Geodesic
An investigation on analytical properties of delayed fractional order HIV model: a case study
Matematičeskaâ biologiâ i bioinformatika, Tome 16 (2021) no. 1, pp. 57-85.

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In this manuscript, we design a fractional order delay differential equation model for HIV transmission with the implementation of three distinct therapies for three different infectious stages. We investigate the positivity of solutions, analyze the stability properties, followed by Hopf bifurcation analysis. To probe the parameters that expedite the spread of infection, uncertainty and sensitivity analysis were performed. The numerical review was carried out to substantiate our theoretical results. Our proposed model parameters have been calibrated to fit yearly data from Afghanistan, Australia, France, Italy, Netherlands and New Zealand. 
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M. Pitchaimani; A. Saranya Devi. An investigation on analytical properties of delayed fractional order HIV model: a case study. Matematičeskaâ biologiâ i bioinformatika, Tome 16 (2021) no. 1, pp. 57-85. http://geodesic.mathdoc.fr/item/MBB_2021_16_1_a5/

[1] HIV/AIDS, World Health Organization report, 2019

[2] L. Cai, X. Li, M. Ghosh, B. Guo, “Stability analysis of an HIV/AIDS epidemic model with treatment”, Journal of Computational and Applied Mathematics, 28 (2009), 313–323 | DOI | MR

[3] E. A. Hernandez-Vargas, R. H. Middleton, “Modeling the three stages in HIV infection”, Journal of Theoretical Biology, 320 (2013), 33–40 | DOI | MR | Zbl

[4] S. S. Swarnali, G. P. Samanta, “Dynamical behavior of an HIV/AIDS epidemic model”, Differential Equations and Dynamical Systems, 22 (2014), 369–395 | DOI | MR | Zbl

[5] L. Simpson, A. B. Gumel, “Mathematical assessment of the role of pre-exposure prophylaxis on HIV transmission dynamics”, Applied Mathematics and Computation, 293 (2017), 168–193 | DOI | MR | Zbl

[6] M. H. Akrami, A. Atabaigi, “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, 64 (2020), 615–633 | DOI | MR | Zbl

[7] L. Wu, Z. Li, Y. Zhang, B. Xie, “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) | MR

[8] A. S. Shaikh, I. N. Shaikh, K. S. Nisar, “A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control”, Advances in Difference Equations, 373 (2020) | MR

[9] Y. Wang, K. Liu, Y. Lou, “An age-structured within-host HIV model with T-cell competition”, Nonlinear Analysis: Real World Applications, 38 (2017), 1–20 | DOI | MR | Zbl

[10] J. Xu, Y. Geng, Y. Zhou, “Global dynamics for an age-structured HIV virus infection model with cellular infection and antiretroviral therapy”, Applied Mathematics and Computation, 22 (2017), 3721–3747 | MR

[11] S. Gakkhar, N. Chavda, “A dynamical model for HIV-TB co-infection”, Applied Mathematics and Computation, 218 (2012), 9261–9270 | DOI | MR | Zbl

[12] C. Pinto, A. Carvalho, “New findings on the dynamics of HIV and TB coinfection models”, Applied Mathematics and Computation, 242 (2014), 36–46 | DOI | MR | Zbl

[13] P. Krishnapriya, M. Pitchaimani, T. M. Witten, “Mathematical analysis of an influenza A epidemic model with discrete delay”, Journal of computational and Applied Mathematics, 324 (2017), 155–172 | DOI | MR | Zbl

[14] C. Monica, M. Pitchaimani, “Analysis of stability and Hopf bifurcation for HIV-1 dynamics 83 with PI and three intacelluar delays”, Nonlinear Analysis:Real World Applications, 27 (2016), 55–69 | DOI | MR | Zbl

[15] P. Krishnapriya, M. Pitchaimani, “Analysis of time delay in viral infection model with immune impairment”, Journal of Applied Mathematics and Computing, 27 (2017), 421–453 | DOI | MR

[16] M. Pitchaimani, C. Monica, M. Divya, “Stability analysis for HIV infection delay model with protease inhibitor”, BioSystems, 114 (2013), 118–124 | DOI

[17] Z. U.A. Zafar, N. Ali, Z. Shah, P. Roy, G. Zaman, W. Deebani, Hopf bifurcation and global dynamics of time delayed Dengue model, Computer Methods and Programs in Biomedicine, 195, 2020 | DOI

[18] Z. U.A. Zafar, N. Ali, G. Zaman, P. Thounthong, C. Tunc, “Analysis and numerical simulations of fractional order Vallis system”, Alexandria Engineering Journal, 59 (2020), 2591–2605 | DOI

[19] Z. U.A. Zafar, “Fractional order Lengyel-Epstein chemical reaction model”, Computational and Applied Mathematics, 38 (2019) | DOI | MR | Zbl

[20] Z. U.A. Zafar, M. Mushtaq, K. Rehan, “A non-integer order dengue internal transmission model”, Advances in Difference Equations, 23 (2018) | MR

[21] Z. U.A. Zafar, K. Rehan, M. Mushtaq, “HIV/AIDS epidemic fractional-order model”, Journal of Difference Equations and Applications, 23 (2017), 1298–1315 | DOI | MR | Zbl

