Team # 44173 Page 5 of 22
• Hot transmission nodes contact with other nodes with the contact rate x1,while ordinary
nodes with the contact rate λ
2
.
• After nodes in state s received the information from nodes in state i,they change into
recovered nodes in a probability of µ,and into ordinary infected nodes in a probability of
1 − µ.
• With the propagation of information,the proportion of three types of nodes will tend to
be stable.
The schematic diagram of information dissemination of social networks with hot transmis-
sion nodes as shown in Figure 1, the solid line shows the information transmission between
two points.
Figure 1: the Information Transmission of Atrioventricular Model Structure Diagrams
Figure 2: the Improved SIR Model
3.1.2 Model Building
According to the characteristics of the transmission above,we can get the information transmis-
sion of atrioventricular model structure diagrams, as shown in Figure 1.
i
0
is the proportion of hot transmission nodes in networks,which is usually fixed.i(t) is the
proportion of ordinary infected nodes in the time of t,which consists of i
1
(t),the ordinary in-
fected nodes generated by hot transmission nodes,and i
2
(t),the ordinary nodes infected nodes
generated by ordinary infected nodes.λ
1
is the contact rate of hot transmission nodes,while λ
2
is the contact rate of ordinary infected nodes.r(t) is the proportion of nodes in state r,µ is the
rate of Immune probability.[3] We can get the model as follows:
ds(t)
dt
= −λ
1
i
0
s(t) − λ
2
s(t)i(t)
di(t)
dt
= µ[λ
1
i
0
s(t) + λ
2
s(t)i(t)]
dr(t)
dt
= (1 − µ)[λ
1
i
0
s(t) + λ
2
s(t)i(t)]
s(t) + i(t) + i
0
+ r(t) = 1
i
0
= i
10
, i(0) = i
20
, s(0) = s
0
, r(0) = r
0
(1)
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