Epidemic process over commute network in Tokyo metropolitan area

E id i P

Epidemic Process o Epidemic Process o p

T k M Tokyo M Tokyo M y

K t Y hi (M iji I tit t f Ad

Kenta Yashima (Meiji Institute for Adva Kenta Yashima (Meiji Institute for Adva Aki S ki (D t t f E l ti

Akira Sasaki (Department of Evolutionar ( p

St di H J

Studies, Hayama, Japan , y , p

Introduction Introduction

We analyze the epidemiological dynamics of an infectious disease spre We analyze the epidemiological dynamics of an infectious disease spre We assume that each person commutes from home to work and back We assume that each person commutes from home to work and back

C f th J Mi i t f L d I f t t d T

Census of the Japanese Ministry of Land, Infrastructure, and Transporp y , , p e tensi e indi id al based sim lations e ha e de eloped a random extensive individual-based simulations, we have developed a random- populations only to the extent captured by the empirically observed ave populations only to the extent captured by the empirically observed ave classes

classes.

A B

C t

Commute ne Commute ne

A

Map of Tokyo m

Map of Tokyo m the central part we the central part we

i i d t

incoming and outg g g Bl e the stations a Blue: the stations a homes) red: the s homes), red: the s

C D

Geographical distr Geographical distr

The distribution

The distribution emerging infectiou emerging infectiou i f t d h t

infected host comm station)

station). )

E id i

Epidemics o Epidemics o

A standard Suscep A standard Suscep dynamics through d dynamics through d

h l f

home place of comp over the whole syst over the whole syst of Tokyo metropolit of Tokyo metropolit an initially infected an initially infected The analytical resu The analytical resu

i d

process in random p

place stations obse place stations obse

P l f fi t i i ti

Power law for first-arriving time Power law for first arriving time

A ti

(d ) til i f ti di i

Average time t g (days) until an infectious disease arrives ( y ) at each home (A) and work population (B) plotted as a at each home (A) and work population (B), plotted as a function of the size

of local populations Both

function of the size N of local populations. Both approximately obey power law:

~

approximately obey power law: t N

Reference: Yashima K and Sasaki A in press Reference: Yashima K and Sasaki A, in press

Conclusion Conclusion

We find that when an initially infected person is randomly chosen amo We find that, when an initially infected person is randomly chosen amo mostly on the population sizes at that person’s home and work but no mostly on the population sizes at that person s home and work, but no epidemic outbreak in a local population is mostly determined by the siz epidemic outbreak in a local population is mostly determined by the siz di t f th i iti ll i f t d l ti f h b t ti W

distance from the initially infected population or from hub stations. We y p p local population is well predicted by a simple power law: it geometrical local population is well predicted by a simple power law: it geometrical

th C t N t k i

over the Commute Network in over the Commute Network in M t lit A

Metropolitan Area Metropolitan Area p

d St d f M th ti l S i K ki J )

anced Study of Mathematical Sciences, Kawasaki, Japan) anced Study of Mathematical Sciences, Kawasaki, Japan)

St di f Bi t G d t U i it f Ad d

ry Studies of Biosystems, Graduate University for Advanced y y , y

E l ti d E l P IIASA)

n; Evolution and Ecology Program, IIASA) ; gy g , )

eading across the commuter network of the Tokyo metropolitan area eading across the commuter network of the Tokyo metropolitan area.

by trains connecting local populations The Urban Transportation by trains connecting local populations. The Urban Transportation

t i d t i l t th t f t I dditi t

rt is used to simulate the movements of commuters. In addition to net ork model that retains the connecti it str ct re among local network model that retains the connectivity structure among local erage connectedness of local populations according to their size erage connectedness of local populations according to their size

t k f T k t lit

etwork of Tokyo metropolitan area etwork of Tokyo metropolitan area

etropolitan area in Kanto region Japan Framed rectangle shows etropolitan area in Kanto region, Japan. Framed rectangle shows

e show in C and D.

Distribution for the station size, the numbers of e show in C and D. B Distribution for the station size, the numbers of

i f il t ti i th T k t lit

going passengers of railway stations, in the Tokyo metropolitan area.

g g p g y , y p

as "home node" (those stations the passengers take from their as "home-node" (those stations the passengers take from their ( g

tations as "work node" (those taken from their workplaces)

tations as work-node (those taken from their workplaces). C

ribution of station sizes in the central part of Tokyo metropolitan area ribution of station sizes in the central part of Tokyo metropolitan area.

for the number of infected hosts 15 days after the introduction of an for the number of infected hosts 15 days after the introduction of an us disease (a Monte Carlo simulation run, in which an initially

us disease (a Monte Carlo simulation run, in which an initially t d b t "T hi " t ti d "H h "

muted between "Tsunashima" station and "Hongo-sanchoume" g

t t k Gl b l id i

n commute network: Global epidemics n commute network: Global epidemics

tible-Infected-Recovered (SIR) model is assumed for epidemic tible-Infected-Recovered (SIR) model is assumed for epidemic daytime transmission at work place and nighttime transmission at daytime transmission at work place and nighttime transmission at

t A Th b bilit f l b l id i ( id i di

mmuters. A The probability of global epidemic (epidemic spreading p y g p ( p p g

tem) PG observed in the IBM simulations for the commute network tem), PG, observed in the IBM simulations for the commute network

an area PG is plotted as a function of the size of home population of an area. PG is plotted as a function of the size of home population of

host (horizontal axis) and that of work population (vertical axis) B host (horizontal axis) and that of work population (vertical axis). B lts for the probability of global epidemic obtained by using branching lts for the probability of global epidemic obtained by using branching

ti t k t i i th i l ti f h d k

reconnection network retaining the size correlation of home and work g erved in Tokyo metropolitan commute data

erved in Tokyo metropolitan commute data.

ong the commuters the probability of an epidemic outbreak depends ong the commuters, the probability of an epidemic outbreak depends

t on the corresponding geographical locations The final size of an t on the corresponding geographical locations. The final size of an ze of that population, being little influenced by that population’s

ze of that population, being little influenced by that population s

l fi d th t th ti til id i tb k i t

also find that the mean time until an epidemic outbreak arrives at a p ly decreases with local population size

ly decreases with local population size.