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Emergence of HIV-1 Drug Resistance During Antiretroviral Treatment

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Abstract

Treating HIV-infected patients with a combination of several antiretroviral drugs usually contributes to a substantial decline in viral load and an increase in CD4+ T cells. However, continuing viral replication in the presence of drug therapy can lead to the emergence of drug-resistant virus variants, which subsequently results in incomplete viral suppression and a greater risk of disease progression. In this paper, we use a simple mathematical model to study the mechanism of the emergence of drug resistance during therapy. The model includes two viral strains: wild-type and drug-resistant. The wild-type strain can mutate and become drug-resistant during the process of reverse transcription. The reproductive ratio ℛ0 for each strain is obtained and stability results of the steady states are given. We show that drug-resistant virus is more likely to arise when, in the presence of antiretroviral treatment, the reproductive ratios of both strains are close. The wild-type virus can be suppressed even when the reproductive ratio of this strain is greater than 1. A pharmacokinetic model including blood and cell compartments is employed to estimate the drug efficacies of both the wild-type and the drug-resistant strains. We investigate how time-varying drug efficacy (due to the drug dosing schedule and suboptimal adherence) affects the antiviral response, particularly the emergence of drug resistance. Simulation results suggest that perfect adherence to regimen protocol will well suppress the viral load of the wild-type strain while drug-resistant variants develop slowly. However, intermediate levels of adherence may result in the dominance of the drug-resistant virus several months after the initiation of therapy. When more doses of drugs are missed, the failure of suppression of the wild-type virus will be observed, accompanied by a relatively slow increase in the drug-resistant viral load.

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References

  • Bajaria, S.H., Webb, G.F., Kirschner, D.E., 2004. Predicting differential responses to structured treatment interruptions during HAART. Bull. Math. Biol. 66, 1093–1118.

    Article  Google Scholar 

  • Bangsberg, D.R., Perry, S., Charlebois, E.D., Clark, R.A., Roberston, M., Zolopa, A.R., Moss, A., 2001. Non-adherence to highly active antiretroviral therapy predicts progression to AIDS. AIDS 15, 1181–1183.

    Article  Google Scholar 

  • Barbour, J.D., Wrin, T., Grant, R.M., Martin, J.N., Segal, M.R., Petropoulos, C.J., Deeks, S.G., 2002. Evolution of phenotypic drug susceptibility and viral replication capacity during long-term virologic failure of protease inhibitor therapy in human immunodeficiency virus-infected adults. J. Virol. 76, 11104–11112.

    Article  Google Scholar 

  • Blower, S.M., Aschenbach, A.N., Gershengorn, H.B., Kahn, J.O., 2001. Predicting the unpredictable: transmission of drug-resistant HIV. Nat. Med. 7, 1016–1020.

    Article  Google Scholar 

  • Blower, S.M., Dowlatabadi, H., 1994. Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example. Int. Stat. Rev. 62, 229–243.

    Article  MATH  Google Scholar 

  • Bofill, M., Janossy, G., Lee, C.A., MacDonald-Burns, D., Phillips, A.N., Sabin, C., Timms, A., Johnson, M.A., Kernoff, P.B., 1992. Laboratory control values for CD4 and CD8 T lymphocytes: implications for HIV-1 diagnosis. Clin. Exp. Immunol. 88, 243–252.

    Article  Google Scholar 

  • Bonhoeffer, S., May, R.M., Shaw, G.M., Nowak, M.A., 1997. Virus dynamics and drug therapy. Proc. Natl. Acad. Sci. USA 94, 6971–6976.

    Article  Google Scholar 

  • Bonhoeffer, S., Nowak, M.A., 1997. Pre-existence and emergence of drug resistance in HIV-1 infection. Proc. Roy. Soc. Lond. B 264, 631–637.

    Article  Google Scholar 

  • Clavel, F., Hance, A.J., 2004. HIV drug resistance. New Engl. J. Med. 350, 1023–1035.

    Article  Google Scholar 

  • Clavel, F., Race, E., Mammano, F., 2000. HIV drug resistance and viral fitness. Adv. Pharmacol. 49, 41–66.

