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Research Article

Analysing transmission dynamics of HIV/AIDS with optimal control strategy and its controlled state

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Pages 499-527 | Received 06 Dec 2020, Accepted 26 Jan 2022, Published online: 08 Jul 2022

References

  • N. Ali, G. Zaman, and A. Saleh Alshomranj, Optimal control strategy of HIV-1 epidemic model for recombinant virus, Cogent Math. 4 (2017), pp. 1–10.
  • E. Asano, L.J. Gross, S. Lenhart, and L.A. Real, Optimal control of vaccine distribution in rabies metapopulation model, Math. Biosci. Eng. 5 (2008), pp. 219–238.
  • E.A. Bakare and C.R. Nwozo, Bifurcation and sensitivity analysis of malaria–schistosomiasis co-infection model, Int. J. Appl. Comput. Math. 3 (2017), pp. 971–1000.
  • J. Carr, Applications of Centre Manifold Theory, Springer Science & Business Media, New York, 1981.
  • C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng. 1(2) (2004), pp. 361–404
  • C. Castillo-Chavez, Z. Feng, and W. Huang, On the computation of R0 and its role on global stability, mathematical approaches for emerging and reemerging infectious diseases: An introduction, IMA Math. Appl. 125 (2002), pp. 229–250.
  • L. Defang and W. Bochu, A novel time delayed HIV/AIDS model with vaccination and antiretroviral therapy and its stability analysis, Appl. Math. Model. 37 (2013), pp. 4608–4625.
  • E. Eisele and R. Siliciano, Redefining the viral reservoirs that prevent HIV-1 eradication, Immunity37 (2012), pp. 377–388.
  • M. Fan, M.Y. Li, and K. wang, Global stability of an SEIS epidemic model with recruitment and a varying total population size, Math. Biosci. 170 (2001), pp. 199–208.
  • W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control, Springer, New York, 1975.
  • E. Jung, S. Iwami, Y. Takeuchi, and T.C Jo, Optimal control strategy for prevention of avian influenza pandemic, J. Theor. Biol. 260 (2009), pp. 220–229.
  • H. Kheiri and M. Jafari, Fractional optimal control of an HIV/AIDS epidemic model with random testing and contact tracing, J. Appl. Math. Comput. 60 (2019), pp. 387–411.
  • H. Kheiri and M. Jafari, Optimal control of a fractional order model for the HIV/AIDS epidemic, Int. J. Biomath. 11(7) (2018), Article ID 1850086.
  • S. Lenhart and J. Workman, Optimal Control Applied to Biological Models, Chapman and Hall/CRC, Boca Raton, Florida, 2007.
  • M.Y. Li and J.S. Muldowney, A geometric approach to global-stability problems, Soc. Ind. Appl. Math. 27 (1996), pp. 1070–1083.
  • A. Mojaver and H. Kheiti, Mathematical analysis of a class of HIV infection models of CD4+ T cells with combined antiretroviral therapy, Appl. Math. Comput. 259 (2015), pp. 258–270.
  • Z. Mukandavire, W. Garira, and J.M. Tchuenche, Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics, Appl. Math. Model. 33 (2009), pp. 2084–2095.
  • S. Mushayabasa, C.P. Bhunu, E.J. Schwartz, G. Magombedze, and J.M. Tchuenche, Socio-economic status and HIV/AIDS dynamics: A modeling approach, World J. Model. Simul. 7 (2011), pp. 243–257.
  • F. Nyabadza, Z. Mukandavire, and S.D. Hove-Musekwa, Modelling the HIV/AIDS epidemic trends in South Africa: Insights from a simple mathematical model, Nonlinear Anal. 12 (2011), pp. 2091–2104.
  • K.O. Okosun, O.D. Makinde, and I. Takaidza, Analysis of the recruitment and industrial human resources management for optimal productivity in the presence of HIV/AIDS epidemic, J. Biol. Phys.39 (2013), pp. 99–121.
  • K.O. Okosun, O.D. Makinde, and I. Takaidza, Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives, Appl. Math. Model. 37 (2013), pp. 3802–3820.
  • E.O. Omondi, R.W. Mbogo, and L.S. Luboobi, Mathematical modelling of the impact of testing, treatment and control of HIV transmission in Kenya, Cogent Math. Stat. 5 (2018), pp. 1–16.
  • E.O. Omondi, R.W. Mbogo, and L.S. Luboobi, A mathematical modelling study of HIV infection in two heterosexual groups in Kenya, Infect. Dis. Model. 4 (2019), pp. 83–98.
  • A.S. Perelson, P. Essunger, Y. Cao, M. Vesanen, A. Hurley, K. Saksela, M. Markowitz, and D.D. Ho, Decay characteristics of HIV-1-infected compartments during combination therapy, Nature 387 (1997), pp. 188–191.
  • L.S. Pontryagin, V.G. Boltyanski, R.V. Gamkrelize, and E.F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley Interscience, New York, 1962.
  • N. Ram, T. Agraj, and S. Dileep, A nonlinear HIV/AIDS model with contact tracing, Appl. Math. Comput. 217 (2011), pp. 9575–9591.
  • P.S. Rivadeneira, C.H. Moog, G.B. Stan, C. Brunet, F. Raffi, V. Ferre, V. Costanza, M.J. Mhawei, F.Biafore, D.A. Quattara, D. Ernst, R. Fonteneau, and X. Xia, Mathematical modeling of HIV dynamics after antiretroviral therapy initiation: A review, BioRes. Open Access 3 (2014), pp. 233–241.
  • B. Seidu, O.D. Makinde, and I.Y. Seini, Mathematical analysis of the effects of HIV-Malaria co-infection on workplace productivity, ActaBiotheoretica 63(2) (2015), pp. 151–182.
  • B. Seidu, O.D. Makinde, and M.I. Daabo, Optimal control analysis of an HIV/AIDS model with linear incidence rate, J. Math. Comput. Sci. 6 (1) (2016), pp. 58–75.
  • B. Seidu and O.D. Makinde, Optimal control of HIV/AIDS in the workplace in the presence of careless individuals, Comput. Math. Methods Med. 2014 (2014),
  • M. Shirazian and M. Hadi Farahi, Optimal control strategy for a fully determined HIV model, Intell. Control Autom. 1 (2010), pp. 15–19.
  • Z. Tailei, J. Manhong, L. Hongbing, Z. Yicang, and W. Ning, Study on a HIV/AIDS model with application to Yunnan province, China, Appl. Math. Model. 35 (2011), pp. 4379–4392.
  • I. Takaidza, O.D. Makinde, and K.O. Okosun, Computational modelling and optimal control of HIV/AIDS transmission in community with substance abuse problem, Adv. Appl. Math. 87 (2014), pp. 31–40.
  • The Centers for Disease Control. http://www.cdc.gov/cholera/index.html. Accessed June 2018.
  • P. van den Driessche and J. Watmough, Reproduction number and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), pp. 29–48.
  • World Health Organization. http://www.who.int/mediacentre/factsheets/fs107/en. Accessed June 2018.