CSIS Discussion Paper No.77 AED Optimal allocation of AED s by maximization of supply effect on demand density Yusuke KATAOKA, Yasushi ASAMI, Yasushi ASARI and Kazuaki KOHRIYAMA Course of Socio-Cultural and Socio-Physical Environmental Studies, Graduate School of Frontier Sciences, University of Tokyo 5--5, Kashiwanoha, Kashiwa-shi, Chiba 77-8568, Japan e-mail: ukataoka@csis.u-tokyo.ac.jp
AED Optimal allocation of AED s by maximization of supply effect on demand density Yusuke KATAOKA, Yasushi ASAMI, Yasushi ASARI and Kazuaki KOHRIYAMA Abstract: A probability density function of demand for automated external defibrillators (AED's), which is based on the distribution of demand points by kernel density estimation method, is estimated from the data on occurrences of cardiopulmonary arrests. The probability that someone can be saved by AED's is formulated using probability of survival to hospital discharge. Supply effect is expressed as demand density multiplied by this probability of saving, and the locations of AED's are optimized by maximizing supply effect in the entire region. The results show that optimal locations tend to cover the center of the city and that the supply effect is approximately proportional to the number of AED's. Keywords:AEDautomated external defibrillator density distribution maximal covering spatial pattern probability of survival to hospital discharge AED Malcom AED et al.004 AED Crocco et al.004 AED AED AED GIS 77-8568 5--5 Graduate School of Frontier Sciences, University of Tokyo E-mailukataoka@csis.u-tokyo.ac.jp AED
AED Sheather and Jones99 ).. (x,y) AED f ( xy, ) i (x i,y i ) Bowman and Azzelini, 997 x x i y y i f ( x, y) = K i K n h () x h y K ( ) n h x, h y () (x,i,y,i ) () n ( x x, i) ( y y ), i f ( x, y) = exp π hhn () x y i= hx hy Silverman, 986 n ()
.. 4) Maximal Covering Location Problem Church and ReVelle974 AED Brotcorne et al., 003 (3) (x,y) (x,j,y,j ) AED n ( ) ( (( ) ( ) )) g x, y = exp a x x, j + y y, j (4) j= American Heart Association, 000 n Alsalloum et al. 006 AED d 3) ( ) = exp( ad ) g d (3) a
(5) AED L ( ) x, y = f ( x, y) g( x, y) dxdy n ( x x, i) ( y y, ) i = exp π hhn x y i= hx hy n 5) ( (( ) ( ) )) exp a x x, j + y y, j dxdy j= d min d min = 4n + ahx + ahy n n a x x a y y exp + ah + ah x x, i + ahx ( x x, ) j erf hx 4ah + x y y, i + ahy ( x y, j) erf hy 4ah + y (, i, j) (, i, j) (5) (5) Maximize L x,, x,,, x, n, y,, y,,, y, n (8) erf( ) subject to d (9) z st, = ( x, s x, t) + ( y, s y, t) dmin s, t t erf ( z) = e dt 0 π (6) AED AED AED 4.. (5) (7) i= j= x y d s,t (9) (7) ( ) 3 4 L ( x,, x,,, x, n, y ),, y,,, y, n = n + ahx + ahy n ( ) ( ) 6) n a x, i x, j a y, i y, j exp i= j= + ahx + ah y (7) ().0 0-9 3 (7).. Sheather and Jones99 3
a=4.3 0-5 80m 5 400m.0 0-3 8) 0 00 00 300 4000.8 0.6 0.4 0. 0 (m) 4.3. AED (8) AED 30 (9) d min =400m (8) 9) 0 30 0 (km) 5.0 0-8 5.0 0-6 3 4.. 4.. (3) 6 0% 7)AED 0 0 (3)
0 点配置 図5 0 点配置 図6 30 点配置 AED の最適配置地点と供給効果の密度分布 30 点配置 AED の最適配置地点と救命確率の密度分布 0 (km) 図 5,6 中の表記については以下の通り AED の最適配置地点 および各々の密度 濃線 需要量密度 淡線 を示す等値線 背景地図として 河川 鉄道 弘前城を表記
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