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4.3.4 Strengths and Weaknesses

● Strengths: By using this simulated annealing algorithm, the total length of the delivery routes

between logistics points will reach an optimum value, thus greatly reducing delivery time and realizing the aim of high-efficient resource sharing.

● Weaknesses: Maybe you've found each optimal paths are not the same, although they only have a little difference. The reason is that SA is a stochastic optimization algorithm, so it takes several times to optimize when we apply this strategy, and each time is different. That is to say, there exists more than one shortest mileage.

Of course, if you shaking your head, then we recommend you to take a flight by Blackhawk helicopter directly. We believe you would be interested in our method.

5 Model Three: How Much Should the Distribution

of Resources be?

5.1 Quantity of the Resources Needed

5.1.1 Introduction

Since the outbreak of the Ebola virus, according to WHO statistics as follows data presented. In order to predict the outbreak areas in need of resources (capital, rescue workers, drugs and so on), we need to measure a variety of factors such as Deaths, Cases, Total expenditure on health as % of GDP, Total expenditure on health per capita, GNI per capita, Nursing and mid and Population. However, the official publication of specific information is limited, Deaths and Cases will be considered as the main factors. For simplicity, we consider only three countries Guinea, Sierra Leone and Liberia. In the case of USD contributed, we create forecast model. ● We establish an AR Time Series model.

We forecast USD by polynomial fitting method. Deaths and Cases in a specific time as independent variables, USD contributed as the dependent variable, we model polynomial fitting to forecast USD contributed values in the future and make a comparison with forecast data provided by WHO.

5.1.2 AR Time Series

From a longer time perspective, changes in the number of infections and deaths to follow certain rules; in the short term, due to changes such as susceptible population density, health measures, regional climate, monsoons, ocean currents and other uncertainties in the virus infection, our predict will be some difficulties. Currently, there are many ways similar to the infectious disease forecasting models and there are classic growth curve, exponential smoothing, etc. However, these methods for short-term fluctuations of certainty is not high. In the course of infectious diseases prediction, AR autoregressive model considers both the spread of the virus phenomenon dependence on time series and interference random fluctuations. Short-term trend for higher prediction accuracy is a method used widely. ● Theoretical groundwork.

Set the original time series model as at?t?1,2,...,11? and verify the sequence of smooth. We choose Daniel inspection which built on the basis of Spearman correlation coefficient.

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Inspection of Spearman correlation coefficient:

H0:?XY?0,H1:?XY?0,

T?qsn?21?q2s(5.1.1) (5.1.2)

, where: ?XYmeans the overall correlation coefficient. Make the following hypothesis test:

H0: series Xt is stationary. H1: series Xt is not stationary(upward or downward trend).

Daniel inspection: Calculate Spearman correlation coefficient qs of ?t,Rt?,t?1,2,...n by time series. If T?t?/2?n?2?, we believe that series is not stationary. If not, series is stationary. ● Construct model.

We calculate qs equals to 0.961 and Tequals to 3.323 based on significant level ? equals to 0.05. We get t?/2 equals to 2.069, and T?t?/2?n?2?, series is not stationary. In addition, series upward trend according to qs?0.

Establish auto regression model predict bt:

yt?c1yt?1?c2yt?2??t,

(5.1.3)

where: c1,c2 means undetermined parameters; ?tmeans random disturbance term. ● Model solution.

Data modeling through March 2014 to November and forecast data from December 2014 to January 2015; if the prediction error is relatively small, the forecast data from February 2015 to March 2015, and otherwise improve the model until satisfied.

Table 8. Cases and Deaths among Guinea, Sierra, Liberia?.

Date Index 2014-3-31 2014-4-23 2014-5-29 2014-6-30 2014-7-30 2014-8-29 2014-9-30 2014-10-29 2014-11-28 2014-12-29 2015-1-31 Cases 122 218 291 413 472 648 1199 1667 2164 2707 2975 Guinea Deaths 80 141 193 303 346 430 739 1018 1327 1708 1944 USD contributed 306,279 3,141,367 645,781 226,291 553,337 4,918,465 38,095,074 20,391,354 59,616,404 117,490,845 16,521,321 Cases 0 0 50 239 574 1026 2437 5338 7312 9446 10740 Sierra Leone Deaths 0 0 6 99 252 422 623 1510 1583 2758 3276 USD contributed * 330,598 96,286 0 1,872,645 51,637,855 384,657,927 165,777,750 138,821,992 75,006,201 27,458,622 Cases 0 0 0 107 391 1378 3834 6535 7635 8018 8745 Liberia Deaths 0 0 0 65 227 694 2069 2413 3145 3423 3746 USD contributed * * * 302,883 1,769,365 4,928,261 45,013,890 72,545,209 197,711,449 136,826,418 63,444,673 Note: * means that there is no statistical data.

