First, drawing from Fiedrich et al. (2000) and the aforementioned statistical data, this study postulates that the nationwide
accumulated number of fatalities (X(t)) during the 5-day test period may follow a negative exponential function given
by bXðtÞ ¼ X
ebðTtÞ , where bXðtÞ is the projection of X(t); X is the total number of nation-wide fatalities reported; b is a positive
parameter determining the shape of g(t). Using the chi-square statistical values with respect to X(t), the goodness-of-fit test
is then conducted. Therein, the corresponding test result indicates that the projections ðbXðtÞÞ yielded from the above negative
exponential from are accepted to capture the time-varying pattern of X(t). Fig. 4 presents both the real and projected
trajectories of nation-wide accumulated fatalities for illustration. Accordingly, this study further assumes that the accumulated
number of fatalities (Xi(t)) associated with a given affected area i in a given time interval t also follows the same negative
exponential form (i.e., bXiðtÞ ¼ Xi
ebðTtÞ ; 8i). The missing data points are then projected to complement the historical
database used for model testing.
The next step is to simulate the instantaneous data points ðxkj
i
ðtÞ; 8ðji; tÞ) in terms of the instantaneous accumulated numbers
of fatalities provided by multiple information sources. As stated in Section 2.1, the proposed model uses these multisource
data points as the input for approximating the accumulated fatality number in each affected area and time interval
via data fusion process. This study considers the local city centers (LC for short), rescue teams (RT for short), and on-spot
reporters (OR for short) as three major types of sources to provide the fatality-related information from each affected area
in each time interval. For simplicity, these multi-source data points ðxkj
i
ðtÞ; 8ðji; tÞÞ are assumed to follow respective normal
distributions characterized with respective mean values (denoted by uLC(t), uRT(t), and uOR(t), respectively) and variance
(n2
LCðtÞ; n2
RT ðtÞ; and n2
ORðtÞ, respectively). The study generates the above dynamic mean values uji ðtÞ by uji ðtÞ ¼ uji ðt 1Þþ
Duji ðtÞ. Wherein, Dukj
i
ðtÞ represents the increment of the mean value of the accumulated fatality number observed by a given
type of source ji in a given affected area i and time interval t, and is assumed to follow a respective uniform distribution rang-