Stability and optimal control of age-structured cell-free and cell-to-cell transmission model of HIV. (English) Zbl 1534.92043
Summary: The human immunodeficiency virus (HIV) can spread more efficiently when infected CD4+ T cells directly interact with uninfected T cells. This interaction forms virological synapses, which lead to the cell-to-cell transmission of HIV. This study considers an age-structured HIV infection model in which both cell-free infection and cell-to-cell transmission occur. We also incorporate the proportion of T cells in latent or exposed class. Equilibrium solutions to our model are derived and then we perform the stability analysis. Optimal control problem for the drug therapy is also considered. Forward-backward scheme is used to solve the optimal control problem numerically. Numerical simulation added to study the effect of cell-to-cell infection. The outcomes of this work are new and complement the existing ones.
© 2023 John Wiley & Sons, Ltd.
© 2023 John Wiley & Sons, Ltd.
Keywords:
age-structured population model; antiretroviral treatment; cell-to-cell transmission; HIV/AIDS model; Lyapunov functionReferences:
| [1] | S.Sierra, B.Kupfer, and R.Kaiser, Basics of virology of HIV‐1, and its replication, J. Clin. Virol.34 (2005), 233-244. |
| [2] | R. V.Culshaw, S.Ruan, and G. F.Webb, A mathematical model of cell‐to‐cell spread of HIV‐1 that includes a time delay, J. Math. Biol.46 (2003), no. 5, 425-444. · Zbl 1023.92011 |
| [3] | G. F.Webb, Population models structured by age, size, and spatial position, Structured population models in biology and epidemiology, Lecture Notes in Mathematics, Vol. 1936, Springer, Berlin, Heidelberg, 2008, pp. 1-49. · Zbl 1138.92029 |
| [4] | S.Anita, Analysis and control of age‐dependent population dynamics, Springer Science & Business Media, Dordrecht, 2013. |
| [5] | H.Inaba, Age‐structured population dynamics in demography and epidemiology, Springer‐Verlag, Singapore, 2017. · Zbl 1370.92010 |
| [6] | W. E.Fitzgibbon, M. E.Parrott, and G. F. A.Webb, A diffusive age‐structured SEIRS epidemic model, Methods Appl. Anal.3 (1996), 358-369. · Zbl 0867.92020 |
| [7] | A.Pazy, Semigroups of linear operators and applications to partial differential equations, Vol. 34, Springer Science & Business Media, New York, 2012. · Zbl 0516.47023 |
| [8] | H. D.Kwon, J.Lee, and S. D.Yang, Optimal control of an age‐structured model of HIV infection, Appl Math. Comput.219 (2012), no. 5, 2766-2779. · Zbl 1308.92065 |
| [9] | E.Numfor, Optimal treatment in a multi‐strain within‐host model of HIV with age structure, J. Math. Anal. Appl.480 (2019), no. 2, 123410. · Zbl 1423.92199 |
| [10] | B. A.Mpheng, R. Y.M’pika Massoukou, and S. C.Oukouomi Noutchie, On the modeling of HIV dynamics driven by cell‐to‐cell and cell‐free transmissions, J. Anal. Appl.18 (2020), 133-143. · Zbl 1466.92200 |
| [11] | M.Kumar and S.Abbas, Global dynamics of an age‐structured model for HIV viral dynamics with latently infected T cells, Math. Comput. Simulation.198 (2022), 237-252. · Zbl 1540.92079 |
| [12] | A. M.Elaiw and N. H.AlShamrani, Stability of a general CTL‐mediated immunity HIV infection model with silent infected cell‐to‐cell spread, Adv. Differ. Equ.2020 (2020), 355. · Zbl 1485.92068 |
| [13] | S.Abbas, S.Tyagi, P.Kumar, V. S.Erturk, and S.Momani, Stability and bifurcation analysis of a fractional‐order model of cell‐to‐cell spread of HIV‐1 with a discrete time delay, Math. Methods Appl. Sci.45 (2022), 7081-7095. · Zbl 1530.92199 |
