Dynamics of a generalized age-structured model for HBV infection with capsids in presence of two treatments
Volume 34, Issue 3, pp 243--256
https://dx.doi.org/10.22436/jmcs.034.03.04
Publication Date: March 18, 2024
Submission Date: December 07, 2023
Revision Date: January 15, 2024
Accteptance Date: February 09, 2024
Authors
E. M. Warrak
- Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, P. O. Box 7955, Sidi Othman, Casablanca, Morocco.
K. Hattaf
- Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, P. O. Box 7955, Sidi Othman, Casablanca, Morocco.
- Equipe de Recherche en Modelisation et Enseignement des Mathematiques (ERMEM), Centre Regional des Metiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco.
N. Yousfi
- Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, P. O. Box 7955, Sidi Othman, Casablanca, Morocco.
Abstract
The main aim of this paper is to propose and analyze the dynamics of a generalized age-structured model for hepatitis B virus (HBV) infection
with HBV DNA-containing capsids and two treatments. Such treatments are pegylated interferon and lamivudine drugs which are used to block new infections
of liver cells and stop viral infection. We first investigate the existence and uniqueness of solutions to the proposed model, as well as the existence of equilibria.
Furthermore, the uniform persistence and the stability analysis are rigorously established by means of characteristic equations and Lyapunov functionals.
Share and Cite
ISRP Style
E. M. Warrak, K. Hattaf, N. Yousfi, Dynamics of a generalized age-structured model for HBV infection with capsids in presence of two treatments, Journal of Mathematics and Computer Science, 34 (2024), no. 3, 243--256
AMA Style
Warrak E. M., Hattaf K., Yousfi N., Dynamics of a generalized age-structured model for HBV infection with capsids in presence of two treatments. J Math Comput SCI-JM. (2024); 34(3):243--256
Chicago/Turabian Style
Warrak, E. M., Hattaf, K., Yousfi, N.. "Dynamics of a generalized age-structured model for HBV infection with capsids in presence of two treatments." Journal of Mathematics and Computer Science, 34, no. 3 (2024): 243--256
Keywords
- HBV infection
- age-structure
- general incidence rate
- uniform persistence
- stability analysis
MSC
References
-
[1]
C. J. Browne, S. S. Pilyugin, Global analysis of age-structured within-host virus model, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1999–2017
-
[2]
R. D. Demasse, A. Ducrot, An age-structured within-host model for multistrain malaria infections, SIAM. J. Appl. Math., 73 (2013), 572–593
-
[3]
J. K. Hale, Asymptotic behavior of dissipative systems, American Mathematical Society, Providence, RI (1988)
-
[4]
J. K. Hale, P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989), 388–395
-
[5]
K. Hattaf, A new class of generalized fractal and fractal-fractional derivatives with non-singular kernels, Fractal Fract., 7 (2023), 1–16
-
[6]
K. Hattaf, A New Mixed Fractional Derivative with Applications in Computational Biology, Computation, 12 (2024), 1–17
-
[7]
K. Hattaf, A. A. Lashari, Y. Louartassi, N. Yousfi, A delayed SIR epidemic model with general incidence rate, Electron. J. Qual. Theory Differ. Equ., 2013 (2013), 9 pages
-
[8]
K. Hattaf, Y. Yang, Global dynamics of an age-structured viral infection model with general incidence function and absorption, Int. J. Biomath., 11 (2018), 18 pages
-
[9]
K. Hattaf, N. Yousfi, A class of delayed viral infection models with general incidence rate and adaptive immune response, Int. J. Dyn. Control, 4 (2016), 254–265
-
[10]
L. Liu, X. Ma, Y. Li, X. Liu, Mathematical analysis of global dynamics and optimal control of treatment for an age-structured HBV infection model, Chaos Solitons Fractals, 177 (2023),
-
[11]
S. Liu, R. Zhang, On an age-structured hepatitis B virus infection model with HBV DNA-containing capsids, Bull. Malays. Math. Sci. Soc., 44 (2021), 1345–1370
-
[12]
P. Magal, Compact attractors for time-periodic age-structured population models, Electron. J. Differential Equations, 2021 (2001), 35 pages
-
[13]
P. Magal, H. R. Thieme, Eventual compactness for semiflows generated by nonlinear age-structured models, Commun. Pure Appl. Anal., 3 (2004), 695–727
-
[14]
P. Magal, X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251–275
-
[15]
K. Manna, Global properties of a HBV infection model with HBV DNA-containing capsids and CTL immune response, Int. J. Appl. Comput. Math., 3 (2017), 2323–2338
-
[16]
K. Manna, S. P. Chakrabarty, Chronic hepatitis B infection and HBV DNA-containing capsids: modeling and analysis, Commun. Nonlinear Sci. Numer. Simul., 22 (2015), 383–395
-
[17]
K. Manna, S. P. Chakrabarty, Combination therapy of pegylated interferon and lamivudine and optimal controls for chronic hepatitis B infection, Int. J. Dynam. Control, 6 (2018), 354–368
-
[18]
K. Manna, K. Hattaf, A generalized distributed delay model for hepatitis B virus infection with two modes of transmission and adaptive immunity: a mathematical study, Math. Methods Appl. Sci., 45 (2022), 11614–11634
-
[19]
P. W. Nelson, M. A. Gilchrist, D. Coombs, J. M. Hyman, A. S. Perelson, 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., 1 (2004), 267–288
-
[20]
S. W. Schalm, J. Heathcote, J. Cianciara, G. Farrell, M. Sherman, B. Willems, A. Dhillon, A. Moorat, J. Barber, D. F. Gray, Lamivudine and alpha interferon combination treatment of patients with chronic hepatitis B infection: a randomised trial, Gut, 46 (2000), 562–568
-
[21]
X.-Y. Wang, K. Hattaf, H.-F. Huo, H. Xiang, Stability analysis of a delayed social epidemics model with general contact rate and its optimal control, J. Ind. Manag. Optim., 12 (2016), 1267–1285
-
[22]
T. Wang, Z. Hu, F. Liao, W. Ma, Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity, Math. Comput. Simulation, 89 (2013), 13–22
-
[23]
, WHO, Hepatitis B, Available online at:https://www.who.int/news-room/fact-sheets/detail/hepatitisb, (2023),