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PN & BioModel Engineering
[email protected] June 2020
PETRI NETS 2020, PARIS
EEEEFFFFFFFFIIIICCCCIIIIEEEENNNNTTTT U U U UNNNNFFFFOOOOLLLLDDDDIIIINNNNGGGG OOOOFFFF
CCCCOOOOLLLLOOOOUUUURRRREEEEDDDD P P P PEEEETTTTRRRRIIII N N N NEEEETTTTSSSS
WWWWIIIITTTTHHHH I I I INNNNTTTTEEEERRRRVVVVAAAALLLL D D D DEEEECCCCIIIISSSSIIIIOOOONNNN D D D DIIIIAAAAGGGGRRRRAAAAMMMMSSSS
SCHWARICK - ROHR - LIU - ASSAF - CHODAK - HEINER
BRANDENBURG TECHNICAL UNIVERSITY COTTBUS-SENFTENBERG
COMPUTER SCIENCE INSTITUTE
HTTPS.//WWW-DSSZ.INFORMATIK.TU-COTTBUS.DE
PN & BioModel Engineering
[email protected] June 2020
PETRI NETS 2020, PARIS
EEEEFFFFFFFFIIIICCCCIIIIEEEENNNNTTTT U U U UNNNNFFFFOOOOLLLLDDDDIIIINNNNGGGG OOOOFFFF
CCCCOOOOLLLLOOOOUUUURRRREEEEDDDD P P P PEEEETTTTRRRRIIII NNNNEEEETTTTSSSS
WWWWIIIITTTTHHHH I I I INNNNTTTTEEEERRRRVVVVAAAALLLL D D D DEEEECCCCIIIISSSSIIIIOOOONNNN D D D DIIIIAAAAGGGGRRRRAAAAMMMMSSSS
SCHWARICK - ROHR - LIU - ASSAF - CHODAK - HEINER
BRANDENBURG TECHNICAL UNIVERSITY COTTBUS-SENFTENBERG
COMPUTER SCIENCE INSTITUTE
PN & BioModel Engineering
[email protected] June 2020
CCCCOOOOLLLLOOOOUUUURRRREEEEDDDD P P P PEEEETTTTRRRRIIII NNNNEEEETTTTSSSS
WHAT FOR ?WHAT FOR ?WHAT FOR ?WHAT FOR ?
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC MODELLING WITH PETRI NETS
Infected
10
Susceptible
83,000 !
Recovered!
Infect Recover
2
THE SIR MODEL [ https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIR_model ]
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC MODELLING WITH PETRI NETS
Infected
10
Susceptible
83,000 !
Recovered!
Infect
MassAction(k_infect)
Recover
MassAction(k_recover)
2
THE SIR MODEL [ https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIR_model ]
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC MODELLING WITH PETRI NETS
THE SIR MODEL [ https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIR_model ]
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
Infected
10
Susceptible
83,000 !
Recovered!
Infect Recover
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
Infected
10
Susceptible
83,000 !
Recovered!
Infect Recover
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
Infected
10
Susceptible
83,000 !
Recovered
RecoveredSusceptible
65,000 !
Infected
10
Infect! Recover
RecoverInfect
2
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
Infected_DE
10
Susceptible_DE
83,000 !
Recovered_DE
Recovered_FRSusceptible_FR
65,000 !
Infected_FR
10
Infect_DE Recover_DE
Recover_FRInfect_FR
2
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
Infected_DE
10
Susceptible_DE
83,000 !
Recovered_DE
Recovered_FRSusceptible_FR
65,000 !
