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