Infectious Disease Spread Prediction Models and Consideration

Transcription

1 1 1 1 SIR BBS SARS truncated SIR truncated Infectious Disease Spread Prediction Models and Consideration Hideo Hirose 1 and Kazuhiro Matsuguma Tatenori Sakumura 1, 1 For infectious disease spread prediction models, pandemic simulations have been dealt with a kind of simulations by scenario. However, when a pandemic occurs, predicting the future using the observed data becomes crucial. The methodology that assumes the model structure and estimates the model parameters using the observed data, which is called the assimilation or the gray box, is also necessary in pandemic analysis. In this paper, we propose a method to estimate such parameters, called the BBS (best-backward solution) method, and discuss the prediction results for observed real cases such as the SARS and the FMD (foot-and-mouth disease). We compare the results with those using the truncated model. We have found that the SIR model provides the worst case predictions even in earlier stages of pandemics contrary to the truncated model. 1. Scientific American 14) ) 2003 SARS 8, ) ,000 17),18) 2010 FMD, foot-and-mouth disease 20),21) FMD 19) 1 SIR 2 MAS 3 truncated MAS SIR 1 Kyushu Institute of Technology 1 c 2010 Information Processing Society of Japan

2 1 2 MADE 11) SIR 3 truncated 2. SIR 2.1 SIR SIR 1),2),5),10) S(t), I(t), R(t) t susceptible infected removed) S (t) = λs(t)i(t), I (t) = λs(t)i(t) γi(t), (1) R (t) = γi(t). λ γ 3),6) 2.2 SIR (1) 12) λ(t) = S(t) S(t + 1), γ(t) = S(t)I(t) R(t + 1) R(t). (2) I(t) λ(t) = S(t) S(t 1), γ(t) = S(t)I(t) R(t) R(t 1). (3) I(t) S(t) + I(t) + R(t) = N N S(t), I(t), R(t) λ γ R(t) I(t) incubation period latent period γ 2.3 BBS BBS best-backward solution method 1) T λ (0) γ (0) T 2) T = t n t 1 (1) 3) T R(t 1 ), R(t 2 ),, R(t n ) 2) ˆR(t 1 ), ˆR(t 2 ),, ˆR(t n ) 2 S 0 = ( ˆR(t j) R(t j)) 2 (4) j λ (1) γ (1) 15) 4) λ (1) λ (0) γ (1) γ (0) 2) 3) λ (1) γ (1) BBS c 2010 Information Processing Society of Japan

3 T 1) T 2) T R(T ) ˆR(T ) truncated T T 1 SARS 23) BBS BBS S p = w j( ˆR(t j) R(t j)) 2 (j/n) p, w j = n, p 1. (5) (j/n)p j=1 j T = t n p = 1, 2 SIR susceptible S(0) SARS S(0) S(0) S(0) R λ γ BBS λ γ S(0) BBS 3. truncated model T F (t) T i 1 T i n i k k { } ni F (Ti ) F (T i 1 ) L T (θ) =. (6) F (T ; θ) i=1 ˆθ ˆN T k ˆN T = r/f (T ; ˆθ), r = n i, (7) i=1 1 BBS SARS T S truncated SARS trunsored 8) truncated 0 trunsored 2 8) truncated 3 c 2010 Information Processing Society of Japan

4 3 9) 1 F (t; µ, σ, β) =, ( < t < ; < µ < ; σ, β > 0). β {1 + exp ( (t µ)/σ)} FMD 2010 FMD ) 24) FMD km 10-20km km 1 2 SIR km 6.5 truncated SIR BBS BBS p = 1 p = 2 SARS FMD SIR S(0) = 300, km 70% 3 10km 10km 90% 10km 4 c 2010 Information Processing Society of Japan

5 3 FMD SIR S(0) = 65, FMD truncated 3) truncated 4 T ˆN T N j = j i=1 n i T = 30 T = T = 50 SIR FMD SARS 2009 A(H1N1)) 5. SIR BBS SARS SIR truncated SIR truncated FMD 30 10km 6.5 SIR FMD 1 10km 70% 2 10km 10km 90% 3 10km Google 5 c 2010 Information Processing Society of Japan

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