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All issues Volume 16 (2021) Math. Model. Nat. Phenom., 16 (2021) 30 References
Issue
Math. Model. Nat. Phenom.
Volume 16, 2021
Mathematical Models and Methods in Epidemiology
Article Number 30
Number of page(s) 32
DOI https://doi.org/10.1051/mmnp/2021024
Published online 26 May 2021
  1. Aide Suisse Contre le SIDA. (2018). Evolution d’une infection par le VIH. www.aids.ch/fr/vivre-avec-vih/aspects-medicaux/evolution.php. [Google Scholar]
  2. AIDS info. (2018). Offering Information on HIV/AIDS Treatment, Prevention and Research. aidsinfo.nih.gov/understanding-hiv-aids/fact-sheets/21/51/hiv-treatment–the-basics.. [Google Scholar]
  3. S. Anita, Vol. 11 of Analysis and control of age-dependent population dynamics. Springer Science & Business Media (2000). [CrossRef] [Google Scholar]
  4. V. Barbu and M. Iannelli, Optimal control of population dynamics. J. Optim. Theory Appl. 102 (1999) 1–14. [Google Scholar]
  5. T. Bernard, K. Diop and P. Vinard, The cost of universal free access for treating HIV/AIDS in low-income countries: the case of Senegal (2008). http://hal.ird.fr/ird-00403656. [Google Scholar]
  6. Centers for Disease Control and Prevention (CDC). (2018). HIV Prevention. https://www.cdc.gov/hiv/basivs/prevention.html. [Google Scholar]
  7. J. Chu, A. Ducrot, P. Magal and S. Ruan, Hopf bifurcation in a size-structured population dynamic model with random growth. J. Differ. Equ. 247 (2009) 956–1000. [CrossRef] [MathSciNet] [Google Scholar]
  8. G. Da Prato and M. Iannelli, Boundary control problems for age-dependent equations. In Vol. 155 of Evolution equations, control theory and biomathematics. Marcel Dekker (1993) 91–100. [Google Scholar]
  9. C.A. da Silva Filho and J.L. Boldrini, An analysis of an optimal control problem for mosquito populations. Nonlinear Anal.: Real World Appl. 42 (2018) 353–377. [Google Scholar]
  10. R. Djidjou-Demasse, J.J. Tewa, S. Bowong and Y. Emvudu, Optimal control for an age-structured model for the transmission of hepatitis B. J. Math. Biol. 73 (2016) 305–333. [CrossRef] [PubMed] [Google Scholar]
  11. O. Diekmann, J.A.P. Heesterbeek and J.A. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990) 365–382. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  12. A. Ducrot, Z. Liu and P. Magal, Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems. J. Math. Anal. Appl. 341 (2008) 501–518. [Google Scholar]
  13. J.W. Eaton and T.B. Hallett, Why the proportion of transmission during early-stage HIV infection does not predict the long-term impact of treatment on HIV incidence. Proc. Natl. Acad. Sci. 111 (2014) 16202–16207. [CrossRef] [Google Scholar]
  14. I. Ekeland, On the variational principle. J. Math. Anal. Appl. 47 (1974) 324–353. [CrossRef] [MathSciNet] [Google Scholar]
  15. L.C. Evans and R.F. Gariepy, Measure Theory and Fini Properties of Functions. CRC Press, Boca Raton (1992). [Google Scholar]
  16. G. Feichtinger, G. Tragler and V.M. Veliov, Optimality conditions for age-structured control systems. J. Math. Anal. Appl. 288 (2003) 47–68. [Google Scholar]
  17. K.R. Fister and S. Lenhart, Optimal control of a competitive system with age-structure. J. Math. Anal. Appl. 291 (2004) 526–537. [CrossRef] [MathSciNet] [Google Scholar]
  18. A.B. Gumel, C.C. McCluskey and P. van den Driessche, Mathematical study of a staged-progression HIV model with imperfect vaccine. Bull. Math. Biol. 68 (2006) 2105–2128. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  19. H. Guo and M.Y. Li, Global dynamics of a staged-progression model for HIV/AIDS with amelioration. Nonlinear Anal.: Real World Appl. 12 (2011) 2529–2540. [CrossRef] [Google Scholar]
  20. J.K. Hale, J.P. LaSalle and M. Slemrod, Theory of a general class of dissipative processes. J. Math. Anal. Appl. 39 (1972) 177–191. [CrossRef] [Google Scholar]
  21. T.D. Hollingsworth, R.M. Anderson and C. Fraser, HIV-1 transmission, by stage of infection. J. Infect. Dis. 198 (2008) 687–693. [CrossRef] [PubMed] [Google Scholar]
  22. J.F. Hutchinson, The biology and evolution of HIV. Annu. Rev. Anthropol. 30 (2001) 85–108. [CrossRef] [Google Scholar]
  23. J.M. Hyman, J. Li and E.A. Stanley, The differential infectivity and staged progression models for the transmission of HIV12. Math. Biosci. 155 (1999) 77–109. [CrossRef] [PubMed] [Google Scholar]
  24. J.M. Hyman, J. Li and E.A. Stanley, The differential infectivity and staged progression models for the transmission of HIV. Math. Biosci. 155 (1999) 77–109. [CrossRef] [PubMed] [Google Scholar]
