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HIV dynamics in sequence space

HIV dynamics in sequence space. Shiwu Zhang Based on [Kamp2002from, Kamp2002co-evolution]. Issues on HIV dynamics. HIV infection in patient HIV development stages. [Santos2001, Hershberg2000, AAMAS-HIVreport] Factors influence (mutation rate, antigenic diversity…)

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HIV dynamics in sequence space

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  1. HIV dynamics in sequence space Shiwu Zhang Based on [Kamp2002from, Kamp2002co-evolution]

  2. Issues on HIV dynamics • HIV infection in patient • HIV development stages. [Santos2001, Hershberg2000, AAMAS-HIVreport] • Factors influence (mutation rate, antigenic diversity…) • Distribution of HIV latency period [Kamp2002from, Kamp2002co-evolution] • HIV epidemic • Spreading on social network [Dezso2002, Satorras2001]

  3. Background: Percolation theory • Occupation probability (Susceptibility) • Clusters • Spanning probability (transmissibility) • Percolation threshold (Pc)

  4. Background: Sequence space • Viral genome & immune receptor: length l • Viral mutation: change one bit (1,2, …) • Constructing a sequence space, size= l • Viral mutation means random walk in space • Dimension: l

  5. Model • Site status • Susceptible S(t) • Site can harbor a virus • Infected v(t) • Site is infected by virus • Recovered R(t) • After immune response (immune memory) • Viral genome is not arbitrary (D0) • Immunological presence (0)

  6. Model (2) • Rules: • Random select site • If the site harbor immune receptor • Mutate with certain probability • If mutate and the mutant match an infected site then set the infected site to recovered • If the site is infected • Mutate with certain probability • If a new strain is generated and corresponds to a susceptible site, the site become infected • For HIV, another rule • Viral strain has probability is(t) to meet an receptor infect it with probability p

  7. Result • Simulation result could capture HIV population dynamics from clinical latency stage to onset on AIDS, but fail to reflect initial immune response • Initial distribution 0 is important factor to affect result • Increasing probability p will shorten waiting time • Distribution of HIV incubation period distribution from simulation fits in well with that from real data

  8. Summary • Characteristics: • Sequence space • Percolation theory • Accounting for important interactions • HIV mutation • Immune cells stimulation • Immune system’s global ability:memory • Shortage: • Omitting physical space • Using strain denote population (without strain size distribution) • Don’t account for initial response

  9. Related Papers • C. Kamp, S. Bornholdt (2002). From HIV infection to AIDS: A dynamically induced percolation transition?, Proc. R. Soc. London B (2002), accepted for publication. http://arxiv.org/abs/cond-mat/0201482 • C. Kamp, S. Bornholdt (2002). Co-evolution of quasispecies: B-cell mutation rates maximize viral error catastrophes, Phys. Rev. Lett. 88, 068104. http://www.tp.umu.se/~kim/Network/Marek/sem.pdf • D. Stauffer, A. Aharony (1992). Introduction to Percolation Theory, (Taylor and Francis, London). • H. Mannion et al. (2000). A Monte Carlo Approach to Population Dynamics of Cell in an HIV Immune Response Model. Theory in Bioscience: 119(94) • U. Hershberg et al.(2001). HIV time hierarchy: Winning the war while losing all the battles. Physica A:289 (1-2). http://arxiv.org/abs/nlin.AO/0006023

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