Susceptible Infectious Epidemic Spreading ODE System (Q3813): Difference between revisions

Latest revision as of 15:57, 4 December 2024

formulations describing the spreading in a susceptible infectious epidemic model on a network with time-dependent spreading rate

Language	Label	Description	Also known as
English	Susceptible Infectious Epidemic Spreading ODE System	formulations describing the spreading in a susceptible infectious epidemic model on a network with time-dependent spreading rate

Statements

instance of

mathematical expression

0 references

defining formula

{\begin{aligned}{\frac {ds_{m}(t)}{dt}}&=-s_{m}(t)*\alpha (t)\sum _{n=1}^{N_{R}}G_{m,n}*i_{n}(t)\\i_{m}(t)&=P_{m}-s_{m}(t)\end{aligned}}

0 references

in defining formula

t

symbol represents

time

0 references

N_{R}

symbol represents

Number of Regions

0 references

i

symbol represents

Number Of Infected Cities

0 references

s

symbol represents

Susceptible Cities

0 references

P

symbol represents

Number of Cities

0 references

G

symbol represents

Contact Network

0 references

\alpha (t)

symbol represents

Spreading Rate (Time-dependent)

0 references

m

symbol represents

Region

0 references

n

0 references

0 references

Conservation of City Numbers

object has role

mathematical expression

0 references

Susceptible Cities ODE

object has role

mathematical expression

0 references

@@ Property / instance of / Property / instance of @@
-mathematical formulation
+mathematical expression
@@ Property / defining formula @@
+ ${\begin{aligned}{\frac {ds_{m}(t)}{dt}}&=-s_{m}(t)*\alpha (t)\sum _{n=1}^{N_{R}}G_{m,n}*i_{n}(t)\\i_{m}(t)&=P_{m}-s_{m}(t)\end{aligned}}$ 
\begin{align} \frac{ds_m(t)}{dt} &= -s_m(t) * \alpha(t) \sum_{n=1}^{N_R} G_{m,n} * i_n(t) \\ i_m(t) &= P_m - s_m(t) \end{align}
+Normal rank
@@ Property / in defining formula @@
+ $t$ 
t
@@ Property / in defining formula: $t$ / rank @@
+Normal rank
@@ Property / in defining formula: $t$ / qualifier @@
+symbol represents: time
@@ Property / in defining formula @@
+ $N_{R}$ 
N_R
@@ Property / in defining formula: $N_{R}$ / rank @@
+Normal rank
@@ Property / in defining formula: $N_{R}$ / qualifier @@
+symbol represents: Number of Regions
@@ Property / in defining formula @@
+ $i$ 
i
@@ Property / in defining formula: $i$ / rank @@
+Normal rank
@@ Property / in defining formula: $i$ / qualifier @@
+symbol represents: Number Of Infected Cities
@@ Property / in defining formula @@
+ $s$ 
s
@@ Property / in defining formula: $s$ / rank @@
+Normal rank
@@ Property / in defining formula: $s$ / qualifier @@
+symbol represents: Susceptible Cities
@@ Property / in defining formula @@
+ $P$ 
P
@@ Property / in defining formula: $P$ / rank @@
+Normal rank
@@ Property / in defining formula: $P$ / qualifier @@
+symbol represents: Number of Cities
@@ Property / in defining formula @@
+ $G$ 
G
@@ Property / in defining formula: $G$ / rank @@
+Normal rank
@@ Property / in defining formula: $G$ / qualifier @@
+symbol represents: Contact Network
@@ Property / in defining formula @@
+ $\alpha (t)$ 
\alpha(t)
@@ Property / in defining formula: $\alpha (t)$ / rank @@
+Normal rank
@@ Property / in defining formula: $\alpha (t)$ / qualifier @@
+symbol represents: Spreading Rate (Time-dependent)
@@ Property / in defining formula @@
+ $m$ 
m
@@ Property / in defining formula: $m$ / rank @@
+Normal rank
@@ Property / in defining formula: $m$ / qualifier @@
+symbol represents: Region
@@ Property / in defining formula @@
+ $n$ 
n
@@ Property / in defining formula: $n$ / rank @@
+Normal rank
@@ Property / in defining formula: $n$ / qualifier @@
+symbol represents: Region
@@ Property / community @@
+MathModDB
@@ Property / community: MathModDB / rank @@
+Normal rank
@@ Property / contains @@
+Conservation of City Numbers
@@ Property / contains: Conservation of City Numbers / rank @@
+Normal rank
@@ Property / contains: Conservation of City Numbers / qualifier @@
+object has role: mathematical expression
@@ Property / contains @@
+Susceptible Cities ODE
@@ Property / contains: Susceptible Cities ODE / rank @@
+Normal rank
@@ Property / contains: Susceptible Cities ODE / qualifier @@
+object has role: mathematical expression

Susceptible Infectious Epidemic Spreading ODE System (Q3813): Difference between revisions

${\begin{aligned}{\frac {ds_{m}(t)}{dt}}&=-s_{m}(t)\alpha (t)\sum _{n=1}^{N_{R}}G_{m,n}i_{n}(t)\\i_{m}(t)&=P_{m}-s_{m}(t)\end{aligned}}$

$t$

$N_{R}$

$i$

$s$

$P$

$G$

$\alpha (t)$

$m$

$n$

Latest revision as of 15:57, 4 December 2024

Statements

Sitelinks

mathematics(0 entries)

Susceptible Infectious Epidemic Spreading ODE System (Q3813): Difference between revisions

d s m ( t ) d t = − s m ( t ) ∗ α ( t ) ∑ n = 1 N R G m , n ∗ i n ( t ) i m ( t ) = P m − s m ( t ) {\displaystyle {\begin{aligned}{\frac {ds_{m}(t)}{dt}}&=-s_{m}(t)*\alpha (t)\sum _{n=1}^{N_{R}}G_{m,n}*i_{n}(t)\\i_{m}(t)&=P_{m}-s_{m}(t)\end{aligned}}}

t {\displaystyle t}

N R {\displaystyle N_{R}}

i {\displaystyle i}

s {\displaystyle s}

P {\displaystyle P}

G {\displaystyle G}

α ( t ) {\displaystyle \alpha (t)}

m {\displaystyle m}

n {\displaystyle n}

Latest revision as of 15:57, 4 December 2024

Statements

Sitelinks

mathematics(0 entries)

${\begin{aligned}{\frac {ds_{m}(t)}{dt}}&=-s_{m}(t)\alpha (t)\sum _{n=1}^{N_{R}}G_{m,n}i_{n}(t)\\i_{m}(t)&=P_{m}-s_{m}(t)\end{aligned}}$

$t$

$N_{R}$

$i$

$s$

$P$

$G$

$\alpha (t)$

$m$

$n$