    Article  Google Scholar 

  • Coffin, J.M., 1995. HIV population dynamics in vivo: implications for genetic variation, pathogenesis, and therapy. Science 267, 483–489.

    Article  Google Scholar 

  • Collier, A.C., Coombs, R.W., Schoenfeld, D.A., Bassett, R.L., Timpone, J., Baruch, A., Jones, M., Facey, K., Whitacre, C., McAuliffe, V.J., Friedman, H.M., Merigan, T.C., Reichman, R.C., Hooper, C., Corey, L., 1996. Treatment of human immunodeficiency virus infection with saquinavir, zidovudine, and zalcitabine. New Engl. J. Med. 334, 1011–1017.

    Article  Google Scholar 

  • Conover, W.J., 1980. Practical Nonparametric Statistics, 2rd edn. Wiley, New York.

    Google Scholar 

  • Coombs, D., Gilchrist, M.A., Percus, J., Perelson, A.S., 2003. Optimal viral production. Bull. Math. Biol. 65, 1003–1023.

    Article  Google Scholar 

  • Deeks, S.G., 2003. Treatment of antiretroviral-drug-resistant HIV-1 infection. Lancet 362, 2002–2011.

    Article  Google Scholar 

  • Deeks, S.G., Grant, R.M., Wrin, T., Paxinos, E.E., Liegler, T., Hoh, R., Martin, J.N., Petropoulos, C.J., 2003. Persistence of drug-resistant HIV-1 after a structured treatment interruption and its impact on treatment response. AIDS 17, 361–370.

    Article  Google Scholar 

  • De Jong, M.D., Veenstra, J., Stilianakis, N.I., Schuurman, R., Lange, J.M., De Boer, R.J., Boucher, C.A., 1996. Host-parasite dynamics and outgrowth of virus containing a single K70R amino acid change in reverse transcriptase are responsible for the loss of human immunodeficiency virus type 1 RNA load suppression by zidovudine. Proc. Natl. Acad. Sci. USA 93, 5501–5506.

    Article  Google Scholar 

  • De Leenheer, P., Smith, H.L., 2003. Virus dynamics: a global analysis. SIAM J. Appl. Math. 63, 1313–1327.

    Article  MATH  MathSciNet  Google Scholar 

  • Dixit, N.M., Markowitz, M., Ho, D.D., Perelson, A.S., 2004. Estimates of intracellular delay and average drug efficacy from viral load data of HIV-infected individuals under antiretroviral therapy. Antivir. Ther. 9, 237–246.

    Google Scholar 

  • Dixit, N.M., Perelson, A.S., 2004. Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracellular delay. J. Theor. Biol. 226, 95–109.

    Article  MathSciNet  Google Scholar 

  • Dixit, N.M., Perelson, A.S., 2005. Influence of drug pharmacokinetics on HIV pathogenesis and therapy. In: Tan, W.-Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS and HIV with Intervention, pp. 287–311. World Scientific, Singapore.

    Google Scholar 

  • Dunn, D.T., Gibb, D.M., Babiker, A.G., Green, H., Darbyshire, J.H., Weller, I.V., 2004. HIV resistance testing: is the evidence really there? Antivir. Ther. 9, 641–648.

    Google Scholar 

  • Ferguson, N.M., Donnelly, C.A., Hooper, J., Ghani, A.C., Fraser, C., Bartley, L.M., Rode, R.A., Vernazza, P., Lapins, D., Mayer, S.L., Anderson, R.M., 2005. Adherence to antiretroviral therapy and its impact on clinical outcome in HIV-infected patients. J. Roy. Soc. Interface 2, 349–363.

    Article  Google Scholar 

  • Fischer, M., Hafner, R., Schneider, C., Trkola, A., Joos, B., Joller, H., Hirschel, B., Weber, R., Gunthard, H.F., Swiss HIV Cohort Study, 2003. HIV RNA in plasma rebounds within days during structured treatment interruptions. AIDS 17, 195–199.

    Article  Google Scholar 

  • Friedland, G.H., Williams, A., 1999. Attaining higher goals in HIV treatment: the central importance of adherence. AIDS 13(Suppl. 1), S61–S72.

