Optimal control of a multi-scale HIV-opioid model

References

• National Institute of Drug Abuse (NIH). Overdose death rates; 2022 Jan. Available from: https://nida.nih.gov/research-topics/trends statistics/overdose-death-rates.
   Google Scholar
• U.S. Department of Health and Human Services. What is the U.S. opioid epidemic? 2019. Available from: https://www.hhs.gov/opioids/about-the-epidemic/index.html.
   Google Scholar
• National Institute for Drug Abuse (NIH). Drug use and viral infections (HIV, hepatitis), drug facts. Available from: https://www.drugabuse.gov/publications/drugfacts/drug-use-viral-infections-hiv-hepatitis.
   Google Scholar
• E. White, C. Comiskey. Heroin epidemics, treatment and ODE modelling. Math Biosci. 2007;208:312–324. doi: 10.1016/j.mbs.2006.10.008
   PubMed Web of Science ®Google Scholar
• F. Nyabadza, S.D. Hove-Musekwa. From heroin epidemics to methamphetamine epidemics: modelling substance abuse in a South African province. Math Biosci. 2010;225:132–140. doi: 10.1016/j.mbs.2010.03.002
   PubMed Web of Science ®Google Scholar
• G.P. Samanta. Dynamic behaviour for a nonautonomous heroin epidemic model with time delay. J Appl Math Comput. 2011;35:161–178. doi: 10.1007/s12190-009-0349-z
   Google Scholar
• B. Fang, X. Li, M. Martcheva, et al. Global stability for a heroin model with two distributed delays. Discrete Contin Dyn Syst Ser B. 2014;19:715–733.
   Web of Science ®Google Scholar
• G. Huang, A. Liu. A note on global stability for a heroin epidemic model with distributed delay. Appl Math Lett. 2013;26:687–691. doi: 10.1016/j.aml.2013.01.010
   Web of Science ®Google Scholar
• J. Liu, T. Zhang. Global behaviour of a heroin epidemic model with distributed delays. Appl Math Lett. 2011;24:1685–1692. doi: 10.1016/j.aml.2011.04.019
   Web of Science ®Google Scholar
• B. Fang, X. Li, M. Martcheva, et al. Global stability for a heroin model with age-dependent susceptibility. J Syst Sci Complex. 2015;28:1243–1257. doi: 10.1007/s11424-015-3243-9
   Web of Science ®Google Scholar
• B. Fang, X.-Z. Li, M. Martcheva, et al. Global asymptotic properties of a heroin epidemic model with treat-age. Appl Math Comput. 2015;263:315–331.
   Web of Science ®Google Scholar
• J. Wang, J. Wang, T. Kuniya. Analysis of an age-structured multi-group heroin epidemic model. Appl Math Comput. 2019;347:78–100.
   Web of Science ®Google Scholar
• J. Yang, X. Li, F. Zhang. Global dynamics of a heroin epidemic model with age structure and nonlinear incidence. Int J Biomath. 2016;9:Article ID 1650033, 20.
   Web of Science ®Google Scholar
• N.A. Battista, L.B. Pearcy, W.C. Strickland. Modeling the prescription opioid epidemic. Bull Math Biol. 2019;81:2258–2289. doi: 10.1007/s11538-019-00605-0
   PubMed Web of Science ®Google Scholar
• S. Cole, S. Wirkus. Modeling the dynamics of heroin and illicit opioid use disorder, treatment, and recovery. Bull Math Biol. 2022;84:Article ID 48, 49. doi: 10.1007/s11538-022-01002-w
   PubMed Web of Science ®Google Scholar
• T. Phillips, S. Lenhart, W.C. Strickland. A data-driven mathematical model of the heroin and fentanyl epidemic in Tennessee. Bull Math Biol. 2021;83:Article ID 97, 27. doi: 10.1007/s11538-021-00925-0
   PubMed Web of Science ®Google Scholar
• S.R. Rivas, A.C. Tessner, E.E. Goldwyn. Calculating prescription rates and addiction probabilities for the four most commonly prescribed opioids and evaluating their impact on addiction using compartment modelling. Math Med Biol. 2021;38:202–217. doi: 10.1093/imammb/dqab001
   PubMed Web of Science ®Google Scholar
• G.K. Befekadu, Q. Zhu. Optimal control of diffusion processes pertaining to an opioid epidemic dynamical model with random perturbations. J Math Biol. 2019;78:1425–1438. doi: 10.1007/s00285-018-1314-y
   PubMed Web of Science ®Google Scholar
• A. Khan, G. Zaman, R. Ullah, et al. Optimal control strategies for a heroin epidemic model with age-dependent susceptibility and recovery-age. AIMS Math. 2021;6:1377–1394. doi: 10.3934/math.2021086
   Web of Science ®Google Scholar
• P.K. Roy. Mathematical models for therapeutic approaches to control HIV disease transmission. Singapore: Springer; 2015.Industrial and Applied Mathematics,
   Google Scholar
• W.-Y. Tan, H. Wu. Deterministic and stochastic models of AIDS epidemics and HIV infections with intervention. Hackensack, NJ: World Scientific Publishing Co. Pte. Ltd.; 2005.
   Google Scholar
• U. Habibah, R.A. Sari. Optimal control analysis of HIV/AIDS epidemic model with an antiretroviral treatment. Aust J Math Anal Appl. 2020;17:Article ID 16, 11.
