THE COUPLED WITHIN-AND BETWEEN-HOST DYNAMICS IN THE EVOLUTION OF HIV/AIDS IN CHINA

Jie Lou; Hongna Zhou; Dong Liang; Zhen Jin; Baojun Song

doi:10.11948/2015056

2015 Volume 5 Issue 4

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Jie Lou, Hongna Zhou, Dong Liang, Zhen Jin, Baojun Song. THE COUPLED WITHIN-AND BETWEEN-HOST DYNAMICS IN THE EVOLUTION OF HIV/AIDS IN CHINA[J]. Journal of Applied Analysis & Computation, 2015, 5(4): 731-750. doi: 10.11948/2015056

Citation:

Jie Lou, Hongna Zhou, Dong Liang, Zhen Jin, Baojun Song. THE COUPLED WITHIN-AND BETWEEN-HOST DYNAMICS IN THE EVOLUTION OF HIV/AIDS IN CHINA[J]. Journal of Applied Analysis & Computation, 2015, 5(4): 731-750. doi: 10.11948/2015056

THE COUPLED WITHIN-AND BETWEEN-HOST DYNAMICS IN THE EVOLUTION OF HIV/AIDS IN CHINA

1 Department of Mathematics, Shanghai University, 99 Shangda Road Shanghai 200444, P. R. China;
2 Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada;
3 Complex Systems Research Center, Shanxi University, Taiyuan, 030006, P. R. China;
4 Department of Mathematical Sciences, Montclair State University, Montclair, NJ 07043, USA

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Abstract

Abstract

In this work, we develop and analyze mathematical models for the coupled within-host and between-host dynamics caricaturing the evolution of HIV/AIDS. The host population is divided into susceptible, the infected without receiving treatment and the infected receiving ART treatment in accordance with China's Four-Free-One-Care Policy. The within-host model is a typical ODE model adopted from literatures. The between-host model incorporates age-since-infection described by a system of integrodifferential equations. The two models are coupled via the viral load and number of CD4+ T cells of within the hosts. For the between-host model with an arbitrarily selected HIV infected individual, we focus on the analyses of the basic reproduction number R₀ and the stabilities of equilibria. Through simulations we also find that the within-host dynamics does influence the between-host dynamics, and the nesting of within-host and between-host play a very important role in the HIV/AIDS evolution.
- Within-host /
- between-host /
- nested model /
- HIV/AIDS
MSC: 39A11;92D30

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References

[1]	L. J. Allen, F. Brauer, P. Van den Driessche and J. Wu, Mathematical epidemiology, Vol. 1945, Springer, 2008. Google Scholar
[2]	R. Antia, B. R. Levin and R. M. May, Within-host population dynamics and the evolution and maintenance of microparasite virulence, American Naturalist, (1994), 457-472. Google Scholar
[3]	R. Antia, B. Levin and P. Williamson, A quantitative model suggests immune memory involves the colocalization of b and th cells, Journal of theoretical biology, 153(3)(1991), 371-384. Google Scholar
[4]	R. Antia and M. Lipsitch, Mathematical models of parasite responses to host immune defences, Parasitology, 115(07)(1997), 155-167. Google Scholar
[5]	R. M. Anderson, Mathematical studies of parasitic infection and immunity, Science, 264(5167)(1994), 1884-1886. Google Scholar
[6]	R. J.de Boer and M. C. Boerlijst, Diversity and virulence thresholds in aids, Proceedings of the National Academy of Sciences, 91(2)(1994), 544-548. Google Scholar
[7]	D. Coombs, M. A. Gilchrist and C. L. Ball, Evaluating the importance of withinand between-host selection pressures on the evolution of chronic pathogens, Theoretical population biology, 72(4)(2007), 576-591. Google Scholar
[8]	O. Diekmann, J. Heesterbeek and J. A. Metz, On the definition and the computation of the basic reproduction ratio r 0 in models for infectious diseases in heterogeneous populations, Journal of mathematical biology, 28(4)(1990), 365-382. Google Scholar
[9]	S. DebRoy, B. M. Bolker and M. Martcheva, Bistability and long-term cure in a within-host model of hepatitis c, Journal of Biological Systems, 19(04) (2011), 533-550. Google Scholar
[10]	M. A. Gilchrist and A. Sasaki, Modeling host-parasite coevolution:a nested approach based on mechanistic models, Journal of Theoretical Biology, 218(3) (2002), 289-308. Google Scholar
[11]	R. M. Granich, C. F.Gilks, C. Dye, K. M.De Cock and B. G. Williams, Universal voluntary hiv testing and immediate antiretroviral therapy-authors' reply, The Lancet, 373(9669)(2009), 1080-1081. Google Scholar
[12]	V. V. Ganusov, C. T. Bergstrom and R. Antia, Within-host population dynamics and the evolution of microparasites in a heterogeneous host population, Evolution, 56(2)(2002), 213-223. Google Scholar
[13]	H. W. Hethcote, The mathematics of infectious diseases, SIAM review, 42(4) (2000), 599-653. Google Scholar
[14]	M. Kaufman, J. Urbain and R. Thomas, Towards a logical analysis of the immune response,Journal of theoretical biology, 114(4)(1985), 527-561. Google Scholar
[15]	J. Lou, Y. Lou and J. Wu, Threshold virus dynamics with impulsive antiretroviral drug effects, Journal of mathematical biology, 65(4)(2012), 623-652. Google Scholar
[16]	X. Li, H. Lu, H. Raymond, Y. Sun, Y. Jia, X. He, S. Fan, Y. Shao, W. McFarland, Y. Xiao, et al., Untested and undiagnosed:barriers to hiv testing among men who have sex with men, beijing, china, Sexually transmitted infections. Google Scholar
[17]	Y. Li, S. Ruan and D. Xiao, The within-host dynamics of malaria infection with immune response, Mathematical Biosciences and Engineering, 8(4)(2011), 999-1018. Google Scholar
[18]	M. Martcheva and X.-Z. Li, Linking immunological and epidemiological dynamics of hiv:the case of super-infection, Journal of biological dynamics, 7(1)(2013), 161-182. Google Scholar
[19]	N. Mideo, S. Alizon and T. Day, Linking within-and between-host dynamics in the evolutionary epidemiology of infectious diseases, Trends in ecology evolution, 23(9)(2008), 511-517. Google Scholar
[20]	M. A. Nowak, R. M. May and R. M. Anderson, The evolutionary dynamics of hiv-1 quasispecies and the development of immunodeficiency disease, Aids, 4(11)(1990), 1095-1104. Google Scholar
[21]	A. S. Perelson, D. E. Kirschner and R. De Boer, Dynamics of hiv infection of cd4 T cells, Mathematical biosciences, 114(1)(1993), 81-125. Google Scholar
[22]	T. C. Porco, J. N. Martin, K. A. Page-Shafer, A. Cheng, E. Charlebois, R. M. Grant and D. H. Osmond, Decline in hiv infectivity following the introduction of highly active antiretroviral therapy, AIDS (London, England), 18(1)(2004), 81. Google Scholar
[23]	E. Szathmary and J. Maynard Smith, The Major Transitions in Evolution, Oxford University Press, 2004. Google Scholar
[24]	A. Sasaki and Y. Iwasa, Optimal growth schedule of pathogens within a host:switching between lytic and latent cycles, Theoretical population biology, 39(2)(1991), 201-239. Google Scholar