019.77104
Nangue A, Rendall AD, Tcheugam BK, Kamdem Simo PS (2022) Analysis of an initial value problem for an extracellular and intracellular model of hepatitis C virus infection. Int J Biomath 15(6):22–50041
doi: 10.1142/S1793524522500413
Nangue A, Tacteu Fokam AW, Guedlai A (2020) Global stability of a delay hcv dynamics model with cellular proliferation. Math Appl Sci Eng
Nangue A, Tiomo Lemofouet P, Ndouvatama S, Kengne E (2020) Global analysis of a generalized viral infection temporal model with cell-to-cell transmission and absorption effect under therapy. Math Appl Sci Eng 1–20
Neumann AU, Lam NP, Dahari H, Gretch DR, Wiley TE, Layden TJ, Perelson AS (1998) Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-[Formula: see text] therapy. Science 282(5386):103–107
pubmed: 9756471
doi: 10.1126/science.282.5386.103
Pan S, Chakrabarty SP (2018) Threshold dynamics of HCV model with cell-to-cell transmission and a non-cytolytic cure in the presence of humoral immunity. Commun Nonlinear Sci Numer Simul 61(2018):180–197
doi: 10.1016/j.cnsns.2018.02.010
Pan S, Chakrabarty SP (2018) Threshold dynamics of HCV model with cell-to-cell transmission and a non-cytolytic cure in the presence of humoral immunity. Commun Nonlinear Sci Numer Simul 61:180–197
doi: 10.1016/j.cnsns.2018.02.010
Pan S, Chakrabarty SP (2020) Hopf bifurcation and stability switches induced by humoral immune delay in hepatitis C. Indian J Pure Appl Math 51(4):1673–1695
doi: 10.1007/s13226-020-0489-2
Pan S, Chakrabarty SP (2022) Analysis of a reaction-diffusion HCV model with general cell-to-cell incidence function incorporating b cell activation and cure rate. Math Comput Simul 193(2022):431–450
doi: 10.1016/j.matcom.2021.10.021
Reluga TC, Dahari H, Perelson AS (2009) Analysis of hepatitis C virus infection models with hepatocyte homeostasis. SIAM J Appl Math 69(4):999–1023
pubmed: 19183708
pmcid: 2633176
doi: 10.1137/080714579
Timpe JM, Stamataki Z, Jennings A, Hu K, Farquhar MJ, Harris HJ, Schwarz A, Desombere I, Roels GL, Balfe P, McKeating JA (2008) Hepatitis C virus cell-cell transmission in hepatoma cells in the presence of neutralizing antibodies. Hepatology 47(1):17–24
pubmed: 17941058
doi: 10.1002/hep.21959
Travis CC, Webb GF (1974) Existence and stability for partial functional differential equations. Trans Am Math Soc 200:395–418
doi: 10.1090/S0002-9947-1974-0382808-3
Wang Wei, Feng Zhaosheng (2023) Global dynamics of a diffusive viral infection model with spatial heterogeneity. Nonlinear Anal Real World Appl 72:103763
doi: 10.1016/j.nonrwa.2022.103763
Wang W, Ma W (2018) A diffusive HIV infection model with nonlocal delayed transmission. Appl Math Lett 75:96–101
doi: 10.1016/j.aml.2017.06.010
Wang W, Ma W (2018) Hepatitis c virus infection is blocked by HMGB1: a new nonlocal and time-delayed reaction-diffusion model. Appl Math Comput 320:633–653
Wang K, Wang W (2007) Propagation of HBV with spatial dependence. Math Biosci 210(1):78–95
pubmed: 17592736
doi: 10.1016/j.mbs.2007.05.004
Wang Wei, Zhang Tongqian (2018) Caspase-1-mediated pyroptosis of the predominance for driving cd4+ t cells death: a nonlocal spatial mathematical model. Bull Math Biol 80(3):540–582
pubmed: 29349609
doi: 10.1007/s11538-017-0389-8
Wang X, Elaiw A, Song X (2012) Global properties of a delayed HIV infection model with ctl immune response. Appl Math Comput 218:9405–9414
doi: 10.1016/j.amc.2012.03.024
Wang F, Huang Y, Zou X (2014) Global dynamics of a PDE in-host viral model. Appl Anal 93:2312–2329
doi: 10.1080/00036811.2014.955797
Wang FB, Huang Y, Zou X (2014) Global dynamics of a PDE in-host viral model. Appl Anal 93(11):2312–2329
doi: 10.1080/00036811.2014.955797
Wang J, Yang J, Kuniya T (2016) Dynamics of a PDE viral infection model incorporating cell-to-cell transmission. J Math Anal Appl 444(2):1542–1564
doi: 10.1016/j.jmaa.2016.07.027
Wang X, Tang X, Wang Z, Li X (2020) Global dynamics of a diffusive viral infection model with general incidence function and distributed delays. Ric Mat 1:1–20
Wordarz D (2003) Hepatitis c virus dynamics and pathology: the role of CTL and antibody responses. J Gen Virol 84(7):1743–1750
doi: 10.1099/vir.0.19118-0
Wordarz D (2005) Mathematical models of immune effector responses to viral infections: Virus control versus the development of pathology. J Comput Appl Math 184(1):301–319
doi: 10.1016/j.cam.2004.08.016
World Health Organization (2016) World Health Organization Global report on access to hepatitis C treatment-Focus on overcoming barriers, tech. rep., available online at. Report, 2016. https://www.who.int/hepatitis /publications/hep-c-access-report/en/
Xiang H, Feng L, Huo H (2013) Stability of the virus dynamics model with Beddington–Deangelis functional. Appl Math Model 37:5414–5423
doi: 10.1016/j.apm.2012.10.033
Xu R, Ma Z (2009) An HBV model with diffusion and time delay. J Theoret Biol 257(3):499–509
doi: 10.1016/j.jtbi.2009.01.001
Xu J, Geng Y, Hou J (2017) Global dynamics of a diffusive and delayed viral infection model with cellular infection and nonlinear infection rate. Comput Math Appl 73(4):640–652
doi: 10.1016/j.camwa.2016.12.032
Yang Y, Zhou J, Ma X, Zhang T (2016) Nonstandard finite difference scheme for a diffusive within-host virus dynamics model with both virus-to-cell and cell-to-cell transmissions. Comput Math Appl 72(4):1013–1020
doi: 10.1016/j.camwa.2016.06.015
Zhao Y, Xu Z (2014) Global dynamics for a delayed hepatitis C virus infection model. Electron J Differ Equ 2014(132):1–18