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Cellular Automata Models on HIV Infection

Cellular Automata Models on HIV Infection. Shiwu Zhang Based on [Hershberg2001, Santos 2001]. Outline. Models on HIV dynamics ODE(Ordinary Differential Equation)model CA(Cellular Automata) model Santos’ CA model Hershberg’s model in “shape space” Our model Reference. ODE models.

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Cellular Automata Models on HIV Infection

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  1. Cellular Automata Models on HIV Infection Shiwu Zhang Based on [Hershberg2001, Santos 2001]

  2. Outline • Models on HIV dynamics • ODE(Ordinary Differential Equation)model • CA(Cellular Automata) model • Santos’ CA model • Hershberg’s model in “shape space” • Our model • Reference

  3. ODE models • Characteristics • Allow extensive mathematical analysis • Reduce low CPU workload • Ignore spatial structure • View elements homogeneous • Fail to account for large-scale emergence • Examples • Kirsher96, Kirsher97, Kirsher98 • Nowak96

  4. CA models • Characteristics • Local interactions • Elements diversity • Spatial structure • High workload • Examples • Santos2001 • Hershberg2001

  5. Stantos’ model in spatial space • Elements • 2-dimension lattice, immune cells with different state • Rules • healthy cells->A1 • A1->A2:  • A2->dead cells • Dead cells->healthy cells/A1 • Results • 3-stage disease development • Spatial aggregation

  6. Hershberg’s model in “shape space” • Elements • Shape space: random lattice, immune cells, HIV • Rules • Local: Immune cells meet HIV in same site • HIV is destroyed • Immune cells duplicate • Diffusion • HIV and Immune cells: jumping among sites

  7. Hershberg’s model (Continued) • Rules • Global: • HIV replicate () • Immune cells is destoryed • Immune cells creation • Results • 3-stage dynamics • HIV High mutation rate-> AIDS • Various latency periods

  8. Motivation • Method: Reasonable-> Convincing • Multi-type elements: T cells, B cells, HIV… • Spatial space& shape space • Accounting for important interactions • HIV high mutation rate • Immune cells stimulation • Immune system’s global ability • Result: • 3-stage dynamics of AIDS • HIV strain diversity • Mechanism influence

  9. Related Papers • 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 • Z.D. Santos et al. (2001). On the dynamics of the evolution of HIV infection. http://arxiv.org/abs/cond-mat/0008081 • Z.D. Santos et al. (2001). Dynamics of HIV infection: A cellular automata approach. PRL: 87(16). • X. Wei et al. Viral dynamics in human immunodeficiency virus type 1 infection. Nature: (373) 1995

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