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The AVI+ model is an extended model of the AVI model, which is a general artifical soceity model for studying social propagation issues, e.g.,the spread of an infectious disease or information diffusion in the society.The core concepts of AVI model include Agent, Virus and Interaction. Besides three core concepts of AVI model, this extended AVI+ model includes other concepts: Role, Rule and Environment (Social environment and Physical environment). Due to introducing more concepts, this AVI+ model can be widely applied.

In the case, we will study the infectious H1N1 virus propagation with the AVI+ model. Meanwhile, the social network conforms to the JGN network, which is a growing and dynamic social network. This social network is based on some rules or assumptions: (1) each agent has a same limit number of social relationships, i.e., every node has the limited degree in the social network. (2) If two agents have connected with a same agent, these two agents possibly connect with each other. Meanwhile, the SEIR epidemiologic differential model is used to describe the spread of the infectious H1N1 virus. Considering the SEIR model, we could use the concept of role and the mechanism of dynamically playing roles to describe the states of the models. We have defined four roles: susceptible, exposed, infected and recovered, and agents can dynamically play these roles according to different situations. If an agent is not infected by the virus, this agent will play susceptible role. When a susceptible agent interacts with an infected agent to be infected to carry the H1N1 virus but cannot infect other agents, this agent will quit the susceptible role to play the exposed role. If an exposed agent can infect other agents, then this agent will quit the exposed role to play the infected role. If an infected agent is recovered to be health and does not carry the infectious H1N1 virus, then this agent will access to immunization and play the recovered role. We have defined several parameters for the social network and the spread of the H1N1 virus.


Each tick, agents can interact with another agent who has social relationship with it. The infected agents also may interact with others, and they can infect the susceptible agents to carry the H1N1 virus.

If an infected agent interacts with an susceptible agent, the susceptible agent will play exposed role with the probability of "exposed-chance", which can be ajusted by users with the slider "exposed-chance". Each tick, an exposed agent may quit the exposed role to play infected role with the probability of "virus-spread-chance", which can also be adjusted by the slider "virus-spread-chance". If an infected is carried the H1N1 virus for "virus-check-frequency" ticks, it will participate the virus check and it may recover to play the recovered role with the probability of "recovery-chance". Meanwhile, this value of the probability can be adjusted by users with the slider "recovery-chance".

Let N is the nodes number of JGN social network, the upper limit links number (np) of this social network is N(N-1)/2, and existed links number is n_e=1/2∑zi (zi is the degree of node i ). The neighboured links number is n_m=1/2∑(zi-1)zi, and r = r0+r1m (m is the pair number of nodes which links with one another) is the speed of nodes link with others. And z* is the upper limit links number of each node. Rules of JGN social network is as follows.
In each tick, randomly choose np r0 pairs of nodes to link with one another. If the chose nodes have not connected with each other and both current links number of two nodes is less than z*, then connect these two nodes.

In each step, proportionate to zi(zi-1) randomly choose nmr1 nodes. For each node, randomly choose a pair of nodes from its neighbour nodes. If the pair of nodes have not connected with each other and links upper number of each node is less than z*, then connect this pair of nodes.

In each step, proportionate to zi randomly choose n_e* R nodes (R is a constant), and randomly choose one neighbour nodes of each these nodes to cancel the link between these two nodes.

The values of parameters N, z*, r0, r1 and R can be adjusted by users with the sliders "number-of-agents", "Z*", "r0", "r1" and "R", respectively.


This section could explain how to use the model, including a description of each of the items in the interface tab.
Press the button "setup" to setup agents, social network and environment.
Press the button "Go" to run the procedure.
The slider "simulation-num" controls the simulation time. When the ticks reached the simulation time, the procedure will stop.
Users can press button "virus-initialization" to initialize the infected agents in the society.
Before press the button "virus-initialization", users should input a number in the box "initial-outbreak-size", and the number should be bigger than 0 and smaller than "number-of-agents".
THe sliders "r0", "r1", "z*", "number-of-agents", "R", "virus-spread-chance", "exposed-chance", "recovery-chance", and "virus-check-frequency" are discussed in “How it Works” above. All these values can be adjusted before press the button "Go".


Before press the button "setup", users should set values for all the sliders and the input box. Usually, users should press button "virus-initialization" after the average degree of the social network is bigger than z*.


Thie model is an extended model of the AVI model. The AVI model can be referenced by the URL:

The references about JGN social network:
1. M. J. Emily, G. Michelle, and M. E. J. Newman, Structure of growing social networks. Physical review E. 64, 046132, 2001.
2. M. E. J. Newman. Properties of highly clustered networks. Physical review E. 68, 026121, 2003.

## Copyright
© College of Computer, National University of Defense Technology.
@ Author: Mingsheng TANG,

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