Infected_FR
10
Infect_DE Recover_DE
ConnectionI ConnectionR
Recover_FRInfect_FR
ConnectionS
2
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
node_AT
node_CH
node_DE
node_FR
node_IT
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
AT,CH,DE,FR,IT
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
node_AT
node_BE
node_CH
node_DE
node_DK
node_ES
node_FR
node_IT
node_NL
node_PT
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
WESTERNEUROPE
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
Infected_AD
Infected_AL
Infected_AT
100
Infected_BA
Infected_BE
Infected_BG
Infected_BY
Infected_CH
Infected_CY
Infected_CZ
Infected_DE
Infected_DK
Infected_EE
Infected_ES
Infected_FI
Infected_FR
Infected_GB
Infected_GR
Infected_HR
Infected_HU
Infected_IE
Infected_IS
Infected_IT
Infected_KL
Infected_LI
Infected_LT
Infected_LU
Infected_LV
Infected_MC
Infected_MD
Infected_ME
Infected_MK
Infected_MT
Infected_NI
Infected_NL
Infected_NO
Infected_PL
Infected_PT
Infected_RO
Infected_RS
Infected_RU
Infected_SE
Infected_SI
Infected_SK
Infected_SM
Infected_UA
Infected_VA
Infected_XK
Recovered_AD
Recovered_AL
Recovered_AT
Recovered_BA
Recovered_BE
Recovered_BG
Recovered_BY Recovered_CH
Recovered_CY
Recovered_CZ
Recovered_DE
Recovered_DK
Recovered_EE
Recovered_ES
Recovered_FI
Recovered_FRRecovered_GB
Recovered_GR
Recovered_HR
Recovered_HU
Recovered_IE
Recovered_IS
Recovered_IT
Recovered_KL
Recovered_LI
Recovered_LT
Recovered_LU
Recovered_LVRecovered_MC
Recovered_MD
Recovered_ME
Recovered_MK
Recovered_MT
Recovered_NI
Recovered_NL
Recovered_NO
Recovered_PL
Recovered_PT
Recovered_RO
Recovered_RS
Recovered_RU
Recovered_SE
Recovered_SI
Recovered_SK
Recovered_SM
Recovered_UA
Recovered_VA
Recovered_XK
Susceptible_AD
77
Susceptible_AL
2,878 !
Susceptible_AT
9,006 !
Susceptible_BA
3,281 !
Susceptible_BE
11,590 !
Susceptible_BG
6,948 !
Susceptible_BY
9,449 !
Susceptible_CH
8,655 !
Susceptible_CY
1,207 !
Susceptible_CZ
10,709 !
Susceptible_DE
83,784 !
Susceptible_DK
5,792 !
Susceptible_EE
1,327 !
Susceptible_ES
46,755 !
Susceptible_FI
5,541 !
Susceptible_FR
65,274!
Susceptible_GB
64,570 !
Susceptible_GR
10,423 !
Susceptible_HR
4,105 !
Susceptible_HU
9,660 !
Susceptible_IE
4,938 !
Susceptible_IS
341
Susceptible_IT
60,462 !
Susceptible_KL
437
Susceptible_LI
38
Susceptible_LT
2,722 !
Susceptible_LU
626
Susceptible_LV
1,886 !
Susceptible_MC
39Susceptible_MD
4,034 !
Susceptible_ME
628Susceptible_MK
2,083 !
Susceptible_MT
442
Susceptible_NI
1,882 !
Susceptible_NL
17,135 !
Susceptible_NO
5,421 !
Susceptible_PL
37,847 !
Susceptible_PT
10,197 !
Susceptible_RO
19,238 !
Susceptible_RS
8,737 !
Susceptible_RU
145,497 !!
Susceptible_SE
10,099 !
Susceptible_SI
2,079 !
Susceptible_SK
5,460 !
Susceptible_SM
34
Susceptible_UA
43,734 !
Susceptible_VA
Susceptible_XK
1,908 !
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
2
2
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
EUROPE
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
node_AH
node_BJ
node_CQ
node_FJ
node_GD
node_GS
node_GX
node_GZ
node_HA
node_HB
node_HE
node_HI
node_HK
node_HL
node_HN
node_JL
node_JS
node_JX
node_LN
node_MO
node_NM
node_NXnode_QH
node_SC
node_SD
node_SH
node_SNnode_SX node_TJ
node_TW
node_XJ
node_XZ
node_YN
node_ZJ
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
CHINA
PN & BioModel Engineering
[email protected] June 2020
EPIDEMIC -> PANDEMIC MODELLING
node_AK
node_AL
node_AR
node_AZ
node_CA
node_CO
node_CT
node_DC
node_DE
node_FL
node_GA
node_HI
node_IA
node_IDnode_IL
node_IN
node_KS
node_KY
node_LA
node_MA
node_MD
node_ME
node_MI
node_MN
node_MO
node_MS
node_MT
node_NC
node_ND
node_NE
node_NH
node_NJ
node_NM
node_NV
node_NY
node_OH
node_OK
node_OR
node_PA
node_PR
node_RI
node_SC
node_SD
node_TN
node_TX
node_US
node_UT
node_VA
node_VT
node_WA
node_WI
node_WV
node_WY
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
USA
PN & BioModel Engineering
[email protected] June 2020
AAAANNNNDDDD TTTTHHHHEEEENNNN TTTTHHHHEEEERRRREEEE WWWWAAAASSSS CCCCOOOOLLLLOOOOUUUURRRR
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
InfectedSusceptible Recovered
Infect Recover
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
Nodes
Susceptible
Nodes
Recovered
Nodes
Infect Recover
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
enum Nodes = {AT, CH, DE, FR, IT};colorsets:
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
Nodes
Susceptible
Nodes
Recovered
Nodes
Infect Recover
1`x
2`x 1`x 1`x1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
enum Nodes = {AT, CH, DE, FR, IT};variables:
Nodes : x;
colorsets:
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
100
100`ATNodes
Susceptible
314,000 !!
