Influence models model how users influence each other in a network.
Nodes are in two status:
==Inactive==:the nodes do not receive the information
==Active==:the nodes have received the information and can spread it to their neighbors
Independent Cascade (IC) 独立级联模型
Nodes activated at time t,have a single chance,at time step t+1,to activate their neighbors
Assume v is activated at time t,for any neighbor w of u,there is a probability p(vw) that node w gets activated at time t+1
IC Model:Algorithm
IC Model:Example
Linear Threshold (LT) 线性阈值模型
At each time step，the active nodes can influence the inactive nodes
Each node has an ==activation threshold==
An inactive node becomes active if the sum of influence degrees ==exceeds== its threshold
LT Model:Algorithm
LT Model:Example
Infection Models （感染性模型/病毒模型）
Infection Models, also called epidemic models, are
used to describe the transmission of communicable
==disease== through individuals
Nodes are in three status:
==Susceptible==:a susceptible node can potentially get
infected by the disease
==Infected==: an infected node has the chance of infecting
susceptible neighbors.
==Recovered==: These are nodes who have recovered from
the disease and hence have complete or partial ==immunity== against the infection.
Susceptible-Infected (SI)
Two status of nodes：
Susceptible（S）
Infected（I）
How to infect
- Once a node is infected，it stays infected forever.
- At each discrete time step，each infected node tries to infect its susceptible（uninfected）neighbors independently with probability p.
SI Model:notations
N:size of the crowd，N=S(t)+I(t)
S(t)：number of susceptible ones at time t
I(t)：number of infected ones at time t
SI Model:Example
Susceptible-Infecte-Recovered (SIR)
Intuition:Some infected nodes may recover，and the recovered ones can no longer get infected and are no longer susceptible.
Three status of nodes:Susceptible（S），Infected（T），Recovered（R）
The infection status of a node changes
β defines the probability of a success infection
γ defines the recovering probability of an infected individual
SIR Model:Example
Susceptible-Infected-Susceptible (SIS)
Intuition:the infected nodes may recover，and the recovered nodes would become susceptible again
Two status of nodes:Susceptible（S），Infected（I）
The infection status of a node changes
β defines the probability of a success infection
γ defines the recovering probability of an infected individual
SIS Model:Example
Susceptible-Infected-Recovered-Susceptible (SIRS)
Intuition:the individuals who have recovered will lose immunity after a certain period of time and will become susceptible again.
The infection status of a node changes
β defines the probability of a success infection
γ defines the recovering probability of an infected individual
λ defines the probability of losing immunity for a recovered node