   Google Scholar
• H. Zhao, P. Wu, S. Ruan. Dynamic analysis and optimal control of a three-age-class HIV/AIDS epidemic model in China. Discrete Contin Dyn Syst Ser B. 2020;25:3491–3521.
   Web of Science ®Google Scholar
• X.-C. Duan, X.-Z. Li, M. Martcheva. Coinfection dynamics of heroin transmission and hiv infection in a single population. J Biol Dyn. 2020;14:116–142. doi: 10.1080/17513758.2020.1726516
   PubMed Web of Science ®Google Scholar
• C. Gupta, N. Tuncer, M. Martcheva. Immuno-epidemiological co-affection model of hiv infection and opioid addiction. Math Biosci Eng. 2022;19:3636–3672. doi: 10.3934/mbe.2022168
   PubMed Web of Science ®Google Scholar
• C. Gupta, N. Tuncer, M. Martcheva. A network immuno-epidemiological model of hiv and opioid epidemics. Math Biosci Eng. 2023;20:4040–4068. doi: 10.3934/mbe.2023189
   PubMed Web of Science ®Google Scholar
• A.N. Timsina, N. Tuncer. Dynamics and optimal control of hiv infection and opioid addiction. In: Tuncer N, Martcheva M, Childs L, Prosper O, editors. Computational and mathematical population dynamics. New Jersey, Boca Raton: World Scientific; 2023 (in press), Chapter 2.
   Google Scholar
• E. Numfor, S. Bhattacharya, S. Lenhart, et al. Optimal control in coupled within-host and between-host models. Math Model Nat Phenom. 2014;9:171–203. doi: 10.1051/mmnp/20149411
   Web of Science ®Google Scholar
• E. Numfor, S. Bhattacharya, M. Martcheva, et al. Optimal control in multi-group coupled within-host and between-host models. In: Proceedings of the Tenth MSU Conference on Differential Equations and Computational Simulations; San Marcos, TX: Texas State Univ.–San Marcos, Dept. Math.; 2016. p. 87–117. (Electronic Journal of Differential Equations Conference; 23).
   Google Scholar
• P. Wu, Z. He, A. Khan. Dynamical analysis and optimal control of an age-since infection HIV model at individuals and population levels. Appl Math Model. 2022;106:325–342. doi: 10.1016/j.apm.2022.02.008
   Web of Science ®Google Scholar
• I. Ekeland. On the variational principle. J Math Anal Appl. 1974;47:324–353. doi: 10.1016/0022-247X(74)90025-0
   Web of Science ®Google Scholar
• M. Nowak, R. May. Virus dynamics: mathematical principles of immunology and virology. New York, USA: Oxford University Press; 2000.
   Google Scholar
• A.S. Perelson, P.W. Nelson. Mathematical analysis of HIV-I: dynamics in vivo. SIAM Rev. 1999;41:3–44. doi: 10.1137/S0036144598335107
   Web of Science ®Google Scholar
• A. Lange, N. Ferguson. Antigenic diversity, transmission mechanisms, and the evolution of pathogens. PLoS Comput Biol. 2009;5(10):e1000536.
   PubMed Web of Science ®Google Scholar
• M. Martcheva. An introduction to mathematical epidemiology. New York: Springer; 2015.Vol. 61 of Texts in Applied Mathematics,
   Google Scholar
• M.A. Gilchrist, D. Coombs. Evolution of virulence: interdependence, constraints, and selection using nested models. Theor Popul Biol. 2006;69:145–153. doi: 10.1016/j.tpb.2005.07.002
   PubMed Web of Science ®Google Scholar
• E. Numfor, S. Bhattacharya, M. Martcheva, et al. Optimal control applied in coupled within-host and between-host models. Math Model Nat Phenom. 2014;9:171–203. doi: 10.1051/mmnp/20149411
   Web of Science ®Google Scholar
• E. Numfor, S. Bhattacharya, M. Martcheva, et al. Optimal control in multi-group coupled within-host and between-host models. Electron J Differ Equ Conf. 2016;23:87–117.
   Google Scholar
• M. Shen, Y. Xiao, L. Rong, et al. Conflict and accord of optimal treatment strategies for HIV infection within and between hosts. Math Biosci. 2019;309:107–117. doi: 10.1016/j.mbs.2019.01.007
   PubMed Web of Science ®Google Scholar
• Centers for Disease Control and Prevention. Effectiveness of prevention strategies to reduce the risk of acquiring or transmitting hiv. Available from: https://www.cdc.gov/hiv/risk/estimates/preventionstrategies.html.
   Google Scholar
• S. Lenhart, J.T. Workman. Optimal control applied to biological models. Boca Raton, FL: Chapman & Hall/CRC; 2007.Chapman & Hall/CRC Mathematical and Computational Biology Series,
   Google Scholar
• V. Barbu. Mathematical methods in optimization of differential systems. Dordrecht: Kluwer Academic Publishers; 1994.
   Google Scholar
• E. Numfor. Optimal treatment in a multi-strain within-host model of hiv with age structure. J Math Anal Appl. 2019;480:Article ID 123410. doi: 10.1016/j.jmaa.2019.123410
   Web of Science ®Google Scholar
• S. Lenhart, J.T. Workman. Optimal control applied to biological models. Baco Raton: Chapman and Hall; 2007.
   Google Scholar