9000`AT++
8000`CH++
83000`DE++
65000`FR++
60000`IT++
Nodes
Recovered
Nodes
Infect Recover
1`x
2`x 1`x 1`x1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
enum Nodes = {AT, CH, DE, FR, IT};variables:
Nodes : x;
colorsets:
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
100
100`ATNodes
Susceptible
314,000 !!
9000`AT++
8000`CH++
83000`DE++
65000`FR++
60000`IT++
Nodes
Recovered
Nodes
Infect Recover
ConnectionIConnectionS ConnectionR
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
enum Nodes = {AT, CH, DE, FR, IT};variables:
Nodes : x; Nodes : y;
colorsets:
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
100
100`ATNodes
Susceptible
314,000 !!
9000`AT++
8000`CH++
83000`DE++
65000`FR++
60000`IT++
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
enum Nodes = {AT, CH, DE, FR, IT};variables:
Nodes : x; Nodes : y;
colorsets:
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
100
100`ATNodes
Susceptible
314,000 !!
9000`AT++
8000`CH++
83000`DE++
65000`FR++
60000`IT++
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
enum Nodes = {AT, CH, DE, FR, IT};colorsets:
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
100
100`ATNodes
Susceptible
314,000 !!
9000`AT++
8000`CH++
83000`DE++
65000`FR++
60000`IT++
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
Matrix = PROD (Nodes, Nodes); enum Nodes = {AT, CH, DE, FR, IT};
colorsets:
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
100
100`ATNodes
Susceptible
314,000 !!
9000`AT++
8000`CH++
83000`DE++
65000`FR++
60000`IT++
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
Matrix = PROD (Nodes, Nodes);Connections = Matrix [ (x=AT & (y=CH | y=DE | y=IT) |
enum Nodes = {AT, CH, DE, FR, IT};colorsets:
(x=CH & (y=AT | =E | y=FR | y=IT) | . . . ];
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
100
100`ATNodes
Susceptible
314,000 !!
9000`AT++
8000`CH++
83000`DE++
65000`FR++
60000`IT++
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
Matrix = PROD (Nodes, Nodes);Connections = Matrix [ (x=AT & (y=CH | y=DE | y=IT) |
enum Nodes = {AT, CH, DE, FR, IT};colorsets:
colorfunction:bool connected (Nodes p, Nodes q) { (p,q) elemOf Connections };
(x=CH & (y=AT | =E | y=FR | y=IT) | . . . ];
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected
100
100`ATNodes
Susceptible
314,000 !!
9000`AT++
8000`CH++
83000`DE++
65000`FR++
60000`IT++
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
AT,CH,DE,FR,IT
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected_AT
Infected_CH
Infected_DE
Infected_FR
Infected_IT
Recovered_AT
Recovered_CHRecovered_DE
Recovered_FR
Recovered_IT
Susceptible_AT
Susceptible_CH
Susceptible_DE
Susceptible_FR
Susceptible_IT
2
2
2
2
2
Infected
100
100`ATNodes
Susceptible
314,000 !!
9000`AT++
8000`CH++
83000`DE++
65000`FR++
60000`IT++
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
AT,CH,DE,FR,IT
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected_AT
100
Infected_BEInfected_CH
Infected_DE
Infected_DK
Infected_ES
Infected_FR
Infected_IT
Infected_NL
Infected_PT
Recovered_AT
Recovered_BE
Recovered_CH
Recovered_DE
Recovered_DK
Recovered_ES
Recovered_FR
Recovered_IT
Recovered_NL
Recovered_PT
Susceptible_AT
9,000 !
Susceptible_BE
11,000 !
Susceptible_CH
8,000 !
Susceptible_DE83,000 !
Susceptible_DK
5,000 !
Susceptible_ES
46,000 !
Susceptible_FR
65,000 !Susceptible_IT
60,000 !
Susceptible_NL
17,000 !
Susceptible_PT
10,000 !
