1、HIV dynamics in sequence spaceShiwu ZhangBased on Kamp2002from, Kamp2002co-evolution1Issues on HIV dynamicsHIV infection in patientHIV development stages. Santos2001, Hershberg2000, AAMAS-HIVreportFactors influence (mutation rate, antigenic diversity)Distribution of HIV latency period Kamp2002from,

2、Kamp2002co-evolutionHIV epidemicSpreading on social network Dezso2002, Satorras20012Background: Percolation theoryOccupation probability (Susceptibility)ClustersSpanning probability (transmissibility)Percolation threshold (Pc)3Background: Sequence spaceViral genome & immune receptor: length lViral m

3、utation: change one bit (1,2, )Constructing a sequence space, size= lViral mutation means random walk in spaceDimension: l4ModelSite statusSusceptible S(t)Site can harbor a virusInfected v(t)Site is infected by virusRecovered R(t)After immune response (immune memory)Viral genome is not arbitrary (D0

4、)Immunological presence (0)5Model (2)Rules:Random select siteIf the site harbor immune receptorMutate with certain probabilityIf mutate and the mutant match an infected site then set the infected site to recoveredIf the site is infectedMutate with certain probabilityIf a new strain is generated and

5、corresponds to a susceptible site, the site become infected For HIV, another ruleViral strain has probability is(t) to meet an receptor infect it with probability p6ResultSimulation result could capture HIV population dynamics from clinical latency stage to onset on AIDS, but fail to reflect initial

6、 immune responseInitial distribution 0 is important factor to affect resultIncreasing probability p will shorten waiting timeDistribution of HIV incubation period distribution from simulation fits in well with that from real data7SummaryCharacteristics:Sequence spacePercolation theoryAccounting for

7、important interactionsHIV mutationImmune cells stimulation Immune systems global ability:memoryShortage:Omitting physical spaceUsing strain denote population (without strain size distribution)Dont account for initial response8Related PapersC. Kamp, S. Bornholdt (2002). From HIV infection to AIDS: A

8、dynamically induced percolation transition?, Proc. R. Soc. London B (2002), accepted for publication. C. Kamp, S. Bornholdt (2002). Co-evolution of quasispecies: B-cell mutation rates maximize viral error catastrophes, Phys. Rev. Lett. 88, 068104. 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