Cellular Automata Models on HIV Infection

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Cellular Automata Models on HIV Infection

• Shiwu Zhang
• Based on Hershberg2001, Santos 2001

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Outline

• Models on HIV dynamics
• ODE(Ordinary Differential Equation)model
• CA(Cellular Automata) model
• Santos CA model
• Hershbergs model in shape space
• Our model
• Reference

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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

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CA models

• Characteristics
• Local interactions
• Elements diversity
• Spatial structure
• High workload
• Examples
• Santos2001
• Hershberg2001

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Stantos model in spatial space

• Elements
• 2-dimension lattice, immune cells with different
  state
• Rules
• healthy cells-gtA1
• A1-gtA2 ?
• A2-gtdead cells
• Dead cells-gthealthy cells/A1
• Results
• 3-stage disease development
• Spatial aggregation

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Hershbergs 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

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Hershbergs model (Continued)

• Rules
• Global
• HIV replicate ()
• Immune cells is destoryed
• Immune cells creation
• Results
• 3-stage dynamics
• HIV High mutation rate-gt AIDS
• Various latency periods

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Motivation

• Method Reasonable-gt 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 systems global ability
• Result
• 3-stage dynamics of AIDS
• HIV strain diversity
• Mechanism influence

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Related Papers

• U. Hershberg et al.(2001). HIV time hierarchy
  Winning the war while losing all the battles.
  Physica A289 (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/c
  ond-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