2
22
2
2
2
2
2
2
2
Infected
Nodes
Susceptible
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
WESTERNEUROPE
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected_AD
Infected_AL
Infected_AT
100
Infected_BA
Infected_BE
Infected_BG
Infected_BY
Infected_CH
Infected_CY
Infected_CZ
Infected_DE
Infected_DK
Infected_EE
Infected_ES
Infected_FI
Infected_FR
Infected_GB
Infected_GR
Infected_HR
Infected_HU
Infected_IE
Infected_IS
Infected_IT
Infected_KL
Infected_LI
Infected_LT
Infected_LU
Infected_LV
Infected_MC
Infected_MD
Infected_ME
Infected_MK
Infected_MT
Infected_NI
Infected_NL
Infected_NO
Infected_PL
Infected_PT
Infected_RO
Infected_RS
Infected_RU
Infected_SE
Infected_SI
Infected_SK
Infected_SM
Infected_UA
Infected_VA
Infected_XK
Recovered_AD
Recovered_AL
Recovered_AT
Recovered_BA
Recovered_BE
Recovered_BG
Recovered_BY Recovered_CH
Recovered_CY
Recovered_CZ
Recovered_DE
Recovered_DK
Recovered_EE
Recovered_ES
Recovered_FI
Recovered_FRRecovered_GB
Recovered_GR
Recovered_HR
Recovered_HU
Recovered_IE
Recovered_IS
Recovered_IT
Recovered_KL
Recovered_LI
Recovered_LT
Recovered_LU
Recovered_LVRecovered_MC
Recovered_MD
Recovered_ME
Recovered_MK
Recovered_MT
Recovered_NI
Recovered_NL
Recovered_NO
Recovered_PL
Recovered_PT
Recovered_RO
Recovered_RS
Recovered_RU
Recovered_SE
Recovered_SI
Recovered_SK
Recovered_SM
Recovered_UA
Recovered_VA
Recovered_XK
Susceptible_AD
77
Susceptible_AL
2,878 !
Susceptible_AT
9,006 !
Susceptible_BA
3,281 !
Susceptible_BE
11,590 !
Susceptible_BG
6,948 !
Susceptible_BY
9,449 !
Susceptible_CH
8,655 !
Susceptible_CY
1,207 !
Susceptible_CZ
10,709 !
Susceptible_DE
83,784 !
Susceptible_DK
5,792 !
Susceptible_EE
1,327 !
Susceptible_ES
46,755!
Susceptible_FI
5,541 !
Susceptible_FR
65,274 !
Susceptible_GB
64,570 !
Susceptible_GR
10,423 !
Susceptible_HR
4,105 !
Susceptible_HU
9,660 !
Susceptible_IE
4,938 !
Susceptible_IS
341
Susceptible_IT
60,462 !
Susceptible_KL
437
Susceptible_LI
38
Susceptible_LT
2,722 !
Susceptible_LU
626
Susceptible_LV
1,886 !
Susceptible_MC
39Susceptible_MD
4,034 !
Susceptible_ME
628Susceptible_MK
2,083 !
Susceptible_MT
442
Susceptible_NI
1,882 !
Susceptible_NL
17,135 !
Susceptible_NO
5,421 !
Susceptible_PL
37,847 !
Susceptible_PT
10,197 !
Susceptible_RO
19,238 !
Susceptible_RS
8,737 !
Susceptible_RU
145,497 !!
Susceptible_SE
10,099 !
Susceptible_SI
2,079 !
Susceptible_SK
5,460 !
Susceptible_SM
34
Susceptible_UA
43,734 !
Susceptible_VA
Susceptible_XK
1,908 !
