This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which they have been designed. We consider also the mutation and multiplication of the virus. An original infection term is derived.
So as to compare our system of differential equations with well-known models, we study some of them and compare their predictions to ours in the reduced case of only one antigenicity. In this particular case, our model does not yield any major qualitative difference. We prove mathematically that, in this case, our model is biologically consistent (positive fields) and has a unique continuous solution for long time evolution. In conclusion, this model improves the ability to simulate more advanced phases of the disease.
Classification: 34-99, 65-05, 65Z05, 92B99, 92C50
Keywords: HIV modeling, antigenic variation, mutation, immune response
@article{MSIA_2010__3_1_1_0, author = {Fran\c{c}ois Dubois and Herv\'e V.J. Le Meur and Claude Reiss}, title = {Mathematical modeling of antigenicity for {HIV} dynamics}, journal = {MathematicS In Action}, pages = {1--35}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {3}, number = {1}, year = {2010}, doi = {10.5802/msia.3}, language = {en}, url = {https://msia.centre-mersenne.org/articles/10.5802/msia.3/} }
TY - JOUR TI - Mathematical modeling of antigenicity for HIV dynamics JO - MathematicS In Action PY - 2010 DA - 2010/// SP - 1 EP - 35 VL - 3 IS - 1 PB - Société de Mathématiques Appliquées et Industrielles UR - https://msia.centre-mersenne.org/articles/10.5802/msia.3/ UR - https://doi.org/10.5802/msia.3 DO - 10.5802/msia.3 LA - en ID - MSIA_2010__3_1_1_0 ER -
François Dubois; Hervé V.J. Le Meur; Claude Reiss. Mathematical modeling of antigenicity for HIV dynamics. MathematicS In Action, Volume 3 (2010) no. 1, pp. 1-35. doi : 10.5802/msia.3. https://msia.centre-mersenne.org/articles/10.5802/msia.3/
[1] Dynamics of Immune Escape during HIV/SIV Infection, PLoS Comput. Biol., Tome 4 (2008) no. 7, e1000103 pages (http://dx.plos.org/10.1371/journal.pcbi.1000103 ) | Article
[2] Viral error catastrophe by mutagenic nucleosides, Annu. Rev. Microbiol., Tome 58 (2004), pp. 183-205
[3] Ordinary Differential Equations, The MIT Press., Massachusetts (1978)
[4] Error-prone polymerization by HIV-1 reverse transcriptase. Contribution of template-primer misalignment, miscoding, and termination probability to mutational hot spots., J. Biol. Chem., Tome 268(14) (1993), p. 10324-34
[5] The error threshold, Virus Res., Tome 107 (1993) no. 2, pp. 117-127
[6] Model Selection and Mixed-Effects Modeling of HIV Infection Dynamics., Bull. Math. Biol., Tome 68 (2006) no. 8, pp. 2005-2025
[7] Identification of host proteins required for HIV infection through a functional genomic screen., Science, Tome 319 (2008) no. 5865, p. 921-6
[8] HIV-1 Infection and Low Steady State Viral Loads., Bull. Math. Biol., Tome 64 (2002), pp. 29-64
[9] Understanding the Failure of CD8+ T-Cell Vaccination against Simian/Human Immunodeficiency Virus, J. Virol., Tome 81 (2007) no. 6, pp. 2838-2848
[10] Target Cell Limited and Immune Control Models of HIV Infection: A Comparison, J. Theor. Biol., Tome 190 (1998), pp. 201-214
[11] Virus dynamics: a global analysis., SIAM J. Appl. Math., Tome 63 (2003) no. 4, pp. 1313-1327
[12] Inhibition of HIV type 1 replication by simultaneous infection of peripheral blood lymphocytes with human immunodeficiency virus types 1 and 2., AIDS Res. Hum. Retroviruses, Tome 17 (2001) no. 4, pp. 295-309
[13] Fidelity and termination of polymerization by reverse transcriptases in vitro., Paris-Sud University (1998) (Ph. D. Thesis)
[14] Virtues of being faithful: can we limit the genetic variation in human immunodeficiency virus?, J. Mol. Med., Tome 76 (1998) no. 9, p. 604-12
[15] Modélisation de la multiplication du virus HIV., Praz-sur-Arly, SMAI (2007)
[16] Viral dynamics in HIV-1 infection., Cell, Tome 93 (1998) no. 5, p. 665-71
