Citation: Mark Kot, Dobromir T. Dimitrov. The dynamics of a simple, risk-structured HIV model[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 4184-4209. doi: 10.3934/mbe.2020232
[1] | R. M. Grant, J. R. Lama, P. L. Anderson, V. McMahan, A. Y. Liu, L. Vargas, et al., Preexposure chemoprophylaxis for HIV prevention in men who have sex with men, N. Engl. J. Med., 363 (2010), 2587-2599. |
[2] | J. M. Baeten, D. Donnell, P. Ndase, N. R. Mugo, J. D. Campbell, J. Wangisi, et al., Antiretroviral prophylaxis for HIV prevention in heterosexual men and women, N. Engl. J. Med., 367 (2012), 399-410. |
[3] | M. C. Thigpen, P. M. Kebaabetswe, L. A. Paxton, D. K. Smith, C. E. Rose, T. M. Segolodi, et al., Antiretroviral preexposure prophylaxis for heterosexual HIV transmission in Botswana, N. Engl. J. Med., 367 (2012), 423-434. |
[4] | J.-M. Molina, C. Capitant, B. Spire, G. Pialoux, L. Cotte, I. Charreau, et al., On-demand preexposure prophylaxis in men at high risk for HIV-1 infection, N. Engl. J. Med., 373 (2015), 2237-2246. |
[5] | S. McCormack, D. T. Dunn, M. Desai, D. I. Dolling, M. Gafos, R. Gilson, et al., Pre-exposure prophylaxis to prevent the acquisition of HIV-1 infection (PROUD): Effective results from the pilot phase of a pragmatic open-label randomised trial, Lancet, 387 (2016), 53-60. |
[6] | D. A. Margolis, J. Gonzalez-Garcia, H.-J. Stellbrink, J. J. Enron, Y. Yazdanpanah, D. Podzamczer, et al., Long-acting intramuscular cabotegravir and rilpivirine in adults with HIV-1 infection (LATTE-2): 96-week results of a randomised, open-label, phase 2b, non-inferiority trial, Lancet, 390 (2017), 1499-1510. |
[7] | J. Cohen, Long-acting drug acts like a short-term AIDS vaccine, Science, 368 (2020), 807. |
[8] | R. D'Amico, D. A. Margolis, Long-acting injectable therapy: An emerging paradigm for the treatment of HIV infection, Curr. Opin. HIV AIDS, 15 (2020), 13-18. |
[9] | M. Kovarova, S. R. Benhabbour, I. Massud, R. A. Spagnuolo, B. Skinner, C. E. Baker, et al., Ultralong-lasting removable drug delivery system for HIV treatment and prevention, Nat. Commun., 9 (2018), 4156. |
[10] | E. D. Weld, C. Flexner, Long-acting implants to treat and prevent HIV infection, Curr. Opin. HIV AIDS, 15 (2020), 33-41. |
[11] | J. Abbasi, Large HIV vaccine trial launches in South Africa, JAMA, 317 (2017), 350. |
[12] | S. de Montigny, B. J. S. Adamson, B. R. Masse, L. P. Garrison, J. G. Kublin, P. B. Gilbert, et al., Projected effectiveness and added value of HIV vaccination campaigns in South Africa: A modeling study, Sci. Rep., 8 (2018), 6066. |
[13] | L. F. Johnson, P. J. White, A review of mathematical models of HIV/AIDS interventions and their implications for policy, Sex. Transm. Infect., 87 (2011), 629-634. |
[14] | J. W. Eaton, N. A. Menzies, J. Stover, V. Cambiano, L. Chindelevitch, A. Cori, et al., Health benefits, costs, and cost-effectiveness of earlier eligibility for adult antiretroviral therapy and expanded treatment coverage: A combined analysis of 12 mathematical models, Lancet Global Health, 2 (2013), e23-e34. |
[15] | R. M. Anderson, G. F. Medley, R. M. May, A. M. Johnson, A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causitive agent of AIDS, IMA J. Math. Appl. Med. Biol., 3 (1986), 229-263. |
[16] | G. P. Garnett, R. M. Anderson, Factors controlling the spread of HIV in heterosexual communities in developing countries: Patterns of mixing between different age and sexual activity classes, Philos. Trans. R. Soc. B, 342 (1993), 137-159. |
[17] | N. J. D. Nagelkerke, S. J. de Vlas, P. Jha, M. Luo, F. A. Plummer, R. Kaul, Heterogeneity in host HIV susceptibility as a potential contributor to recent HIV prevalence declines in Africa, AIDS, 23 (2009), 125-130. |
[18] | G. Rozhnova, M. F. S. vand der Loeff, J. C. M. Heijne, M. E. Kretzschmar, Impact of heterogeneity in sexual behavior on effectiveness in reducing HIV transmission with test-and-treat strategy, PLoS Comp. Biol., 12 (2016), e1005012. |
[19] | M. J. Keeling, P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, Princeton, 2008. |
[20] | J. A. Jacquez, C. P. Simon, J. Koopman, L. Sattenspiel, T. Perry, Modeling and analyzing HIV transmission: the effect of contact patterns, Math. Biosci., 92 (1988), 119-199. |