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
2
2
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
EUROPE
Infected
Nodes
Susceptible
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected_AD
Infected_AL
Infected_AT
100
Infected_BA
Infected_BE
Infected_BG
Infected_BY
Infected_CH
Infected_CY
Infected_CZ
Infected_DE
Infected_DK
Infected_EE
Infected_ES
Infected_FI
Infected_FR
Infected_GB
Infected_GR
Infected_HR
Infected_HU
Infected_IE
Infected_IS
Infected_IT
Infected_KL
Infected_LI
Infected_LT
Infected_LU
Infected_LV
Infected_MC
Infected_MD
Infected_ME
Infected_MK
Infected_MT
Infected_NI
Infected_NL
Infected_NO
Infected_PL
Infected_PT
Infected_RO
Infected_RS
Infected_RU
Infected_SE
Infected_SI
Infected_SK
Infected_SM
Infected_UA
Infected_VA
Infected_XK
Recovered_AD
Recovered_AL
Recovered_AT
Recovered_BA
Recovered_BE
Recovered_BG
Recovered_BY Recovered_CH
Recovered_CY
Recovered_CZ
Recovered_DE
Recovered_DK
Recovered_EE
Recovered_ES
Recovered_FI
Recovered_FRRecovered_GB
Recovered_GR
Recovered_HR
Recovered_HU
Recovered_IE
Recovered_IS
Recovered_IT
Recovered_KL
Recovered_LI
Recovered_LT
Recovered_LU
Recovered_LVRecovered_MC
Recovered_MD
Recovered_ME
Recovered_MK
Recovered_MT
Recovered_NI
Recovered_NL
Recovered_NO
Recovered_PL
Recovered_PT
Recovered_RO
Recovered_RS
Recovered_RU
Recovered_SE
Recovered_SI
Recovered_SK
Recovered_SM
Recovered_UA
Recovered_VA
Recovered_XK
Susceptible_AD
77
Susceptible_AL
2,878 !
Susceptible_AT
9,006 !
Susceptible_BA
3,281 !
Susceptible_BE
11,590 !
Susceptible_BG
6,948 !
Susceptible_BY
9,449 !
Susceptible_CH
8,655 !
Susceptible_CY
1,207 !
Susceptible_CZ
10,709 !
Susceptible_DE
83,784 !
Susceptible_DK
5,792 !
Susceptible_EE
1,327 !
Susceptible_ES
46,755!
Susceptible_FI
5,541 !
Susceptible_FR
65,274 !
Susceptible_GB
64,570 !
Susceptible_GR
10,423 !
Susceptible_HR
4,105 !
Susceptible_HU
9,660 !
Susceptible_IE
4,938 !
Susceptible_IS
341
Susceptible_IT
60,462 !
Susceptible_KL
437
Susceptible_LI
38
Susceptible_LT
2,722 !
Susceptible_LU
626
Susceptible_LV
1,886 !
Susceptible_MC
39Susceptible_MD
4,034 !
Susceptible_ME
628Susceptible_MK
2,083 !
Susceptible_MT
442
Susceptible_NI
1,882 !
Susceptible_NL
17,135 !
Susceptible_NO
5,421 !
Susceptible_PL
37,847 !
Susceptible_PT
10,197 !
Susceptible_RO
19,238 !
Susceptible_RS
8,737 !
Susceptible_RU
145,497 !!
Susceptible_SE
10,099 !
Susceptible_SI
2,079 !
Susceptible_SK
5,460 !
Susceptible_SM
34
Susceptible_UA
43,734 !
Susceptible_VA
Susceptible_XK
1,908 !
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
2
2
2
Infected_AH
Infected_BJ
Infected_CQ
Infected_FJ
Infected_GD
Infected_GS
Infected_GX
Infected_GZ
Infected_HA
Infected_HB
Infected_HE
Infected_HIInfected_HK
Infected_HL
Infected_HN
Infected_JL
Infected_JS
Infected_JX
Infected_LN
Infected_MO
Infected_NM
Infected_NX
Infected_QH
Infected_SC
Infected_SD
Infected_SH
Infected_SNInfected_SX
Infected_TJ
Infected_TW
Infected_XJ
Infected_XZ
Infected_YN
Infected_ZJ
Recovered_AH
Recovered_BJ
Recovered_CQ
Recovered_FJ
Recovered_GD
Recovered_GS
Recovered_GX
Recovered_GZ
Recovered_HA
Recovered_HB
Recovered_HE
Recovered_HIRecovered_HK
Recovered_HL
Recovered_HN
Recovered_JL
Recovered_JS
Recovered_JX
Recovered_LN
Recovered_MO
Recovered_NM
Recovered_NX
Recovered_QH
Recovered_SC
Recovered_SD
Recovered_SH
Recovered_SNRecovered_SX
Recovered_TJ
Recovered_TW
Recovered_XJ
Recovered_XZ
Recovered_YN
Recovered_ZJ
Susceptible_AH
63,240 !
Susceptible_BJ
21,540 !
Susceptible_CQ
31,020 !
Susceptible_FJ
39,410 !
Susceptible_GD
113,460 !!
Susceptible_GS
26,370 !
Susceptible_GX
49,260 !
Susceptible_GZ
36,000 !
Susceptible_HA
96,050 !
Susceptible_HB
59,170 !
Susceptible_HE
75,560 !
Susceptible_HI
9,340 !
Susceptible_HK
7,451 !
Susceptible_HL
37,730 !