[17] Global stability of steady solutions for a model in virus dynamics., Math. Model. Numer. Anal., Tome 37 (2003) no. 4, pp. 709-723
[18] Beyond Tsg101: the role of Alix in ’ESCRTing’ HIV-1., Nat. Rev. Microbiol., Tome 5 (2007) no. 12, p. 912-6
[19] Practical Identifiability of HIV Dynamics Models., Bull. Math. Biol., Tome 69 (2007) no. 8, p. 2493-513
[20] KP-1212/1461, a nucleoside designed for the treatment of HIV by viral mutagenesis., Antivir. Res, Tome 67 (2005), pp. 1-9
[21] Applied and Computational Complex Analysis, John Wiley, New-York (1974)
[22] Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay., Proc. Natl. Acad. Sci. USA, Tome 93 (1996), pp. 7247-7251
[23] Fidelity of HIV-1 reverse transcriptase copying a hypervariable region of the HIV-1 env gene., Virology, Tome 199 (1994) no. 2, p. 323-30
[24] Template misalignment in multisubunit RNA polymerases and transcription fidelity., Mol. Cell., Tome 24 (2006) no. 2, p. 257-66
[25] Ancestral and consensus envelope immunogens for HIV-1 subtype C., Virology, Tome 352 (2006) no. 2, p. 438-49
[26] Reduction of the rate of poliovirus protein synthesis through large-scale codon deoptimization causes attenuation of viral virulence by lowering specific infectivity., J. Virol., Tome 80 (2006) no. 19, p. 9687-96
[27] Mechanism of action of a novel viral mutagenic covert nucleotide: molecular interaction with HIV-1 reverse transcriptase and host cell DNA polymerases., Antivir. Res., Tome 67 (2005), pp. 10-17
[28] Effect of drug efficacy and the eclipse phase of the viral life cycle on estimates of HIV viral dynamic parameters., J. Acquir. Immune Defic. Syndr., Tome 26 (2001) no. 5, pp. 405-412
[29] Population dynamics of immune responses to persistent viruses., Science, Tome 272 (1996), pp. 74-79
[30] Virus dynamics. Mathematical Principles of Immunology and Virology, Oxford University Press (2000)
[31] On the dynamics of certain models describing the HIV infection., Dynamics and Games in Science, in honour of Mauricio Peixoto and David Rand, Springer-Verlag (2010)
[32] Modelling viral and immune system dynamics, Nature Rev. Immunol., Tome 2 (2002), pp. 28-36
[33] Mathematical analysis of HIV-1 dynamics in vivo., SIAM Review, Tome 41 (1999) no. 1, pp. 3-44
[34] HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time., Science, Tome 271 (1996) no. 5255, p. 1582-6
[35] CD4+ Target cell availability determines the dynamics of immune escape and reversion in vivo., J. Virol., Tome 82 (2008) no. 8, p. 4091-101
[36] Extralymphatic virus sanctuaries as a consequence of potent T-cell activation., Nat. Med., Tome 13 (2007) no. 11, p. 1316-23
[37] Turnover of CD4 and CD8 lymphocytes in HIV-1 infection as measured by Ki-67 antigen, J. Exp. Medecine, Tome 187 (1998) no. 8, pp. 1295-1303
[38] The SAEM algorithm for group comparison tests in longitudinal data analysis based on non-linear mixed-effects model., Stat Med., Tome 26 (2007) no. 27, p. 4860-75
[39] Comparison of three kinetic models of HIV-1 implications for optimization of treatment., J. Theor. Biol., Tome 221 (2003), pp. 519-541
[40] Efficiency of human immunodeficiency virus type 1 postentry infection processes: evidence against disproportionate numbers of defective virions., J. Virol., Tome 81 (2007) no. 8, p. 4367-70
[41] A stochastic model for early HIV-1 population dynamics., J. Theor. Biol., Tome 195 (1998) no. 4, p. 451-63
[42] Mathematical analysis of the global dynamics of a model for HIV infection of T cells., Math. Biosci., Tome 200 (2006) no. 1, pp. 44-57
[43] Cell factors stimulate human immunodeficiency virus type 1 reverse transcription in vitro., J. Virol., Tome 82 (2008) no. 3, p. 1425-37
[44] Infection dynamics in HIV-specific CD4 T cells: does a CD4 T cell boost benefit the host or the virus?, Math. Biosci., Tome 209 (2007) no. 1, pp. 14-29
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