| [14] | S.Anita, Optimal harvesting for a nonlinear age‐dependent population dynamics, J. Math. Anal. Appl.226 (1998), no. 1, 6-22. · Zbl 0980.92027 |
| [15] | N. H.AlShamrani, Stability of a general adaptive immunity HIV infection model with silent infected cell‐to‐cell spread, Chaos Solitons Fractals150 (2021), 110422. · Zbl 1498.92112 |
| [16] | J.Wang, J.Lang, and X.Zou, Analysis of an age structured HIV infection model with cell‐free infection and cell‐to‐cell transmission, Nonlinear Anal. Real World Appl.34 (2017), 75-96. · Zbl 1352.92174 |
| [17] | Y.Wang, K.Qi, and D.Jiang, An HIV latent infection model with cell‐to‐cell transmission and stochastic perturbation, Chaos Solitons Fractals151 (2021), 111215. · Zbl 1498.92269 |
| [18] | K.Chang and Q.Zhang, Numerical approximation of basic reproduction number for an age‐structured HIV infection model with both cell‐free and cell‐to‐cell transmissions, Math. Methods Appl. Sci.44 (2021), 12851-12859. · Zbl 1512.92097 |
| [19] | N.Bai and R.Xu, Backward bifurcation and stability analysis in a within‐host HIV model with both cell‐free infection and cell‐to‐cell transmission, and anti‐retroviral therapy, Math. Comput. Simulation200 (2022), 162-185. · Zbl 1540.92173 |
| [20] | N.Akbari, R.Asheghi, and M.Nasirian, Stability and dynamic of HIV‐1 mathematical model with logistic target cell growth, treatment rate, cure rate and cell‐to‐cell spread, Taiwanese J. Math.26 (2022), 411-441. · Zbl 1494.34121 |
| [21] | N.Akbari and R.Asheghi, Optimal control of an HIV infection model with logistic growth, celluar and homural immune response, cure rate and cell‐to‐cell spread, Bound. Value Probl.2022 (2022), 5. · Zbl 1496.92040 |
| [22] | P. K.Srivastava and P.Chandra, Modeling the dynamics of HIV and [( CD{4}^{+} \]\) T cells during primary infection, Nonlinear Anal. Real World Appl.11 (2010), 612-618. · Zbl 1181.37122 |
| [23] | P. K.Srivastava, M.Banerjee, and P.Chandra, Modeling the drug therapy for HIV infection, J. Biol. Syst.17 (2009), 213-223. · Zbl 1342.92103 |
| [24] | P. K.Srivastava, M.Banerjee, and P.Chandra, A primary infection model for HIV and immune response with two discrete time delays, Differ. Equ. Dyn. Syst.18 (2010), 385-399. · Zbl 1216.34084 |
| [25] | X.Cao, A. K.Roy, F.Al Basir, and P. K.Roy, Global dynamics of HIV infection with two disease transmission routes—a mathematical model, Vol. 2022, 2020, pp. 8. |
| [26] | P. K.Roy, A. K.Roy, E. N.Khailov, F.Al Basir, and E. V.Grigorieva, A model of the optimal immunotherapy of psoriasis by introducing IL‐10 and IL‐22 inhibitors, J. Biol. Syst.28 (2020), no. 3, 609-639. · Zbl 1451.92173 |
| [27] | A. K.Roy, M.Nelson, and P. K.Roy, A control‐based mathematical study on psoriasis dynamics with special emphasis on IL 21 and IFN interaction network, Math. Methods Appl. Sci.44 (2021), no. 17, 13403-13420. · Zbl 1483.34065 |
| [28] | G.Huang, X.Liu, and Y.Takeuchi, Lyapunov functions and global stability for age‐structured HIV infection model, SIAM J. Appl. Math.72 (2012), no. 1, 25-38. · Zbl 1238.92032 |
| [29] | D. E.Kirschner and G. F. A.Webb, Mathematical model of combined drug therapy of HIV infection, Comput. Math. Methods Med.1 (1997), no. 1, 25-34. · Zbl 0925.92073 |
| [30] | N.Dorratoltaj, S.Ciupe, S.Eubank, P.Borrow, P.Pellegrino, and I.Williams, Mathematical modeling of HIV viral dynamics and immune response during Antiretroviral treatment interruptions, F1000Research5 (2016), 1-31. |
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.
