Modelling the transmission dynamics and optimal control strategies for HIV infection in China

References

• H. Abboubakar, J.C. Kamgang, L.N. Nkamba, and D. Tieudjo, Bifurcation thresholds and optimal control in transmission dynamics of arboviral diseases, J. Math. Biol. 76(1–2) (2018), pp. 379–427.
   PubMed Web of Science ®Google Scholar
• T. Bastys, V. Gapsys, N.T. Doncheva, R. Kaiser, B.L. Groot, and O.V. Kalinina, Consistent prediction of mutation effect on drug binding in HIV-1 protease using alchemical calculations, J. Chem. Theory. Comput. 14(7) (2018), pp. 3397–3408.
   PubMed Web of Science ®Google Scholar
• J.E. Bennett, R. Dolin, and M.J. Blaser, Principles and practice of infectious diseases, Elsevier Health Sci. 8(5) (2010), pp. 326.
   Google Scholar
• L. Cai, X. Li, M. Ghosh, and B. Guo, Stability analysis of an HIV/AIDS epidemic model with treatment, J. Comput. Appl. Math. 229(1) (2009), pp. 313–323.
   Web of Science ®Google Scholar
• S.A. Carvalho, S.O.D. Silva, and I.D.C. Charret, Mathematical modeling of dengue epidemic: Control methods and vaccination strategies, Theory Biosci. 138(2) (2019), pp. 223–239.
   PubMed Web of Science ®Google Scholar
• A.N. Chatterjee and P.K. Roy, Antiviral drug treatment along with immune activator IL-2: A control-based mathematical approach for HIV infection, Int. J. Control 85(2) (2012), pp. 220–237.
   Web of Science ®Google Scholar
• Chinese Center for Disease Control and Prevention, Bureau of disease control and prevention, available at http://www.nhc.gov.cn/jkj/s2907/new_list.shtml?tdsourcetag=s_pcqq_aiomsg. Accessed 13 December 2022.
   Google Scholar
• N. Chitnis, J.M. Cushing, and J.M. Hyman, Bifurcation analysis of a mathematical model for Malaria transmission, SIAM. J. Appl. Math. 67(1) (2006), pp. 24–45.
   Web of Science ®Google Scholar
• R. Denysiuk, C.J. Silva, and D.F.M. Torres, Multiobjective approach to optimal control for a tuberculosis model, Optim. Methods Softw. 30(4) (2015), pp. 893–910.
   Google Scholar
• P. Dreessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180(1–2) (2002), pp. 29–48.
   PubMedGoogle Scholar
• B. Dubey, P. Dubey, and U.S. Dubey, Dynamics of an SIR model with nonlinear incidence and treatment rate, Appl. Appl. Math. Int. J. 10(2) (2015), pp. 718–737.
   Google Scholar
• S. Ghosh, A.N. Chatterjee, P.K. Roy, N. Grigorenko, E. Khailov, and E. Grigorieva, Mathematical modeling and control of the cell dynamics in Leprosy, Comput. Math. Model. 32 (2021), pp. 52–74.
   Google Scholar
• M.S. Gottlieb, H.M. Schanker, P.T. Fan, A. Saxon, J.D. Weisman, and I. Pozalski, Pneumocystis pneumonia-losangeles, MMWR Morb. Mortal. Wkly. Rep. 30(21) (1981), pp. 250–252.
   PubMedGoogle Scholar
• R.M. Granich, C.F. Gilks, C. Dye, K.M.D. Cock, and B.G. Williams, Universal voluntary hiv testing with immediate antiretroviral therapy as a strategy for elimination of hiv transmission: A mathematical model, The Lancet 373 (2009), pp. 48–57.
   PubMed Web of Science ®Google Scholar
• S. Hota, F. Agusto, H.R. Joshi, and S. Lenhart, Optimal control and stability analysis of and epidemic model with education campaign and treatment, Dyn. Syst. Differ. Equ. Appl. AIMS Proc. 2015 (2015), pp. 621–634.
   Google Scholar
• S.D. Hove-Musekwa and F. Nyabadza, The dynamics of an HIV/AIDS model with screened disease carriers, Comput. Math. Methods Med. 10(4) (2015), pp. 287–305.
   Google Scholar
• J. M. Hyman and E.Ann Stanley, Using mathematical models to understand the AIDS epidemic, Math. Biosci. 90(1–2) (1988), pp. 415–473.
   Web of Science ®Google Scholar
• H.R. Joshi, Optimal control of an HIV immunology model, Optim. Control Appl. Methods 23 (2002), pp. 199–213.
   Web of Science ®Google Scholar
• H.R. Joshi, S. Lenhart, S. Hota, and F. Agusto, Optimal control of an SIR model with changing behavior through an education campaign, Electron. J. Differ. Equ. 2015(50) (2015), pp. 1–14.
   Google Scholar
• J.P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadephia, 1976.
   Google Scholar
• S. Lenhart and J.T. Workman, Optimal Control Applied to Biological Models, Chapman and Hall, London, 2007.
   Google Scholar
• J. Li, Y. Yang, and Y. Zhou, Global stability of an epidemic model with latent stage and vaccination, Nonlinear Anal. Real World Appl. 12(4) (2011), pp. 2163–2173.
   Web of Science ®Google Scholar
• R. Liu, J. Wu, and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput. Math. Methods Med. 8(3) (2007), pp. 153–164.
   Google Scholar
• J. Lou, J. Cheng, Y. Li, C. Zhang, H. Xing, Y. Ruan, and Y. Shao, Comparison of different strategies for controlling HIV/AIDS spreading in MSM, Infect. Dis. Model. 3 (2018), pp. 293–300.
