Backward bifurcation on HIV/AIDS SEI₁I₂TAR model with multiple interactions between sub-populations

References

• Abidemi, A., Owolabi, K. M., & Pindza, E. (2022). Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission. Physica A, 597, 127259. doi:10.1016/j.physa.2022.127259
   Web of Science ®Google Scholar
• Bi, K., Chen, Y., Wu, C., & Ben-Arieh, D. (2020). A Memetic algorithm for solving optimal control problems of Zika virus epidemic with equilibriums and backward. Communications in Nonlinear Science and Numerical Simulation, 84, 105176. doi:10.1016/j.cnsns.2020.105176
   Web of Science ®Google Scholar
• Brauer, F., & Chavez, C. C. (2016). Mathematical models in population biology and epidemiology (2nd ed.). New York: Springer Verlag.
   Google Scholar
• Buonomo, B., & Vargas-De-León, C. (2013). Stability and bifurcation analysis of a vector-bias model of malaria transmission. Mathematical Biosciences, 242(1), 59–67. doi:10.1016/j.mbs.2012.12.001
   PubMed Web of Science ®Google Scholar
• Cai, L., Guo, S., & Wang, S. (2014). Analysis of an extended HIV/AIDS epidemic model with treatment. Applied Mathematics and Computation, 236, 621–627. doi:10.1016/j.amc.2014.02.078
   Web of Science ®Google Scholar
• Cai, L., Li, X., Ghosh, M., & Guo, B. (2009). Stability analysis of an HIV/AIDS epidemic model with treatment. Journal of Computational and Applied Mathematics, 229(1), 313–323. doi:10.1016/j.cam.2008.10.067
   Web of Science ®Google Scholar
• Castillo-Chavez, C., & Song, B. (2004). Dynamical models of tuberculosis and their applications. Mathematical Biosciences and Engineering: MBE, 1(2), 361–404. doi:10.3934/mbe.2004.1.361
   PubMed Web of Science ®Google Scholar
• Chitnis, N., Cushing, J. M., & Hyman, J. M. (2006). Bifurcation analysis of a mathematical model for malaria transmission. SIAM Journal on Applied Mathematics, 67(1), 24–45. doi:10.1137/050638941
   Web of Science ®Google Scholar
• Erfanian, H. R., & Noori Skandari, M. H. (2011). Optimal control of an HIV model. Journal of Mathematics and Computer Science, 02(04), 650–658. doi:10.22436/jmcs.02.04.09
   Google Scholar
• Fatimah, M., Aldila, D., & Handari, B. D. (2021). Backward bifurcation arises from the smoking transmission model considering media campaign. Journal of Physics: Conference Series, 1722(1), 012004. doi:10.1088/1742-6596/1722/1/012004
   Google Scholar
• Gerberrya, D. J., & Philipa, A. M. (2016). The effect of the incidence function on the existence of backward bifurcation. Letters in Biomathematics, 1(3), 181–199.
   Google Scholar
• Greenhalgh, D., & Hay, G. (1997). Mathematical modelling of the spread of HIV/AIDS amongst injecting drug users. IMA Journal of Mathematics Applied in Medicine and Biology, 14(1), 11–38.
   PubMedGoogle Scholar
• Gumel, A. B. (2012). Cute paper that expands on previous results. Journal of Mathematical Analysis and Applications. 395(1), 355–365. doi:10.1016/j.jmaa.2012.04.077
   Web of Science ®Google Scholar
• Habibah, U., Trisilowati, T., & Muzaqi, M. H. (2021d). Stability analysis of HIV/AIDS model with interaction between educated and infected (not consuming ARV) subpopulations. International Journal of Mathematics Trends and Technology, 67(8), 103–111. doi:10.14445/22315373/IJMTT-V67I8P512
   Google Scholar
• Habibah, U., Trisilowati, D. I., Muzaqi, M. H., Tania, T. R., & AlFaruq, L. U. (2021b). Stability analysis of HIV/AIDS model with educated subpopulation. CAUCHY: Jurnal Matematika Murni Dan Aplikasi, 6(4), 188–199. doi:10.18860/ca.v6i4.10275
   Google Scholar
• Habibah, U., Trisilowati, Muzaqi, M. H., Tania, T. R., & AlFaruq, L. U. (2021c). Mathematical HIV/AIDS model with multi-interaction between infected and educated subpopulations and its local stability. Advances in Engineering Research, 209, 272–280.
   Google Scholar
• Habibah, U., Trisilowati, Pradana, Y. L., & Villadystian, W. (2021a). Mathematical model of HIV/AIDS with two different stages of infection subpopulation and its stability analysis. Engineering Letters, 29(1), 1–9.
   Web of Science ®Google Scholar
• Heffernan, J. M., Smith, R. J., & Wahl, L. M. (2005). Perspectives on the basics reproductive Ratio. Journal of the Royal Society, Interface, 2(4), 281–293. doi:10.1098/rsif.2005.0042
   PubMed Web of Science ®Google Scholar
• Huo, H. F., & Chen, R. (2015). Stability of an HIV/AIDS treatment model with different stages. Discrete Dynamics in Nature and Society, 2015, 630503.
