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Том 16   Выпуск 1   Год 2021
Питчаймани М., Саранья Деви А.

Исследование аналитических свойств модели дробного порядка с запаздыванием на реальных данных по распространению ВИЧ

Математическая биология и биоинформатика. 2021;16(1):57-85.

doi: 10.17537/2021.16.57.

Список литературы

  1. HIV/AIDS - World Health Organization report (2019).
  2. Cai L., Li X., Ghosh M., Guo B. Stability analysis of an HIV/AIDS epidemic model with treatment. Journal of Computational and Applied Mathematics. 2009;28:313-323. doi: 10.1016/j.cam.2008.10.067
  3. Hernandez-Vargas E.A.,Middleton R.H. Modeling the three stages in HIV infection. Journal of Theoretical Biology. 2013;320:33-40. doi: 10.1016/j.jtbi.2012.11.028
  4. Swarnali S.S., Samanta G.P. Dynamical behavior of an HIV/AIDS epidemic model. Differential Equations and Dynamical Systems. 2014;22:369-395. doi: 10.1007/s12591-013-0173-7
  5. Simpson L., Gumel A. B. Mathematical assessment of the role of pre-exposure prophylaxis on HIV transmission dynamics. Applied Mathematics and Computation. 2017;293:168-193. doi: 10.1016/j.amc.2016.07.043
  6. Akrami M.H., Atabaigi A. Hopf and forward bifurcation of an integer and fractional-order SIR epidemic model with logistic growth of the susceptible individuals. Journal of Applied Mathematics and Computing. 2020;64:615-633. doi: 10.1007/s12190-020-01371-2
  7. Wu L., Li Z., Zhang Y., Xie B. Complex Behavior Analysis of a Fractional-Order Land Dynamical Model with Holling-II Type Land Reclamation Rate on Time Delay. Discrete Dynamics in Nature and Society. 2020;2020. doi: 10.1155/2020/1053283
  8. Shaikh A.S., Shaikh I.N., Nisar K.S. A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control. Advances in Difference Equations. 2020;373. doi: 10.20944/preprints202004.0140.v1
  9. Wang Y., Liu K., Lou Y. An age-structured within-host HIV model with T-cell competition. Nonlinear Analysis: Real World Applications. 2017;38:1-20. doi: 10.1016/j.nonrwa.2017.04.002
  10. Xu J., Geng Y., Zhou Y. Global dynamics for an age-structured HIV virus infection model with cellular infection and antiretroviral therapy. Applied Mathematics and Computation. 2017;22:3721-3747. doi: 10.1016/j.amc.2017.01.064
  11. Gakkhar S., Chavda N. A dynamical model for HIV-TB co-infection. Applied Mathematics and Computation. 2012;218:9261-9270. doi: 10.1016/j.amc.2012.03.004
  12. Pinto C., Carvalho A. New findings on the dynamics of HIV and TB coinfection models. Applied Mathematics and Computation. 2014;242:36-46. doi: 10.1016/j.amc.2014.05.061
  13. Krishnapriya P., Pitchaimani M., Witten T.M. Mathematical analysis of an influenza A epidemic model with discrete delay. Journal of computational and Applied Mathematics. 2017;324:155-172. doi: 10.1016/j.cam.2017.04.030
  14. Monica C., Pitchaimani M. Analysis of stability and Hopf bifurcation for HIV-1 dynamics with PI and three intacelluar delays. Nonlinear Analysis:Real World Applications. 2016;27:55-69. doi: 10.1016/j.nonrwa.2015.07.014
  15. Krishnapriya P., Pitchaimani M. Analysis of time delay in viral infection model with immune impairment. Journal of Applied Mathematics and Computing. 2017;27:421-453. doi: 10.1007/s12190-016-1044-5
  16. Pitchaimani M., Monica C., Divya M. Stability analysis for HIV infection delay model with protease inhibitor. BioSystems. 2013;114:118-124. doi: 10.1016/j.biosystems.2013.08.003
  17. Zafar Z.U.A., Ali N., Shah Z., Roy P., Zaman G., Deebani W. Hopf bifurcation and global dynamics of time delayed Dengue model, Computer Methods and Programs in Biomedicine. 2020;195. doi: 10.1016/j.cmpb.2020.105530
  18. Zafar Z.U.A., Ali N., Zaman G., Thounthong P., Tunc C. Analysis and numerical simulations of fractional order Vallis system. Alexandria Engineering Journal. 2020;59:2591-2605. doi: 10.1016/j.aej.2020.04.023
  19. Zafar Z.U.A. Fractional order Lengyel–Epstein chemical reaction model. Computational and Applied Mathematics. 2019;38. doi: 10.1007/s40314-019-0887-4
  20. Zafar Z.U.A., Mushtaq M., Rehan K. A non-integer order dengue internal transmission model. Advances in Difference Equations. 2018;23. doi: 10.1186/s13662-018-1472-7
  21. Zafar Z.U.A, Rehan K., Mushtaq M. HIV/AIDS epidemic fractional-order model. Journal of Difference Equations and Applications. 2017;23:1298-1315. doi: 10.1080/10236198.2017.1321640
  22. Zafar Z.U.A, Rehan K., Mushtaq M. Fractional-order scheme for bovine babesiosis disease and tick populations. Advances in Difference Equations. 2017;86. doi: 10.1186/s13662-017-1133-2
  23. Kheiri H., Jafari M. Optimal control of a fractional-order model for the HIV/AIDS epidemic. International Journal of Biomathematics. 2018;11. doi: 10.1142/S1793524518500869
