nach oben

Journal of Applied Mathematics and Computing

Erschienen in:

18.07.2020 | Original Research

Stability dynamics of a delayed generalized Chikungunya virus infection model

verfasst von: Taofeek O. Alade, Ahmed M. Elaiw, Saud M. Alsulami

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, a general nonlinear Chikungunya virus (CHIKV) dynamics model is formulated and analyzed. We assume that, the production, removal and proliferation rates of all compartments as well as the incidence rate of infection are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The model is incorporated by two types of discrete time delays. We prove the nonnegativity and boundedness of the solutions of the model. We established the global stability of the steady states of the model by constructing suitable Lyapunov functionals. The numerical simulations are performed to illustrate our theoretical results. The effect of time delay on the virus dynamics is studied.

Vorheriger Artikel Modified Newton-PHSS method for solving nonlinear systems with positive definite Jacobian matrices

Nächster Artikel Bounded positive solutions of an iterative three-point boundary-value problem with integral boundary condtions

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Perelson, A.S., Nelson, P.W.: Mathematical analysis of HIV-I: dynamics in vivo. SIAM Rev. 41, 3–44 (1999)MathSciNetMATH

Nowak, M.A., Bangham, C.R.M.: Population dynamics of immune responses to persistent viruses. Science 272, 74–79 (1996)

Nowak, M.A., May, R.M.: Virus Dynamics: Mathematical Principles of Immunology and Virology. Oxford University, Oxford (2000)MATH

Elaiw, A.M., Hassanien, I.A., Azoz, S.A.: Global stability of HIV infection models with intracellular delays. J. Korean Math. Soc. 49(4), 779–794 (2012)MathSciNetMATH

Roy, P.K., Chatterjee, A.N., Greenhalgh, D., Khan, Q.J.A.: Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model. Nonlinear Anal.: Real World Appl. 14, 1621–1633 (2013)MathSciNetMATH

Connell McCluskey, C., Yang, Y.: Global stability of a diffusive virus dynamics model with general incidence function and time delay. Nonlinear Anal.: Real World Appl. 25, 64–78 (2015)MathSciNetMATH

Elaiw, A.M., AlShamrani, N.H.: Stability of a general delay-distributed virus dynamics model with multi-staged infected progression and immune response. Math. Methods Appl. Sci. 40(3), 699–719 (2017)MathSciNetMATH

Elaiw, A.M., Raezah, A.A.: Stability of general virus dynamics models with both cellular and viral infections and delays. Math. Methods Appl. Sci. 40(16), 5863–5880 (2017)MathSciNetMATH

Li, X., Fu, S.: Global stability of a virus dynamics model with intracellular delay and CTL immune response. Math. Methods Appl. Sci. 38, 420–430 (2015)MathSciNetMATH

10.

Elaiw, A.M., Alshaikh, M.A.: Stability analysis of a general discrete-time pathogen infection model with humoral immunity. J. Differ. Equ. Appl. 25(8), 1149–1172 (2019)MathSciNetMATH

11.

Hattaf, K., Yousfi, N., Tridane, A.: Mathematical analysis of a virus dynamics model with general incidence rate and cure rate. Nonlinear Anal.: Real World Appl. 13(4), 1866–1872 (2012)MathSciNetMATH

12.

Elaiw, A.M., AlShamrani, N.H.: Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays. Math. Methods Appl. Sci. 36, 125–142 (2018)MathSciNetMATH

13.

Elaiw, A.M., AlShamrani, N.H.: Global stability of a delayed adaptive immunity viral infection with two routes of infection and multi-stages of infected cells. Commun. Nonlinear Sci. Numer. Simul. 86, Article ID 105259 (2020)MathSciNetMATH

14.

Elaiw, A.M., Alade, T.O., Alsulami, S.M.: Global dynamics of delayed CHIKV infection model with multitarget cells. J. Appl. Math. Comput. (2018). https://doi.org/10.1007/s12190-018-1215-7CrossRefMATH

15.

Bellomo, N., Painter, K.J., Tao, Y., Winkler, M.: Occurrence vs. absence of taxis-driven instabilities in a May–Nowak model for virus infection. SIAM J. Appl. Math. 79(5), 1990–2010 (2019)MathSciNetMATH

16.