    Google Scholar 

  • Gabrielson, J., Weiner, D., 2000. Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications. Swedish Pharmaceutical Press, Stockholm.

    Google Scholar 

  • Gulick, R.M., 2002. Structured treatment interruption in patients infected with HIV. Drugs 62, 245–253.

    Article  Google Scholar 

  • Haase, A.T., Henry, K., Zupancic, M., Sedgewick, G., Faust, R.A., Melroe, H., Cavert, W., Gebhard, K., Staskus, K., Zhang, Z.Q., Dailey, P.J., Balfour, H.H. Jr., Erice, A., Perelson, A.S., 1996. Quantitative image analysis of HIV-1 infection in lymphoid tissue. Science 274, 985–989.

    Article  Google Scholar 

  • Havlir, D.V., Eastman, S., Gamst, A., Richman, D.D., 1996. Nevirapine-resistant human immunodeficiency virus: kinetics of replication and estimated prevalence in untreated patients. J. Virol. 70, 7894–7899.

    Google Scholar 

  • Heffernan, J.M., Wahl, L.M., 2005. Treatment interruptions and resistance: a review. In: Tan, W.-Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS and HIV with Intervention, pp. 423–456. World Scientific, Singapore.

    Google Scholar 

  • Hlavacek, W.S., Stilianakis, N.I., Notermans, D.W., Danner, S.A., Perelson, A.S., 2000. Influence of follicular dendritic cells on decay of HIV during antiretroviral therapy. Proc. Natl. Acad. Sci. USA 97, 10966–10971.

    Article  Google Scholar 

  • Hlavacek, W.S., Wofsy, C., Perelson, A.S., 1999. Dissociation of HIV-1 from follicular dendritic cells during HAART: mathematical analysis. Proc. Natl. Acad. Sci. USA 96, 14681–14686.

    Article  Google Scholar 

  • Hockett, R.D., Kilby, J.M., Derdeyn, C.A., Saag, M.S., Sillers, M., Squires, K., Chiz, S., Nowak, M.A., Shaw, G.M., Bucy, R.P., 1999. Constant mean viral copy number per infected cell in tissues regardless of high, low, or undetectable plasma HIV RNA. J. Exp. Med. 189, 1545–1554.

    Article  Google Scholar 

  • Huang, Y., Rosenkranz, S.L., Wu, H., 2003. Modeling HIV dynamics and antiviral response with consideration of time-varying drug exposures, adherence and phenotypic sensitivity. Math. Biosci. 184, 165–186.

    Article  MATH  MathSciNet  Google Scholar 

  • Kepler, T.B., Perelson, A.S., 1998. Drug concentration heterogeneity facilitates the evolution of drug resistance. Proc. Natl. Acad. Sci. USA 95, 11514–11519.

    Article  MATH  Google Scholar 

  • Kim, H., Perelson, A.S., 2006. Dynamic characteristics of HIV-1 reservoirs. Curr. Opin. HIV AIDS 1, 152–156.

    Google Scholar 

  • Kirschner, D.E., Webb, G.F., 1997. Understanding drug resistance for monotherapy treatment of HIV infection. Bull. Math. Biol. 59, 763–786.

    Article  MATH  Google Scholar 

  • Larder, B.A., Darby, G., Richman, D.D., 1989. HIV with reduced sensitivity to zidovudine (AZT) isolated during prolonged therapy. Science 243, 1731–1734.

    Article  Google Scholar 

  • Larder, B.A., Kemp, S.D., 1989. Multiple mutations in HIV-1 reverse transcriptase confer high-level resistance to zidovudine (AZT). Science 246, 1155–1158.

    Article  Google Scholar 

  • Larder, B.A., 1996. Nucleosides and foscarnet-mechanisms. In: Richman, D.D., (Ed.), Antiviral Drug Resistance. Wiley, New York.

    Google Scholar 

  • Lori, F., Maserati, R., Foli, A., Seminari, E., Timpone, J., Lisziewicz, J., 2000. Structured treatment interruptions to control HIV-1 infection. Lancet 355, 287–288.