   PubMedGoogle Scholar
• M. Marsudi, N. Hidayat, and R.B.E. Wibowo, Application of optimal control strategies for the spread of HIV in a population, Res. J. Life Sci. 4(1) (2017), pp. 1–9.
   Google Scholar
• N.H. Marsudi and R.B.E. Wibowo, Optimal control and sensitivity analysis of HIV model with public health education campaign and antiretroviral therapy, AIP Conf. Proc. 2021 (2018), Article ID 060033.
   Google Scholar
• J. Mondal, P. Samui, and A.N. Chatterjee, Effect of SOF/VEL antiviral therapy for HCV treatment, Lett. Biomath. 8(1) (2021), pp. 191–213.
   Google Scholar
• Z. Mukandavire, W. Garira, and J.M. Tchuenche, Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics, Appl. Math. Model. 33(4) (2009), pp. 2084–2095.
   Web of Science ®Google Scholar
• National Healthcare Security Administration, Notice of the general office of the state council on printing and distributing the '14th five-year' national medical security plan, available at https://www.nhsa.gov.cn/art/2021/9/29/art_37_6137.html, Accessed 29 September 2021.
   Google Scholar
• 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. Real World Appl. 12(4) (2011), pp. 2091–2104.
   Web of Science ®Google Scholar
• L.S. Pontryagin, The mathematical theory of optimal processes and differential games, J. Oper. Res. Soc. 16(4) (1985), pp. 493–494.
   Google Scholar
• A. Rachah and D.F.M. Torres, Mathematical modelling, simulation, and optimal control of the 2014 Ebola outbreak in West Africa, Discrete Dyn. Nat. Soc. 2015 (2015), pp. 1–9.
   Web of Science ®Google Scholar
• H.S. Rodrigues, M.T.T. Monteiro, and D.F.M. Torres, Vaccination models and optimal control strategies to dengue, Math. Biosci. 247(1) (2014), pp. 1–12.
   PubMedGoogle Scholar
• P.K. Roy, S. Chowdhury, A.N. Chatterjee, J. Chattopadhyay, and R. Norman, A mathematical model on CTL mediated control of HIV infection in a long term drug therapy, J. Biol. Syst. 21(3) (2013), pp. 7–9.
   Web of Science ®Google Scholar
• P.K. Roy, S. Saha, and F.A. Basir, Effect of awareness programs in controlling the disease HIV/AIDS: An optimal control theoretic approach, Adv. Differ. Equ. 2015(1) (2015), pp. 1–18.
   Google Scholar
• A.K. Roy, M. Nelson, and P.K Roy, A control-based mathematical study on psoriasis dynamics with special emphasis on IL-21 and IFN-γ interaction network, Math. Methods Appl. Sci. 7 (2021), pp. 1–18.
   Google Scholar
• H.V. Rooyen, R.V. Barnabas, J.M. Baeten, Z. Phakathi, P. Joseph, M. Krows, T. Hong, P.M. Murnane, P.M. Murnane, and C. Celum, High HIV testing uptake and linkage to care in a novel program of home-based HIV counseling and testing with facilitated referral in Kwazulu-natal, south Africa, J. Acquir. Immune Defic. Syndr. 64(1) (2013), pp. e1–e8.
   PubMed Web of Science ®Google Scholar
• X. Rui, Global stability of an HIV-1 infection model with saturation infection and intracellular delay, J. Math. Anal. Appl. 375(1) (2011), pp. 75–81.
   Web of Science ®Google Scholar
• R. Safiel, E.S. Massawe, and O.D. Makinde, Modelling the effect screening and treatment on transmission of HIV/AIDS infection in a population american, Am. J. Math. Stat. 2(4) (2012), pp. 75–88.
   Google Scholar
• Z. Shuai and P. Van den driessche, Global stability of infectious disease models using lyapunov functions, SIAM J. Appl. Math. 73(4) (2013), pp. 1513–1532.
   Web of Science ®Google Scholar
• C.J. Silva and D. Torres, Global stability for a HIV/AIDS model, Commun. Fac. Sci. Univ. Ank. Ser.67(1) (2017), pp. 93–101.
   Google Scholar
• X. Song and A.U. Neumann, Global stability and periodic solution of the viral dynamics, J. Math. Anal. Appl. 329(1) (2007), pp. 281–297.
   Web of Science ®Google Scholar
• X. Song, X. Zhou, and X. Zhao, Properties of stability and hopf bifurcation for a HIV infection model with time delay, Appl. Math. Model. 34(1) (2010), pp. 1511–1523.
   Google Scholar
• A. Suryanto and I. Darti, Optimal control of an HIV model with changing behavior through an education campaign, screening and treatment, IOP Conf. Ser. Mater. Sci. Eng. 546 (2019), Article ID 052043.
   Google Scholar
• A. Tripathi, R. Naresh, and D. Sharma, Modelling the effect of screening of unaware infectives on the spread of HIV infection, Appl. Math. Comput. 184(2) (2007), pp. 1053–1068.
   Web of Science ®Google Scholar
• K. Wang, W. Wang, H. Pang, and X. Liu, Complex dynamic behavior in a viral model with delayed immune response, Physica D 226(2) (2007), pp. 197–208.
   Web of Science ®Google Scholar
• B. Wang, J. Mondal, P. Samui, A.N. Chatterjee, and A. Yusuf, Effect of an antiviral drug control and its variable order fractional network in host COVID-19 kinetics, Eur. Phys. J. Spec. Top. 231 (2022), pp. 1–15.
   Web of Science ®Google Scholar
• T. Zhang, M. Jia, H. Luo, Y. Zhou, and N. Wang, Study on a HIV/AIDS model with application to Yunnan province, China, Appl. Math. Model. 35(9) (2011), pp. 4379–4392.
   Web of Science ®Google Scholar