[21] | J. M. Hyman, E. A. Stanley, Using mathematical models to understand the AIDS epidemic, Math. Biosci., 90 (1988), 415-473. |
[22] | A. Azizi, K. Rios-Soto, A. Mubayi, J. M. Hyman, A risk-based model for predicting the impact of using condoms on the spread of sexually transmitted infections, Infect. Dis. Model., 2 (2017), 100-112. |
[23] | S. Busenberg, C. Castillo-Chavez, A general solution of the problem of mixing of subpopulations and its application to risk- and age-structured epidemic models for the spread of AIDS, IMA J. Math. Appl. Med. Biol., 8 (1991), 1-29. |
[24] | O. Diekmann, H. Heesterbeek, T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics, Princeton University Press, Princeton, 2013. |
[25] | D. Juher, J. Ripoll, J. Saldana, Analysis and Monte Carlo simulations of a model for the spread of infectious diseases in heterogeneous metapopulations, Phys. Rev. E, 80 (2009), 041920. |
[26] | N. Masuda, Effects of diffusion rates on epidemic spreads in metapopulation networks, New J. Phys., 12 (2010), 093009. |
[27] | G. Tanaka, C. Urabe, K. Aihara, Random and targeted interventions for epidemic control in metapopulation models, Sci. Rep., 4 (2015), 5522. |
[28] | M. Liu, J. Zhang, Z. Li, Y. Sun, Modeling epidemic in metapopulation networks with heterogeneous diffusion rates, Math. Biosci. Eng., 16 (2019), 7085-7097. |
[29] | Y. Xiao, S. Tang, Y. Zhou, R. J. Smith, J. Wu, N. Wang, Predicting the HIV/AIDS epidemic and measuring the effect of mobility in mainland China, J. Theor. Biol., 317 (2013), 271-285. |
[30] | A. Isdory, E. Moreithi, D. J. T. Sumpter, The impact of human mobility on HIV transmission in Kenya, PLoS One, 10 (2015), e0142805. |
[31] | G. Chowell, L. Sattenspiel, S. Bansal, C. Viboud, Mathematical models to characterize early epidemic growth: a review, Phys. Life Rev., 18 (2016), 66-97. |
[32] | A. C. Pipkin, A Course on Integral Equations, Springer-Verlag, New York, 1991. |
[33] | R. P. Kanwal, Linear Integral Equations, Birkhauser, Boston, 1997. |
[34] | L. Sattenspiel, The Geographic Spread of Infectious Diseases: Models and Applications, Princeton University Press, Princeton, 2009. |
[35] | J. V. Uspensky, Theory of Equations, McGraw-Hill Book Company, New York, 1948. |
[36] | J. H. Wilkinson, C. Reinsch, Handbook for Automatic Computation: Volume II: Linear Algebra, Springer-Verlag, Berlin, 1971. |
[37] | W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1997. |
[38] | M.-C. Boily, R. Poulin, B. Masse, Some methodological issues in the study of sexual networks: from model to data to model, Sex. Transm. Dis., 27 (2000), 558-571. |
[39] | F. Liljeros, C. R. Edling, L. A. Nunes Amaral, Sexual networks: implications for the transmission of sexually transmitted infections, Microbes Infect., 5 (2003), 189-196. |
[40] | J. L. Marcus, L. B. Hurley, D. S. Krakower, S. Alexeeff, M. J. Silverberg, J. E. Volk, Use of electronic health record data and machine learning to identify candidates for HIV pre-exposure prophylaxis: A modeling study, Lancet HIV, 6 (2019), e688-e695. |
[41] | W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics., Proc. R. Soc. A, 115 (1927), 700-721. |
[42] | R. M. Anderson, Discussion: The Kermack-McKendrick epidemic threshold theorem, Bull. Math. Biol., 53 (1991), 3-32. |
[43] | J. O. Lloyd-Smith, P. C. Cross, C. J. Briggs, M. Daugherty, W. M. Getz, J. Latto, et al., Should we expect population thresholds for worldlife disease?, Trends Ecol. Evol., 20 (2005), 511-519. |
[44] | M. G. Neubert, H. Caswell, Alternatives to resilience for measuring the responses of ecological systems to perturbations, Ecology, 78 (1997), 653-665. |
[45] | M. G. Neubert, T. Klanjscek, H. Caswell, Reactivity and transient dynamics of predator-prey and food web models, Ecol. Modell., 179 (2004), 23-38. |
[46] | L. N. Trefethen, M. Embree, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators, Princeton University Press, Princeton, 2005. |
[47] | S. P. Ellner, D. Z. Childs, M. Rees, Data-Driven Modelling of Structured Populations: A Practical Guide to the Integral Projection Model, Springer, Cham, Switzerland, 2016. |