    Article  Google Scholar 

  • Mansky, L.M., Temin, H.M., 1995. Lower in vivo mutation rate of human immunodeficiency virus type 1 than that predicted from the fidelity of purified reverse transcriptase. J. Virol. 69, 5087–5094.

    Google Scholar 

  • Markowitz, M., Louie, M., Hurley, A., Sun, E., Di Mascio, M., Perelson, A.S., Ho, D.D., 2003. A novel antiviral intervention results in more accurate assessment of human immunodeficiency virus type 1 replication dynamics and T-cell decay in vivo. J. Virol. 77, 5037–5038.

    Article  Google Scholar 

  • McLean, A.R., Nowak, M.A., 1992. Competition between zidovudine-sensitive and zidovudine-resistant strains of HIV. AIDS 6, 71–79.

    Article  Google Scholar 

  • Miller, V., Sabin, C., Hertogs, K., Bloor, S., Martinez-Picado, J., D’Aquila, R., Larder, B., Lutz, T., Gute, P., Weidmann, E., Rabenau, H., Phillips, A., Staszewski, S., 2000. Virological and immunological effects of treatment interruptions in HIV-1 infected patients with treatment failure. AIDS 14, 2857–2867.

    Article  Google Scholar 

  • Mohri, H., Bonhoeffer, S., Monard, S., Perelson, A.S., Ho, D.D., 1998. Rapid turnover of T lymphocytes in SIV-infected rhesus macaques. Science 279, 1223–1227.

    Article  Google Scholar 

  • Mugavero, M.J., Hicks, C.B., 2004. HIV resistance and the effectiveness of combination antiretroviral treatment. Drug Discov. Today Ther. Strateg. 1, 529–535.

    Article  Google Scholar 

  • Murray, J.M., Perelson, A.S., 2005. Human immunodeficiency virus: quasi-species and drug resistance. Multiscale Model. Simul. 3, 300–311.

    Article  MATH  MathSciNet  Google Scholar 

  • Nowak, M.A., Bonhoeffer, S., Shaw, G.M., May, R.M., 1997. Anti-viral drug treatment: dynamics of resistance in free virus and infected cell populations. J. Theor. Biol. 184, 203–217.

    Article  Google Scholar 

  • Nowak, M.A., May, R.M., 2000. Virus Dynamics: Mathematical Principles of Immunology and Virology. Oxford University Press, London.

    MATH  Google Scholar 

  • Ortiz, G.M., Wellons, M., Brancato, J., Vo, H.T., Zinn, R.L., Clarkson, D.E., Van Loon, K., Bonhoeffer, S., Miralles, G.D., Montefiori, D., Bartlett, J.A., Nixon, D.F., 2001. Structured antiretroviral treatment interruptions in chronically HIV-1-infected subjects. Proc. Natl. Acad. Sci. USA 98, 13288–13293.

    Article  Google Scholar 

  • Perelson, A.S., Essunger, P., Cao, Y., Vesanen, M., Hurley, A., Saksela, K., Markowitz, M., Ho, D.D., 1997. Decay characteristics of HIV-1-infected compartments during combination therapy. Nature 387, 188–191.

    Article  Google Scholar 

  • Perelson, A.S., Essunger, P., Ho, D.D., 1997. Dynamics of HIV-1 and CD4+ lymphocytes in vivo. AIDS 11(Suppl. A), S17–S24.

    Google Scholar 

  • Perelson, A.S., Kirschner, D.E., De Boer, R., 1993. Dynamics of HIV infection of CD4+ T cells. Math. Biosci. 114, 81–125.

    Article  MATH  Google Scholar 

  • Perelson, A.S., Nelson, P.W., 2002. Modeling viral infections. Proc. Symp. Appl. Math. 59, 139–172.

    MathSciNet  Google Scholar 

  • Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M., Ho, D.D., 1996. HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science 271, 1582–1586.

    Article  Google Scholar 

  • Phillips, A.N., Youle, M., Johnson, M., Loveday, C., 2001. Use of a stochastic model to develop understanding of the impact of different patterns of antiretroviral drug use on resistance development. AIDS 15, 2211–2220.