[22] Zafar Z. U.A, K. Rehan, M. Mushtaq, “Fractional-order scheme for bovine babesiosis disease and tick populations”, Advances in Difference Equations, 86 (2017) | MR | Zbl

[23] H. Kheiri, M. Jafari, “Optimal control of a fractional-order model for the HIV/AIDS epidemic”, International Journal of Biomathematics, 11 (2018) | DOI | MR | Zbl

[24] S. Mondal, A. Lahiri, N. Bairagi, “Analysis of a fractional order eco-epidemiological model with prey infection and type 2 functional response”, Mathematical Methods in the Applied Sciences, 40 (2017), 6776–6789 | DOI | MR | Zbl

[25] Fatmawati, E. M. Shaiful, M. I. Utoyo, “A Fractional-Order Model for HIV Dynamics in a Two-Sex Population”, International Journal of Mathematics and Mathematical Sciences, 2018 (2018), 1–11 | DOI | MR

[26] A. A.M. Arafa, M. Khalil, A. Sayed, “A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay”, Complexity, 2019 (2019), 1–13 | DOI

[27] A. M. El-Sayed, A. A. Arafa, M. Khalil, A. Sayed, “Backward bifurcation in a fractional order epidemiological model”, Progress in Fractional Differentiation and Applications, 3 (2017), 281–287 | DOI

[28] A. M. El-Sayed, A. A. Arafa, M. Khalil, A. Sayed, “Mathematical Model of Vector-Borne Plant Disease with Memory on the Host and the Vector”, Progress in Fractional Differentiation and Applications, 2 (2016), 277–285 | DOI

[29] A. A.M. Arafa, S. Z. Rida, M. Khalil, “The effect of anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) described by a fractional order model”, Applied Mathematical Modelling, 37 (2013), 2189–2196 | DOI | MR | Zbl

[30] A. A.M. Arafa, Rida S.Z, M. Khalil, “Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection”, Nonlinear Biomedical Physics, 6 (2012), 1–7 | DOI

[31] A. A.M. Arafa, S. Z. Rida, M. Khalil, “A fractional-order model of HIV infection: numerical solution and comparisons with data of patients”, International Journal of Biomathematics, 7 (2014) | DOI | MR

[32] M. Das, G. Samanta, “Stability analysis of a fractional ordered COVID-19 model”, Computational and Mathematical Biophysics, 9 (2021), 22–45 | DOI | MR | Zbl

[33] M. Das, G. Samanta, “A delayed fractional order food chain model with fear effect and prey refuge”, Mathematics and Computers in Simulation, 178 (2020), 218–245 | DOI | MR | Zbl

[34] Y. Yan, C. Kou, “Stability analysis for a fractional differential model of HIV infection of CD4$^+$ T-Cells with time delay”, Mathematics and Computers in Simulation, 82 (2012), 1572–1585 | DOI | MR | Zbl

[35] X. Wang, Z. Wang, “Dynamic Analysis of a Delayed Fractional-Order SIR Model with Saturated Incidence and Treatment Functions”, International Journal of Bifurcation and Chaos, 28 (2018) | MR

[36] F. A. Rihan, Q. M. Al-Mdallal, H. J. AlSakaji, A. Hashish, “A fractional-order epidemic model with time-delay and nonlinear incidence rate”, Chaos, Solitons and Fractals, 126 (2019), 97–105 | DOI | MR | Zbl

[37] F. A. Rihan, S. Lakshmanan, A. H. Hashish, R. Rakkiyappan, E. Ahmed, “Fractional-order delayed predator-prey systems with Holling type-II functional response”, Nonlinear Dynamics, 50 (2015), 777–789 | DOI | MR

[38] A. Carvalho, C. M.A. Pinto, “A delay fractional order model for the co-infection of malaria and HIV/AIDS”, International Journal of Dynamics and Control, 5 (2017), 168–186 | DOI | MR

[39] R. Chinnathambi, F. A. Rihan, H. J. Alsakaji, “A fractional-order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections”, Mathematical Methods in the Applied Sciences, 2019, 1–15 | MR

[40] B. R. Sontakke, A. S. Shaikh, “Properties of Caputo Operator and Its Applications to Linear Fractional Differential Equations”, International Journal of Engineering Research and Applications, 5 (2015), 22–27

[41] O. Diekmann, J. A.P. Heesterbeek, J. A.J. Metz, “On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations”, Journal of Mathematical Biology, 28 (1990), 365–382 | DOI | MR | Zbl

[42] S. Marino, I. B. Hogue, C. J. Ray, D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology”, Journal of Theoretical Biology, 254 (2008), 178–196 | DOI | MR | Zbl

[43] S. Bhalekar, V. Daftardar-Gejji, “A Predictor-Corrector Scheme for Solving Nonlinear Delay Differential Equations of Fractional Order”, Journal of Fractional Calculus and Applications, 1 (2011), 1–9 | Zbl

[44] P. A. Naik, “Global dynamics of a fractional-order SIR epidemic model with memory”, International Journal of Biomathematics, 13 (2020) | MR

[45] WHO. Global Health Observatory data repository. HIV/AIDS , 2020 (Retrieved : 2020-07-09) https://apps.who.int/gho/data/view.main