网络传播动力学

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SIS model on correlated SF networks
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SIS model on correlated SF networks
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http://vlab.infotech.monash.edu.au/simulations/networks/virus-outbreak/demo/
Fully Mixed
Complex Networks
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SIS model on ER networks
SIS Model on ER Networks
effective infection rate：

Mean Field reaction equation for the density of infected nodes:
Select a node with probability proportional to
ka and immunize a random acquaintance of this node.
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Strategy III
Select a random node and immunize one of
to ka, where k is the number of connections
and tunes the probability of preferentially
selecting high-connectivity or low-connectivity
nodes.
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Strategy II
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Uniform Immunization
In homogeneous networks,
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Uniform Immunization
In SF networks,
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Targeted Immunization
In SF networks,
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Strategy I
Immunize a node with probability proportional
For the steady state solution:
Epidemic threshold:
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SIS model on ER networks
10
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SIS model on BA networks
Mean Field reaction equation for the density of infected nodes: ER BA Then for the steady state:
its acquaintances i, with probability kia proportional to ki , where ki represents the degree of the neighbor.
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Strategy IV
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di (t ) i (t ) s (t ) i (t ) dt ds (t ) i (t ) s (t ) dt dr (t ) i (t ) dt i (t ) s (t ) r (t ) 1
疾病扩散条件：
1
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Epidemic Dynamics on Complex Networks
Y Axis Title
1.0
0.8
0.8
Y Axis Title
0.6
0.6
0.4
0.4
0.2
0.2
0.0 0 2 4 6 8 10
0.0 0 2 4 6 8 10
5
X Axis Title
X Axis Title
SIR Model
6
SIR Model （susceptible-infected-refractory）
i (t )
x 10 3.5 3 2.5 2 1.5 1 0.5 0 0 100 200 300 400 500 600
di(t)/dt
0.8
1 1 (1/ i0 1)e t
1.0
5
0.6
0.4
0.2
0.0 0 2 4 6 8
10
3
Time
SIS Model
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SIS Model（susceptible-infected-susceptible）
di (t ) i (t ) s (t ) i (t ) dt ds (t ) i (t ) s (t ) dt i (t ) s (t ) 1
1.0
effective infection rate：
1
i ( ) 0
1
i() 1 1/
复杂网络传播动力学
吴 俊 国防科大信息系统与管理学院管理系
1
ห้องสมุดไป่ตู้
Spreading Dynamics on Complex Networks
Disease
Computer virus Rumor ……
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SI Model （susceptible-infected）
di (t ) i (t )(1 i (t )) dt i (t ) s (t ) 1
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SIS model on BA networks
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SIS model on BA networks
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SIS model on uncorrelated SF networks
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SIS model on correlated SF networks
Connectivity matrix C