    Article  Google Scholar 

  • Ramratnam, B., Bonhoeffer, S., Binley, J., Hurley, A., Zhang, L., Mittler, J.E., Markowitz, M., Moore, J.P., Perelson, A.S., Ho, D.D., 1999. Rapid production and clearance of HIV-1 and hepatitis C virus assessed by large volume plasma apheresis. Lancet 354, 1782–1785.

    Article  Google Scholar 

  • Ribeiro, R.M., Bonhoeffer, S., 2000. Production of resistant HIV mutants during antiretroviral therapy. Proc. Natl. Acad. Sci. USA 97, 7681–7686.

    Article  MATH  Google Scholar 

  • Ribeiro, R.M., Bonhoeffer, S., Nowak, M.A., 1998. The frequency of resistant mutant virus before antiviral therapy. AIDS 12, 461–465.

    Article  Google Scholar 

  • Richman, D.D., 1992. Selection of zidovudine-resistant variants of human immunodeficiency virus by therapy. Curr. Top. Microbiol. Immunol. 176, 131–142.

    Google Scholar 

  • Richman, D.D., 1996. The implications of drug resistance for strategies of combination antiviral chemotherapy. Antivir. Res. 29, 31–33.

    Article  Google Scholar 

  • Richman, D.D., 2000. Principles of HIV resistance testing and overview of assay performance characteristics. Antivir. Ther. 5, 27–31.

    Google Scholar 

  • Richman, D.D., Havlir, D., Corbeil, J., Looney, D., Ignacio, C., Spector, S.A., Sullivan, J., Cheeseman, S., Barringer, K., Pauletti, D., et al., 1994. Nevirapine resistant mutations of human immunodeficiency virus type 1 selected during therapy. J. Virol. 68, 1660–1666.

    Google Scholar 

  • Roberts, D.E., Ribeiro, R.M., 2001. Comparison of different treatment regimens for the emergence of new resistance under therapy. J. Acquir. Immune Defic. Syndr. 27, 331–335.

    Google Scholar 

  • Sedaghat, A.R., Siliciano, R.F., 2004. Immunodeficiency in HIV-1 infection. In: Wormser, G. (Ed.), AIDS and Other Manifestations of HIV Infection, 4th edn., pp. 265–283. Elsevier, Amsterdam.

    Google Scholar 

  • Sethi, A.K., Celentano, D.D., Gange, S.J., Moore, R.D., Gallant, J.E., 2003. Association between adherence to antiretroviral therapy and human immunodeficiency virus drug resistance. Clin. Infect. Dis. 37, 1112–1118.

    Article  Google Scholar 

  • Shiri, T., Garira, W., Musekwa, S.D., 2005. A two-strain HIV-1 mathematical model to assess the effects of chemotherapy on disease parameters. Math. Biosci. Eng. 2, 811–832.

    MATH  MathSciNet  Google Scholar 

  • Smith, R.J., 2006. Adherence to antiretroviral HIV drugs: how many doses can you miss before resistance emerges? Proc. Roy. Soc. B 273, 617–624.

    Google Scholar 

  • Smith, R.J., Wahl, L.M., 2005. Drug resistance in an immunological model of HIV-1 infection with impulsive drug effects. Bull. Math. Biol. 67, 783–813.

    Article  MathSciNet  Google Scholar 

  • Snedecor, S.J., 2003. Comparison of three kinetic models of HIV-1 infection: implications for optimization of treatment. J. Theor. Biol. 221, 519–541.

    Article  MathSciNet  Google Scholar 

  • Stafford, M.A., Corey, L., Cao, Y., Daar, E.S., Ho, D.D., Perelson, A.S., 2000. Modeling plasma virus concentration during primary HIV infection. J. Theor. Biol. 203, 285–301.

    Article  Google Scholar 

  • St Clair, M.H., Martin, J.L., Tudor-Williams, G., Bach, M.C., Vavro, C.L., King, D.M., Kellam, P., Kemp, S.D., Larder, B.A., 1991. Resistance to ddI and sensitivity to AZT induced by a mutation in HIV-1 reverse transcriptase. Science 253, 1557–1559.