  24. Mondal S., Lahiri A., Bairagi N. Analysis of a fractional order eco-epidemiological model with prey infection and type 2 functional response. Mathematical Methods in the Applied Sciences. 2017;40:6776-6789. doi: 10.1002/mma.4490
  25. Fatmawati, Shaiful E.M., Utoyo M.I. A Fractional-Order Model for HIV Dynamics in a Two-Sex Population. International Journal of Mathematics and Mathematical Sciences. 2018;2018:1-11. doi: 10.1155/2018/6801475
  26. Arafa A.A.M., Khalil M., Sayed A. A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay. Complexity. 2019;2019:1-13. doi: 10.1155/2019/4291017
  27. El-Sayed A.M., Arafa A.A., Khalil M., Sayed A. Backward bifurcation in a fractional order epidemiological model. Progress in Fractional Differentiation and Applications. 2017;3:281-287. doi: 10.18576/pfda/030404
  28. El-Sayed A.M., Arafa A.A., Khalil M., Sayed A. Mathematical Model of Vector-Borne Plant Disease with Memory on the Host and the Vector. Progress in Fractional Differentiation and Applications. 2016;2:277-285. doi: 10.18576/pfda/020405
  29. Arafa A.A.M., Rida S.Z., Khalil M. The effect of anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) described by a fractional order model. Applied Mathematical Modelling. 2013;37:2189-2196. doi: 10.1016/j.apm.2012.05.002
  30. Arafa A.A.M., Rida S.Z, Khalil M. Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection. Nonlinear Biomedical Physics. 2012;6:1-7. doi: 10.1186/1753-4631-6-1
  31. Arafa A.A.M., Rida S.Z., Khalil M. A fractional-order model of HIV infection: numerical solution and comparisons with data of patients. International Journal of Biomathematics. 2014;7. doi: 10.1142/S1793524514500363
  32. Das M., Samanta G. Stability analysis of a fractional ordered COVID-19 model. Computational and Mathematical Biophysics. 2021;9:22-45. doi: 10.1515/cmb-2020-0116
  33. Das M., Samanta G. A delayed fractional order food chain model with fear effect and prey refuge. Mathematics and Computers in Simulation. 2020;178:218-245. doi: 10.1016/j.matcom.2020.06.015
  34. Yan Y., Kou C. Stability analysis for a fractional differential model of HIV infection of CD4+T-Cells with time delay. Mathematics and Computers in Simulation. 2012;82:1572-1585. doi: 10.1016/j.matcom.2012.01.004
  35. Wang X., Wang Z. Dynamic Analysis of a Delayed Fractional-Order SIR Model with Saturated Incidence and Treatment Functions. International Journal of Bifurcation and Chaos. 2018;28. doi: 10.1142/S0218127418501808
  36. Rihan F.A., Al-Mdallal Q.M., AlSakaji H.J., Hashish A. A fractional-order epidemic model with time-delay and nonlinear incidence rate, Chaos, Solitons and Fractals, 2019;126:97-105. doi: 10.1016/j.chaos.2019.05.039
  37. Rihan F.A., Lakshmanan S., Hashish A. H., Rakkiyappan R., Ahmed E. Fractional-order delayed predator–prey systems with Holling type-II functional response. Nonlinear Dynamics. 2015;50:777-789. doi: 10.1007/s11071-015-1905-8
  38. Carvalho A., Pinto C.M.A. A delay fractional order model for the co-infection of malaria and HIV/AIDS. International Journal of Dynamics and Control . 2017;5:168-186. doi: 10.1007/s40435-016-0224-3
  39. Chinnathambi R., Rihan F.A., Alsakaji H.J. A fractional-order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections. Mathematical Methods in the Applied Sciences. 2019:1-15. doi: 10.1002/mma.5676
  40. Sontakke B.R., Shaikh A.S. Properties of Caputo Operator and Its Applications to Linear Fractional Differential Equations. International Journal of Engineering Research and Applications. 2015;5:22-27.
  41. Diekmann O., Heesterbeek J.A.P., Metz J.A.J. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology. 1990;28:365-382. doi: 10.1007/BF00178324
  42. Marino S., Hogue I.B., Ray C.J., Kirschner D.E. A methodology for performing global uncertainty and sensitivity analysis in systems biology. Journal of Theoretical Biology. 2008;254:178-196. doi: 10.1016/j.jtbi.2008.04.011
  43. Bhalekar S., Daftardar-Gejji V. A Predictor-Corrector Scheme for Solving Nonlinear Delay Differential Equations of Fractional Order. Journal of Fractional Calculus and Applications. 2011;1:1-9.
  44. Naik P.A. Global dynamics of a fractional-order SIR epidemic model with memory. International Journal of Biomathematics. 2020;13. doi: 10.1142/S1793524520500710
  45. WHO. Global Health Observatory data repository. HIV/AIDS. https://apps.who.int/gho/data/view.main; 2020. Retrieved: 2020-07-09.
Содержание
Оригинальная статья
Мат. биол. и биоинф.
2021;16(1):57-85
doi: 10.17537/2021.16.57
опубликована на англ. яз.

Аннотация (англ.)
Аннотация (рус.)
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