● Based on Table 8, we get AR prediction model by Least Squares. Guinea:

Cases: yt?0.9797yt?1?0.1245yt?2??t, Deaths: yt?0.7860yt?1?0.2280yt?2??t. (5.1.4)

? Data comes from WHO.

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Sierra Leone:

Cases: yt?0.9866yt?1?0.08719yt?2??t, Deaths: yt?1.355yt?1?0.2047yt?2??t. (5.1.5) Liberia:

Cases: yt?1.222yt?1?0.4862yt?2??t, Deaths: yt?0.3745yt?1?0.4052yt?2??t.

(5.1.6)

● With the help of SPSS, we get predictive values about Deaths and Cases, relative error, and forecast chart about Deaths and Cases.

Table 9. Predictive values about Deaths and Cases & relative error (RE).

Date Index 2014-3-31 2014-4-23 2014-5-29 2014-6-30 2014-7-30 2014-8-29 2014-9-30 2014-10-29 2014-11-28 2014-12-29 2015-1-31 2015-2-31 2015-3-31 Cases 121 210 268 430 488 613 980 1701 2078 2490 3039 3202 3350 RE 0.82% 3.67% 7.90% 4.12% 3.39% 5.40% 18.27% 2.04% 3.97% 8.02% 2.15% / / Guinea Deaths 78 132 163 330 321 457 790 1030 1529 1693 1875 2018 2037 RE 2.50% 6.38% 15.54% 8.91% 7.23% 6.28% 6.90% 1.18% 15.22% 0.88% 3.55% / / Cases 0 0 45 257 583 1290 2730 5209 7109 9864 10076 11902 11870 Sierra Leone RE 0.00% 0.00% 10.00% 7.53% 1.57% 25.73% 12.02% 2.42% 2.78% 4.43% 6.18% / / Deaths 0 0 4 102 270 410 659 1344 1735 2980 3411 3602 3799 RE 0.00% 0.00% 33.33% 3.03% 7.14% 2.84% 5.78% 10.99% 9.60% 8.05% 4.12% / / Cases 0 0 0 90 421 1562 4002 6420 7801 8106 8932 9291 9428 RE 0.00% 0.00% 0.00% 15.89% 7.67% 13.35% 4.38% 1.76% 2.17% 1.10% 2.14% / / Liberia Deaths 0 0 0 49 249 720 2401 2692 2893 3291 3901 4312 4592 RE 0.00% 0.00% 33.33% 3.03% 7.14% 2.84% 5.78% 10.99% 9.60% 8.05% 4.12% / / Note: the blue time is situation values.

● Draw statistic charts by Table 9.

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Figure 8. Forecast chart about Deaths and Cases.

As shown in Figure 8, from left to right, the first and the second forecasts on Deaths and Cases about Guinea; the third and the forth forecasts on Deaths and Cases about Sierra Leone; the fifth and the sixth forecasts on Deaths and Cases about Liberia.

Observed variation of graph, we concluded that both Deaths and Cases in July 2014 to November showing a substantial increase. Result of analysis is that the African climate during this period stimulated the spread of Ebola virus. Besides, the comprehensive international rescue teams began to support in the affected areas until September 2014.

We speculate that even if the medical team arrived in Africa, it is difficult to eliminate the epidemic in a short time. In the early rescue, it took time for medical teams to adapt to the African climate and challenge to integrate resources. Besides, primary medical supplies are in shortage and the effective cure for Ebola vaccine has not been developed now. In most cases, we can only resort to bury the bodies and isolation to control the spread of the epidemic.

Thankfully, the rescue team has made remarkable achievements in November. As shown in Figure 8, the curve trend is slowing down, Deaths and Cases have been effectively curbed after November 2014. Establishment of predictive models can help people predict trends, take timely measures to supply medical resources and improve resource allocation.

5.1.3 Polynomial Regression

Table 10. Predictive values about USD contributed & relative error (RE).

Date Index 2014-3-31 2014-4-23 2014-5-29 2014-6-30 2014-7-30 2014-8-29 2014-9-30 2014-10-29 2014-11-28 2014-12-29 2015-1-31 2015-2-31 2015-3-31 Guinea USD contributed 315,267 3,341,467 656,719 207,810 578,101 5,481,220 24,903,496 24,071,634 64,918,291 87,891,849 20,903,244 12,903,444 12,243,024 RE 2.93% 6.37% 1.69% 8.17% 4.48% 11.44% 34.63% 18.05% 8.89% 25.19% 26.52% / / Sierra Leone USD contributed * 319526 92781 0 1590826 56934832 277822978 147838401 184734832 78923010 31893743 28893743 30893743 RE 0.00% 3.35% 3.64% 0.00% 15.05% 10.26% 27.77% 10.82% 33.07% 5.22% 16.15% / / Liberia USD contributed * * * 289826 2098292 4582123 49893728 78748383 247893636 92773729 65283383 58283391 55278201 RE 0.00% 0.00% 0.00% 4.31% 18.59% 7.02% 10.84% 8.55% 25.38% 32.20% 2.90% / /