    Article  Google Scholar 

  • Stilianakis, N.I., Boucher, C.A., De Jong, M.D., Van Leeuwen, R., Schuurman, R., De Boer, R.J., 1997. Clinical data sets of human immunodeficiency virus type 1 reverse transcriptase-resistant mutants explained by a mathematical model. J. Virol. 71, 161–168.

    Google Scholar 

  • Tang, J.W., Pillay, D., 2004. Transmission of HIV-1 drug resistance. J. Clin. Virol. 30, 1–10.

    Article  Google Scholar 

  • Tesoriero, J., French, T., Weiss, L., Waters, M., Finkelstein, R., Agins, B., 2003. Stability of adherence to highly active antiretroviral therapy over time among clients enrolled in the treatment adherence demonstration project. J. Acquir. Immune Defic. Syndr. 33, 484–493.

    Google Scholar 

  • Tchetgen, E., Kaplan, E.H., Friedland, G.H., 2001. Public health consequences of screening patients for adherence to highly active antiretroviral therapy. J. Acquir. Immune Defic. Syndr. 26, 118–129.

    Article  Google Scholar 

  • Vergu, E., Mallet, A., Golmard, J.L., 2002. The role of resistance characteristics of viral strains in the prediction of the response to antiretroviral therapy in HIV infection. J. Acquir. Immune Defic. Syndr. 30, 263–270.

    Google Scholar 

  • Wahl, L.M., Nowak, M.A., 2000. Adherence and drug resistance: predictions for therapy outcome. Proc. Roy. Soc. Lond. B 267, 835–843.

    Article  Google Scholar 

  • Wei, X., Ghosh, S.K., Taylor, M.E., Johnson, V.A., Emini, E.A., Deutsch, P., Lifson, J.D., Bonhoeffer, S., Nowak, M.A., Hahn, B.H., Saag, M.S., Shaw, G.M., 1995. Viral dynamics in human-immunodeficiency-virus type-1 infection. Nature 373, 117–122.

    Article  Google Scholar 

  • Wein, L.M., D’Amato, R.M., Perelson, A.S., 1998. Mathematical analysis of antiretroviral therapy aimed at HIV-1 eradication or maintenance of low viral loads. J. Theor. Biol. 192, 81–98.

    Article  Google Scholar 

  • Wodarz, D., Lloyd, A.L., 2004. Immune responses and the emergence of drug-resistant virus strains in vivo. Proc. Roy. Soc. Lond. B 271, 1101–1109.

    Article  Google Scholar 

  • Wu, H., Huang, Y., Acosta, E.P., Park, J.G., Yu, S., Rosenkranz, S.L., Kuritzkes, D.R., Eron, J.J., Perelson, A.S., Gerber, J.G., 2006. Pharmacodynamics of antiretroviral agents in HIV-1 infected patients: using viral dynamic models that incorporate drug susceptibility and adherence. J. Pharmacokinet. Pharmacodyn. 33, 399–419.

    Article  Google Scholar 

  • Wu, H., Huang, Y., Acosta, E.P., Rosenkranz, S.L., Kuritzkes, D.R., Eron, J.J., Perelson, A.S., Gerber, J.G., 2005. Modeling long-term HIV dynamics and antiretroviral response: effects of drug potency, pharmacokinetics, adherence, and drug resistance. J. Acquir. Immune Defic. Syndr. 39, 272–283.

    Article  Google Scholar 

  • Yuan Chen, H., Di Mascio, M., Perelson, A.S., Ho, D.D., Zhang, L., 2007. Determination of virus burst size in vivo using a single-cycle SIV in rhesus macaques, submitted.

  • Zhang, L., Ramratnam, B., Tenner-Racz, K., He, Y., Vesanen, M., Lewin, S., Talal, A., Racz, P., Perelson, A.S., Korber, B.T., Markowitz, M., Ho, D.D., 1999. Quantifying residual HIV-1 replication in patients receiving combination antiretroviral therapy. New Engl. J. Med. 340, 1605–1613.

    Article  Google Scholar 

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Rong, L., Feng, Z. & Perelson, A.S. Emergence of HIV-1 Drug Resistance During Antiretroviral Treatment. Bull. Math. Biol. 69, 2027–2060 (2007). https://doi.org/10.1007/s11538-007-9203-3

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