Elaiw, A.M., Alshaikh, M.A.: Stability of discrete-time HIV dynamics models with three categories of infected CD4\(^{+} \) T-cells. Adv. Differ. Equ. 2019, Article Number: 407 (2019)MathSciNet

17.

Bellomo, N., Tao, Y.: Stabilization in a chemotaxis model for virus infection. Discrete Continu. Dyn. Syst.-Ser. S 13(2), 105–117 (2020)MathSciNetMATH

18.

Elaiw, A.M., Alade, T.O., Alsulami, S.M.: Stability of a within-host Chikungunya virus dynamics model with latency. J. Comput. Anal. Appl. 26(5), 777–790 (2019)

19.

Elaiw, A.M., Alade, T.O., Alsulami, S.M.: Analysis of latent CHIKV dynamics models with general incidence rate and time delays. J. Biol. Dyn. 12(1), 700–730 (2018)MathSciNetMATH

20.

Elaiw, A.M., Alade, T.O., Alsulami, S.M.: Analysis of latent CHIKV dynamics model with time delays. J. Comput. Anal. Appl. 27(1), 19–36 (2019)MATH

21.

Huang, D., Zhang, X., Guo, Y., Wang, H.: Analysis of an HIV infection model with treatments and delayed immune response. Appl. Math. Model. 40(4), 3081–3089 (2016)MathSciNetMATH

22.

Wang, K., Fan, A., Torres, A.: Global properties of an improved hepatitis B virus model. Nonlinear Anal.: Real World Appl. 11, 3131–3138 (2010)MathSciNetMATH

23.

Neumann, A.U., Lam, N.P., Dahari, H., Gretch, D.R., Wiley, T.E., Layden, T.J., Perelson, A.S.: Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science 282, 103–107 (1998)

24.

Elaiw, A.M., Alade, T.O., Alsulami, S.M.: Global stability of within-host virus dynamics models with multitarget cells. Mathematics 6, 118 (2018). https://doi.org/10.3390/math6070118CrossRef

25.

Elaiw, A.M., Alade, T.O., Alsulami, S.M.: Analysis of within-host CHIKV dynamics models with general incidence rate. Int. J. Biomath. (2018). https://doi.org/10.1142/S1793524518500626MathSciNetCrossRefMATH

26.

Cai, L.M., Li, X.Z., Fang, B., Ruan, S.: Global properties of vector host model with time delays. J. Math. Biol. 74(6), 1397–1423 (2017)MathSciNetMATH

27.

Li, M., Shu, H.: Global dynamics of a mathematical model for HTLV-I infection of CD4+ T-cells. Appl. Math. Model. 35(7), 3587–3595 (2011)MathSciNetMATH

28.

Wang, Y., Liu, X.: Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays. Math. Comput. Simul. 138, 31–48 (2017)MathSciNet

29.

WHO: Chikungunya: fact sheet (2017). http://www.who.int/mediacentre/factsheets/fs327/en/

30.

Dumont, Y., Chiroleu, F.: Vector control for the chikungunya disease. Math. Biosci. Eng. 7, 313–345 (2010)MathSciNetMATH

31.

Dumont, Y., Tchuenche, J.M.: Mathematical studies on the sterile insect technique for the chikungunya disease and aedes albopictus. J. Math. Biol. 65(5), 809–854 (2012)MathSciNetMATH

32.

Dumont, Y., Chiroleu, F., Domerg, C.: On a temporal model for the chikungunya disease: modeling, theory and numerics. Math. Biosci. 213, 80–91 (2008)MathSciNetMATH

33.

Moulay, D., Aziz-Alaoui, M., Cadivel, M.: The chikungunya disease: modeling, vector and transmission global dynamics. Math. Biosci. 229, 50–63 (2011)MathSciNetMATH

34.

Moulay, D., Aziz-Alaoui, M., Kwon, H.D.: Optimal control of chikungunya disease: larvae reduction, treatment and prevention. Math. Biosci. Eng. 9, 369–392 (2012)MathSciNetMATH

35.

Manore, C.A., Hickmann, K.S., Xu, S., Wearing, H.J., Hyman, J.M.: Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus. J. Theor. Biol. 356, 174–191 (2014)MathSciNetMATH

36.