Susceptible_HN
68,990 !
Susceptible_JL
27,040 !
Susceptible_JS
80,510 !
Susceptible_JX
46,480 !
Susceptible_LN
43,590 !
Susceptible_MO
631
Susceptible_NM
25,340 !
Susceptible_NX
6,880 !
Susceptible_QH
6,030 !
Susceptible_SC
83,410 !
Susceptible_SD
100,470 !!
Susceptible_SH
24,240 !
Susceptible_SN
38,640 !
Susceptible_SX
37,180 !
Susceptible_TJ
15,600 !
Susceptible_TW
23,780 !
Susceptible_XJ
24,870 !
Susceptible_XZ
3,440 !
Susceptible_YN
48,300 !
Susceptible_ZJ
57,370 !
2
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
CHINA
EUROPE
Infected
Nodes
Susceptible
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
PN & BioModel Engineering
[email protected] June 2020
PANDEMIC MODELLING WITH COLOURED NETS
Infected_AD
Infected_AL
Infected_AT
100
Infected_BA
Infected_BE
Infected_BG
Infected_BY
Infected_CH
Infected_CY
Infected_CZ
Infected_DE
Infected_DK
Infected_EE
Infected_ES
Infected_FI
Infected_FR
Infected_GB
Infected_GR
Infected_HR
Infected_HU
Infected_IE
Infected_IS
Infected_IT
Infected_KL
Infected_LI
Infected_LT
Infected_LU
Infected_LV
Infected_MC
Infected_MD
Infected_ME
Infected_MK
Infected_MT
Infected_NI
Infected_NL
Infected_NO
Infected_PL
Infected_PT
Infected_RO
Infected_RS
Infected_RU
Infected_SE
Infected_SI
Infected_SK
Infected_SM
Infected_UA
Infected_VA
Infected_XK
Recovered_AD
Recovered_AL
Recovered_AT
Recovered_BA
Recovered_BE
Recovered_BG
Recovered_BY Recovered_CH
Recovered_CY
Recovered_CZ
Recovered_DE
Recovered_DK
Recovered_EE
Recovered_ES
Recovered_FI
Recovered_FRRecovered_GB
Recovered_GR
Recovered_HR
Recovered_HU
Recovered_IE
Recovered_IS
Recovered_IT
Recovered_KL
Recovered_LI
Recovered_LT
Recovered_LU
Recovered_LVRecovered_MC
Recovered_MD
Recovered_ME
Recovered_MK
Recovered_MT
Recovered_NI
Recovered_NL
Recovered_NO
Recovered_PL
Recovered_PT
Recovered_RO
Recovered_RS
Recovered_RU
Recovered_SE
Recovered_SI
Recovered_SK
Recovered_SM
Recovered_UA
Recovered_VA
Recovered_XK
Susceptible_AD
77
Susceptible_AL
2,878 !
Susceptible_AT
9,006 !
Susceptible_BA
3,281 !
Susceptible_BE
11,590 !
Susceptible_BG
6,948 !
Susceptible_BY
9,449 !
Susceptible_CH
8,655 !
Susceptible_CY
1,207 !
Susceptible_CZ
10,709 !
Susceptible_DE
83,784 !
Susceptible_DK
5,792 !
Susceptible_EE
1,327 !
Susceptible_ES
46,755!
Susceptible_FI
5,541 !
Susceptible_FR
65,274 !
Susceptible_GB
64,570 !
Susceptible_GR
10,423 !
Susceptible_HR
4,105 !
Susceptible_HU
9,660 !
Susceptible_IE
4,938 !
Susceptible_IS
341
Susceptible_IT
60,462 !
Susceptible_KL
437
Susceptible_LI
38
Susceptible_LT
2,722 !
Susceptible_LU
626
Susceptible_LV
1,886 !
Susceptible_MC
39Susceptible_MD
4,034 !
Susceptible_ME
628Susceptible_MK
2,083 !
Susceptible_MT
442
Susceptible_NI
1,882 !
Susceptible_NL
17,135 !
Susceptible_NO
5,421 !
Susceptible_PL
37,847 !
Susceptible_PT
10,197 !
Susceptible_RO
19,238 !
Susceptible_RS
8,737 !
Susceptible_RU
145,497 !!
Susceptible_SE
10,099 !
Susceptible_SI
2,079 !
Susceptible_SK
5,460 !
Susceptible_SM
34
Susceptible_UA
43,734 !
Susceptible_VA
Susceptible_XK
1,908 !