  25. M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics. Giadini Editori e Stampatori, Pisa (1994). [Google Scholar]
  26. H. Inaba, On a new perspective of the basic reproduction number in heterogeneous environments. J. Math. Biol. 65 (2012) 309–348. [CrossRef] [PubMed] [Google Scholar]
  27. M.E. Kretzschmar, M.F.S. van der Loeff, P.J. Birrell, D. De Angelis and R.A. Coutinho, Prospects of elimination of HIV with test-and-treat strategy. Proc. Natl. Acad. Sci. 110 (2013) 15538–15543. [CrossRef] [Google Scholar]
  28. O.A. Ladyzhenskaya, On the determination of minimal global attractors for the Navier-Stokes and other partial differential equations. Uspekhi Mat. Nauk 42 (1987) 25–60. [Google Scholar]
  29. S. Lenhart and J.T. Workman, Optimal control applied to biological models. CRC Press (2007). [CrossRef] [Google Scholar]
  30. X. Lin, H.W. Hethcote and P. Van den Driessche, An epidemiological model for HIV/AIDS with proportional recruitment. Math. Biosci. 118 (1993) 181–195. [CrossRef] [PubMed] [Google Scholar]
  31. P. Magal and S. Ruan, On semilinear Cauchy problems with non-dense domain. Adv. Differ. Equ. 14 (2009) 1041–1084. [Google Scholar]
  32. P. Magal and S. Ruan, Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models. Am. Math. Soc. (2009). [Google Scholar]
  33. P. Magal, C.C. McCluskey and G.F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model. Appl. Anal. 89 (2010) 1109–1140. [Google Scholar]
  34. P. Magal, Compact attractors for time-periodic age-structured population models. Electr. J. Differ. Equ. (2001). [Google Scholar]
  35. C.C. McCluskey, A model of HIV/AIDS with staged progression and amelioration. Math. Biosci. 181 (2003) 1–16. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  36. E. Numfor, S. Bhattacharya, M. Martcheva and S. Lenhart, Optimal control in multi-group coupled within-host and between-host models. Electr. J. Differ. Equ. 2016 (2016) 87–117. [CrossRef] [Google Scholar]
  37. R.N. Nsubuga, R.G. White, B.N. Mayanja and L.A. Shafer, Estimation of the HIV basic reproduction number in rural South West Uganda: 1991–2008. PloS one 9 (2014) e83778. [CrossRef] [PubMed] [Google Scholar]
  38. A. Pazy, Semigroups of Linear Operator and Applications to Partial Differential Equations. Appl. Math. Sci. 44 (1983). [CrossRef] [Google Scholar]
  39. A.S. Perelson and P.W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41 (1999) 3–44. [CrossRef] [MathSciNet] [Google Scholar]
  40. S.D. Pinkerton, Probability of HIV transmission during acute infection in Rakai. Natl. Inst. Health Uganda. AIDS Behavior 12 (2008) 677–684. [CrossRef] [PubMed] [Google Scholar]
  41. G. Rozhnova, M.F.S. van der Loeff, J.C. Heijne and M.E. Kretzschmar, Impact of heterogeneity in sexual behavior on effectiveness in reducing HIV transmission with test-and-treat strategy. PLoS Comput. Biol. 12 (2016) e1005012. [CrossRef] [PubMed] [Google Scholar]
  42. A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, et al., Global sensitivity analysis: the primer. John Wiley & Sons (2008). [Google Scholar]
  43. G.R. Sell and Y. You, Dynamics of Evolutionary Equations. Springer, New York (2002). [CrossRef] [Google Scholar]
  44. M. Shen, Y. Xiao and L. Rong, Global stability of an infection-age structured HIV-1 model linking within-host and between-host dynamics. Math. Biosci. 263 (2015) 37–50. [CrossRef] [PubMed] [Google Scholar]
  45. H.L. Smith and H.R. Thieme, Vol. 118 of Dynamical systems and population persistence. American Mathematical Soc. (2011). [Google Scholar]
  46. H.R. Thieme, ”Integrated semigroups” and integrated solutions to abstract Cauchy problems. J. Math. Anal. Appl. 152 (1990) 416–447. [CrossRef] [Google Scholar]
  47. H.R. Thieme, Quasi-compact semigroups via bounded perturbation. Advances in Mathematical Population Dynamics-Molecules, Cells and Man, edited by O. Arino, D. Axelrod, and M. Kimmel. Worlds Scientific (1997) 691–713. [Google Scholar]
  48. H.R. Thieme, Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators. J. Differ. Equ. 250 (2011) 3772–3801. [CrossRef] [MathSciNet] [Google Scholar]
  49. United Nations Programme on HIV/AIDS (UNAIDS) (2016). Global AIDS Update 2016. www.unaids.org. [Google Scholar]
  50. G.F. Webb, Theory of nonlinear age-dependent population dynamics. CRC Press (1985). [Google Scholar]
  51. R. Weston and B. Marett, HIV infection pathology and disease progression. Vol. 1 of Clinical Pharmacist (2009). [Google Scholar]
  52. World Health Organization (WHO) (2017). www.who.int/features/qa/71/fr/. [Google Scholar]

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