Yakob, L., Clements, A.C.: A mathematical model of chikungunya dynamics and control: the major epidemic on Reunion Island. PLoS ONE 8, e57448 (2013)

37.

Liu, X., Stechlinski, P.: Application of control strategies to a seasonal model of chikungunya disease. Appl. Math. Model. 39, 3194–3220 (2015)MathSciNetMATH

38.

Huang, G., Takeuchi, Y., Ma, W.: Lyapunov functionals for delay differential equations model of viral infections. SIAM J. Appl. Math. 70(7), 2693–2708 (2010)MathSciNetMATH

39.

Wang, L., Li, M.Y.: Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells. Math. Biosci. 200(1), 44–57 (2006)MathSciNetMATH

40.

Leenheer, P.D., Smith, H.L.: Virus dynamics: a global analysis. SIAM J. Appl. Math. 63(4), 1313–1327 (2003)MathSciNetMATH

41.

Huang, G., Takeuchi, Y., Ma, W.: Lyapunov functionals for delay differential equations model of viral infections. SIAM J. Appl. Math. 70(7), 2693–2708 (2010)MathSciNetMATH

42.

Georgescu, P., Hsieh, Y.H.: Global stability for a virus dynamics model with nonlinear incidence of infection and removal. SIAM J. Appl. Math. 67(2), 337–353 (2006)MathSciNetMATH

43.

Elaiw, A.M., AlShamrani, N.H.: Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal. Nonlinear Anal.: Real World Appl. 26, 161–190 (2015)MathSciNetMATH

44.

Hale, J.K., Verduyn Lunel, S.: Introduction to Functional Differential Equations. Springer, New York (1993)MATH

45.

Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, San Diego (1993)MATH

46.

Yang, X., Chen, L., Chen, J.: Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models. Comput. Math. Appl. 32(4), 109–116 (1996)MathSciNetMATH

47.

Diekmann, O., Heesterbeek, J., Metz, J.A.: On the definition and the computation of the basic reproduction ratio R\(_{{0}} \) in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990)MathSciNetMATH

48.

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)MathSciNetMATH

49.

Korobeinikov, A.: Global properties of basic virus dynamics models. Bull. Math. Biol. 66(4), 879–883 (2004)MathSciNetMATH

50.

Elaiw, A.M.: Global properties of a class of HIV models. Nonlinear Anal.: Real World Appl. 11(4), 2253–2263 (2010)MathSciNetMATH

51.

Elaiw, A.M., Alshehaiween, S.F., Hobiny, A.D.: Global properties of a delay-distributed HIV dynamics model including impairment of B-cell functions. Mathematics 7(9), Article Number: 837 (2019)

52.

Elaiw, A.M., Elnahary, E.K., Raezah, A.A.: Effect of cellular reservoirs and delays on the global dynamics of HIV. Adv. Differ. Equ. 2018(1), Article Number: 85 (2018)MathSciNetMATH

53.

Elaiw, A.M., Raezah, A.A., Azoz, S.A.: Stability of delayed HIV dynamics models with two latent reservoirs and immune impairment. Adv. Differ. Equ. 2018(1), Article Number: 414 (2018)

54.

Hobiny, A.D., Elaiw, A.M., Almatrafi, A.: Stability of delayed pathogen dynamics models with latency and two routes of infection. Adv. Differ. Equ. f2018(1), Article Number: 276 (2018)

55.

Elaiw, A.M., Elnahary, E.K.: Analysis of general humoral immunity HIV dynamics model with HAART and distributed delays. Mathematics, 7(2). Article Number: 157 (2019)

Titel: Stability dynamics of a delayed generalized Chikungunya virus infection model
verfasst von: Taofeek O. Alade
Ahmed M. Elaiw
Saud M. Alsulami
Publikationsdatum: 18.07.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2021
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-020-01405-9

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1-2/2021

Inertial iterative algorithms for common solution of variational inequality and system of variational inequalities problems

Controllability results for fractional semilinear delay control systems

Periodic solution and dynamical analysis for a delayed food chain model with general functional response and discontinuous harvesting

Cacti with maximal general sum-connectivity index

A stochastic mutualism model with saturation effect and impulsive toxicant input in a polluted environment

Modified Newton-PHSS method for solving nonlinear systems with positive definite Jacobian matrices