1 / 9

Cellular Automata Models in HIV Dynamics: A Comparative Study

Explore various cellular automata models based on ODEs for HIV infection dynamics, including Santos' CA model in spatial space and Hershberg's model in shape space. Learn the 3-stage disease development, spatial aggregation, and the impact of high mutation rates on AIDS progression. Discover how these models account for interactions among immune cells, HIV, and shape space elements.

meghang
Download Presentation

Cellular Automata Models in HIV Dynamics: A Comparative Study

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related