A Cellular Automata Model on HIV Infection (2)

Shiwu Zhang

Based on [Pandey et al’s work]

Review: CA models on HIV(1)

• Characteristics– Local interactions

– Inhomogeneous elements

– Spatial structure

– High workload

• Examples– Santos2001

– Hershberg2001

Review: CA models on HIV(1)

– Santos’ CA model• One type cell with 4 different states on one site

• No mutation

• 3-stage evolution: different time scale

– Hershberg’s model in “shape space”• Virtual space, 2 types of cells

• Mutation

• 3-stage evolution: different time scale

Pandey’s model: Introduction(1)

• Elements– 2-dimension or 3-dimension lattice, – Four types of entities:

• Macrophage(M)• Helper(H)• Cytotoxic cells(C)• Antigen/Viral carrier cells(V)

– Entity States: • 0: low concentration • 1: high concentration

Pandey’s model: Introduction(2)• Rules

– Boolean expression(4)

– viral mutation(10)

– Fuzzy set

– CA sum rules

Pandey’s model: Result

• Populations of Cells and virus– Initial immune response

• Influence factors:– Viral mutation rate– Initial concentrations of cells– Cellular mobility

Comparison: our model• 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:memory

• Result:– 3-stage dynamics of AIDS

– HIV strain diversity

– Mechanism influence

Related Papers• R.B. Pandey. (1998). A stochastic cellular automata approach to

cellular dynamics for HIV: effect of viral mutation. Theory in Bioscience: 117(32)

• H. Mannion et al. (2000). Effect of Mutation on Helper T-cells and Viral Population: A Computer Simulation Model for HIV. Theory in Bioscience: 119(10)

• H. Mannion et al. (2000). A Monte Carlo Approach to Population Dynamics of Cell in an HIV Immune Response Model. Theory in Bioscience: 119(94)

• A. Mielke and R.B. Pandey. (1998). A computer simulation study of cell population in a fuzzy interaction model for mutating HIV. Physica A:251 (430).

• R.B. Pandey et al. (2000). Effect of Cellular Mobility on Immune Response. Physica A:283 (447).