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
2
2
2
Infected_AK
Infected_AL
Infected_AR
Infected_AZ
Infected_CA
Infected_CO
Infected_CT
Infected_DC
Infected_DE
Infected_FL
Infected_GA
Infected_HI
Infected_IA
Infected_ID
Infected_IL
Infected_IN
Infected_KS
Infected_KY
Infected_LA
Infected_MA
Infected_MD
Infected_ME
Infected_MI
Infected_MN
Infected_MO
Infected_MS
Infected_MT
Infected_NC
Infected_ND
Infected_NE
Infected_NH
Infected_NJ
Infected_NM
Infected_NV
Infected_NY
100
Infected_OH
Infected_OKInfected_OR
Infected_PA
Infected_PR
Infected_RI
Infected_SC
Infected_SD
Infected_TN
Infected_TX
Infected_US
Infected_UT
Infected_VA
Infected_VT
Infected_WA
Infected_WI
Infected_WV
Infected_WY
Recovered_AK
Recovered_AL
Recovered_AR
Recovered_AZ Recovered_CA
Recovered_CO
Recovered_CT
Recovered_DC
Recovered_DE
Recovered_FL
Recovered_GA
Recovered_HI
Recovered_IA
Recovered_ID
Recovered_IL
Recovered_IN
Recovered_KS
Recovered_KY
Recovered_LA
Recovered_MA
Recovered_MD
Recovered_ME
Recovered_MI
Recovered_MN
Recovered_MO
Recovered_MS
Recovered_MT
Recovered_NC
Recovered_ND
Recovered_NE
Recovered_NH
Recovered_NJ
Recovered_NM
Recovered_NV
Recovered_NY
Recovered_OH
Recovered_OK
Recovered_OR
Recovered_PA
Recovered_PR
Recovered_RI
Recovered_SC
Recovered_SD
Recovered_TN
Recovered_TX
Recovered_US
Recovered_UT
Recovered_VA
Recovered_VT
Recovered_WA
Recovered_WI
Recovered_WV
Recovered_WY
Susceptible_AK
731
Susceptible_AL
4,903 !
Susceptible_AR
3,017 !
Susceptible_AZ
7,278 !
Susceptible_CA
39,512 !
Susceptible_CO
5,758 !
Susceptible_CT
3,565 !
Susceptible_DC
705
Susceptible_DE
973
Susceptible_FL
21,477 !
Susceptible_GA
10,617 !
Susceptible_HI
1,415 !
Susceptible_IA
3,155 !
Susceptible_ID
1,787 !
Susceptible_IL
12,671 !
Susceptible_IN
6,732 !
Susceptible_KS
2,913 !
Susceptible_KY
4,467 !
Susceptible_LA
4,648 !
Susceptible_MA
6,949 !
Susceptible_MD
6,045 !
Susceptible_ME
1,344 !
Susceptible_MI
9,986 !
Susceptible_MN
5,639 !
Susceptible_MO
6,137 !
Susceptible_MS
2,976 !
Susceptible_MT
1,068 !
Susceptible_NC
10,488 !
Susceptible_ND
762
Susceptible_NE
1,934 !
Susceptible_NH
1,359 !
Susceptible_NJ
8,882 !
Susceptible_NM
2,096 !Susceptible_NV
3,080 !
Susceptible_NY
19,453 !
Susceptible_OH
11,689 !
Susceptible_OK
3,956 !
Susceptible_OR
4,217 !
Susceptible_PA
12,801 !
Susceptible_PR
3,193 !
Susceptible_RI
1,059 !
Susceptible_SC
5,148 !
Susceptible_SD
884
Susceptible_TN
6,833 !
Susceptible_TX
28,995 !
Susceptible_US
104
Susceptible_UT
3,205 !
Susceptible_VA
8,535 !
Susceptible_VT
623
Susceptible_WA
7,614 !
Susceptible_WI
5,822 !
Susceptible_WV
1,792 !