   Web of Science ®Google Scholar
• Huo, H. F., Chen, R., & Wang, X. Y. (2016). Modelling and stability of HIV/AIDS epidemic model with treatment. Applied Mathematical Modelling, 40(13-14), 6550–6559. doi:10.1016/j.apm.2016.01.054
   Web of Science ®Google Scholar
• Karaagac, B., & Owolabi, K. M. (2021). Numerical analysis of polio model: A mathematical approach to epidemiological model using derivative with Mittag–Leffler Kernel. Mathematical Methods in the Applied Sciences, 2021, 1–18.
   Google Scholar
• Liu, Y., & Liu, X. (2018). Global properties and bifurcation analysis of an HIV-1 infection mode; with two target cells. Computational and Applied Mathematics, 37(3), 3455–3472. doi:10.1007/s40314-017-0523-0
   Google Scholar
• Martcheva, M. (2015). An introduction to mathematical epidemiology. Applied Mathematics, 61. Springer New York: Springer Verlag.
   Google Scholar
• Ministry of Health Republic of Indonesia. (2022). Cegah HIV-AIDS, Kemenkes Perluas Akses Pencegahan Pada Perempuan. Kementerian Kesehatan Republik Indonesia: Anak dan Remaja.
   Google Scholar
• Mishra, A. M., Purohit, S. D., Owolabi, K. M., & Sharma, Y. D. (2020). A nonlinear epidemiological model considering asymptotic and quarantine classes for SARS CoV-2 virus. Chaos, Solitons, and Fractals, 138, 109953. doi:10.1016/j.chaos.2020.109953
   PubMed Web of Science ®Google Scholar
• Murray, J. D. (2002). Mathematical biology: An introduction (3rd ed.). New York: Springer-Verlag.
   Google Scholar
• Mushayabasa, S., & Bhunu, C. P. (2011). Modeling HIV transmission dynamics among male prisoners in Sub-Saharan Africa. IAENG Inter. J. Appl. Math, 41(1), 62–67.
   Google Scholar
• Naik, P. A., Owolabi, K. M., Yavuz, M., & Zu, J. (2020). Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells. Chaos, Solitons and Fractals, 140, 110272. doi:10.1016/j.chaos.2020.110272
   Web of Science ®Google Scholar
• Naik, P. A., Zu, J., & Owolabi, K. M. (2020). Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control. Chaos, Solitons, and Fractals, 138, 109826. doi:10.1016/j.chaos.2020.109826
   PubMed Web of Science ®Google Scholar
• Naik, P. A., Zu, J., & Owolabi, K. M. (2021). Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order. Physica A, 545, 123816. doi:10.1016/j.physa.2019.123816
   Web of Science ®Google Scholar
• Omondi, E. O., Mbogo, R. W., & Luboobi, L. S. (2018). Mathematical analysis of sex-structured population model of HIV infection in Kenya. Letters in Biomathematics, 1(5), 174–194.
   Google Scholar
• Rois, M. A., Trisilowati, & Habibah, U. (2021). Local sensitivity analysis of COVID-19 epidemic with quarantine and isolation using normalized index. Telematika, 14(1), 13–24. doi:10.35671/telematika.v14i1.1191
   Google Scholar
• Sangsawang, S., Humphries, U. W., Khan, A., & Pongsumpun, P. (2023). Sensitivity analysis of cassava mosaic disease with saturation incidence rate model. AIMS Mathematics, 8(3), 6233–6254. doi:10.3934/math.2023315
   Google Scholar
• Tunc, C. (2002). A study of the stability and boundedness of the solutions of nonlinear differential equations of the fifth order. Indian Journal of Pure and Applied Mathematics, 33(4), 519–529.
   Web of Science ®Google Scholar
• Tunc, C. (2007). About uniform boundedness and convergence of solutions of certain non-linear differential equations of fifth-order. Bulletin of the Malaysian Mathematical Sciences Society, 30(1), 1–12.
   Web of Science ®Google Scholar
• Tunc, C. (2009). A new result on the boundedness of solutions to a nonlinear differential equation of fifth-order with delay. Kuwait Journal of Science & Engineering, 36, 15–31.
   Google Scholar
• Ulfa, B., Trisilowati., & Kusumawinahyu, W. M. (2018). Dynamical analysis of HIV/AIDS epidemic model with treatment. Journal of Experimental Life Science, 8, 1.
   Google Scholar
• Wibowo, Ratno Bagus Edy, Hidayat, Noor, Marsudi. (2016) A Sensitivity analysis of the impact of educational campaign, screening and therapy on the spread of HIV infection. Nonlinear Analysis and Differential Equations, 4, 327–341. doi:10.12988/nade.2016.63126
   Google Scholar
• World Health Organization. (2023). HIV-AIDS. https://www.who.int/health-topics/hiv-aids.
   Google Scholar