Susceptible_WY
578
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
Infected_AH
Infected_BJ
Infected_CQ
Infected_FJ
Infected_GD
Infected_GS
Infected_GX
Infected_GZ
Infected_HA
Infected_HB
Infected_HE
Infected_HIInfected_HK
Infected_HL
Infected_HN
Infected_JL
Infected_JS
Infected_JX
Infected_LN
Infected_MO
Infected_NM
Infected_NX
Infected_QH
Infected_SC
Infected_SD
Infected_SH
Infected_SNInfected_SX
Infected_TJ
Infected_TW
Infected_XJ
Infected_XZ
Infected_YN
Infected_ZJ
Recovered_AH
Recovered_BJ
Recovered_CQ
Recovered_FJ
Recovered_GD
Recovered_GS
Recovered_GX
Recovered_GZ
Recovered_HA
Recovered_HB
Recovered_HE
Recovered_HIRecovered_HK
Recovered_HL
Recovered_HN
Recovered_JL
Recovered_JS
Recovered_JX
Recovered_LN
Recovered_MO
Recovered_NM
Recovered_NX
Recovered_QH
Recovered_SC
Recovered_SD
Recovered_SH
Recovered_SNRecovered_SX
Recovered_TJ
Recovered_TW
Recovered_XJ
Recovered_XZ
Recovered_YN
Recovered_ZJ
Susceptible_AH
63,240 !
Susceptible_BJ
21,540 !
Susceptible_CQ
31,020 !
Susceptible_FJ
39,410 !
Susceptible_GD
113,460 !!
Susceptible_GS
26,370 !
Susceptible_GX
49,260 !
Susceptible_GZ
36,000 !
Susceptible_HA
96,050 !
Susceptible_HB
59,170 !
Susceptible_HE
75,560 !
Susceptible_HI
9,340 !
Susceptible_HK
7,451 !
Susceptible_HL
37,730 !
Susceptible_HN
68,990 !
Susceptible_JL
27,040 !
Susceptible_JS
80,510 !
Susceptible_JX
46,480 !
Susceptible_LN
43,590 !
Susceptible_MO
631
Susceptible_NM
25,340 !
Susceptible_NX
6,880 !
Susceptible_QH
6,030 !
Susceptible_SC
83,410 !
Susceptible_SD
100,470 !!
Susceptible_SH
24,240 !
Susceptible_SN
38,640 !
Susceptible_SX
37,180 !
Susceptible_TJ
15,600 !
Susceptible_TW
23,780 !
Susceptible_XJ
24,870 !
Susceptible_XZ
3,440 !
Susceptible_YN
48,300 !
Susceptible_ZJ
57,370 !
2
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
2
2
2
2
2
2
2
22
2
2
2
2
2
2
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
CHINA
EUROPE
Infected
Nodes
Susceptible
Nodes
Recovered
Nodes
Infect Recover
ConnectionI
[connected(x,y)]
ConnectionS
[connected(x,y)]
ConnectionR
[connected(x,y)]
x
y
1`x
2`x 1`x
xy
1`x
x
y
1`x
USA
PN & BioModel Engineering
[email protected] June 2020
WWWWHHHHAAAATTTT NNNNEEEEEEEEDDDDSSSS TTTTOOOO BBBBEEEE CCCCHHHHAAAANNNNGGGGEEEEDDDD::::
CCCCOOOOLLLLOOOOUUUURRRR SSSSEEEETTTTSSSS + + + + IIIINNNNIIIITTTTIIIIAAAALLLL MMMMAAAARRRRKKKKIIIINNNNGGGG
PN & BioModel Engineering
[email protected] June 2020
SIMULATING AND ANALYSING PANDEMIC MODELS
JOINT WORK WITH DAVID GILBERT, SHANNON CONNOLLY, BRUNEL UNIVERSITY, LONDON
PN & BioModel Engineering
[email protected] June 2020
HHHHOOOOWWWW TTTTOOOO UUUUNNNNFFFFOOOOLLLLDDDD EEEEFFFFFFFFIIIICCCCIIIIEEEENNNNTTTTLLLLYYYY ? ? ? ?
PN & BioModel Engineering
[email protected] June 2020
HHHHOOOOWWWW TTTTOOOO UUUUNNNNFFFFOOOOLLLLDDDD EEEEFFFFFFFFIIIICCCCIIIIEEEENNNNTTTTLLLLYYYY ? ? ? ?
PN & BioModel Engineering
[email protected] June 2020
HHHHOOOOWWWW TTTTOOOO UUUUNNNNFFFFOOOOLLLLDDDD EEEEFFFFFFFFIIIICCCCIIIIEEEENNNNTTTTLLLLYYYY ? ? ? ?
WWWWWWWWWWWW----DDDDSSSSSSSSZZZZ....IIIINNNNFFFFOOOORRRRMMMMAAAATTTTIIIIKKKK....TTTTUUUU----CCCCOOOOTTTTTTTTBBBBUUUUSSSS....DDDDEEEE
SSSSNNNNOOOOOOOOPPPPYYYY
MMMMAAAARRRRCCCCIIIIEEEE
SSSSPPPPIIIIKKKKEEEE
