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(TMC) based on NMC and EL.
From the news above, we should be aware that the delay of relief supplies makes epidemic control difficult. Considering rescue resources limited and the absence of vaccine available, the international community is dedicated to protecting the world from infectious disease threats by strengthening the global community’s ability to respond them rapidly and effectively. Otherwise, the number of new Ebola cases may keep going up at current situation.
To alleviate this problem, our team come up with the classified delivery system of health centers and the optimal distance model of distribution, which can be applicable to different investment costs.
We assume that:
● International rescue teams can unified distribution of resources when classify delivery system of health centers.
● The values of the “funding grouped by destination country table” from UNMEER is realistic.
4.2 Better Medical Center
4.2.1 NMC& TMC
We have built a delivery system that is based on the NMCs and TMC. The logistics process is that the supplies are firstly delivered to TMC, then to NMCs. In this paper, we have gained the EL of each countries above. Obviously, it’s beneficial to allocate the needed supplies through known Epidemic Level. The delivery system is showed as Figure 2.
Total Medical CenterSierra LeoneNMCNational Medical CenterGuinea NMCLiberia NMCMali NMCNigeria NMCCases
Figure 2. New medical center.
The center of gravity method is used to confirm the address of NMCs, the objective function is
MinTC??ViRiD,
(4.2.1)
To gain the smallest TC, the coordinate of focus must satisfy those condition:
n?F??ViRixi?x/?xii?1???xi?x?yi?y2??2?2?0, (4.2.2)
n?F??ViRiyi?y/?yii?1???x?x???y?y?ii2?0. (4.2.3)
● We have known the distribution data of Ebola. Within a small range, Longitude and latitude can be considered as the grid of Cartesian Coordinate System. The distance of points can be
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calculated as Euclidean distance.
● The coordinate points are calculated by using follow formulas. The more accurate data will be gained through the iteration algorithm that is shown in Figure 3.
VRx/D?x?， VR/D?iiiiiii(4.2.4)
y??VRx/D. ?VR/Diiiiiii(4.2.5)
StartInput an Approximated Initial valueUse the known value xi, yi to solve xi+1, yi+1NOTC is lower?YESOutput the Final value Figure 3. The flow chart of focus iteration algorithm.
● We have adopted the optimization function fminunc() in Matlab to calculate for our target points, which are NMCs of each country.
● Similarly, the TMC point can be confirm by known NMC points and EL of each nations.
Table 5. Outbreak locations, NMC locations and TMC location.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 NMC TMC Guinea Liberia Sierra Leone Latitude Longitude Latitude Longitude Latitude Longitude 11.74 -12.37 7.14 -11.05 9.17 -12.95 10.92 -12.55 6.78 -10.76 8.45 -13.24 9.95 -13.58 6.71 -10.58 8.26 -13.03 10.69 -12.43 7.1 -9.64 8.74 -12.72 10.58 -12.72 6.34 -9.84 9.36 -12.45 9.58 -12.99 6.94 -8.76 9.56 -11.42 11.13 -11.23 5.33 -8.63 8.2 -12.63 10.06 -10.71 / / 8.84 -12.05 10.95 -10.22 / / 8.84 -10.84 11.57 -9.74 / / 7.53 -12.25 10.36 -9.36 / / 7.9 -11.71 9.54 -10.036 / / 8.12 -11.3 8.58 -10.43 / / 8.18 -10.75 9.17 -9.53 / / / / 8.69 -9.57 / / / / 7.84 -8.91 / / / / 7.93 -8.41 / / / / 8.91 -8.25 / / / / 10.7357 -12.6583 6.8096 -10.6912 8.6964 -12.7735 Mali: (12.6206, -8.0133 ) Nigeria: (8.9411, -7.4554) (8.3387, -11.4557)
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Note: NMC of Nigeria which is Nigerian capital is not marked.
Figure 4. Total Medicine Center (TMC) and National Medicine Center (NMC)?.
4.2.2 Analysis of Result
From Figure 5, you must wonder how long it may take to ship essential relief goods or newly developed vaccines to destination by a medium-sized transport helicopter. Don’t worry. Our solution just follows.
Suppose you are on the flight of UH-60 Blackhawk helicopter (cruising speed 200km/h), which showed strong power in the battle against Ebola on West Africa. And you'll be clear after seeing the form below.
NMC of Guinea3.0544h1.4145h2.4007hTMCNMC of Mali3.0271h3.4063hNMC of Liberia1.5474h0.9362h2.2481h0.7579hNMC of Sierra Leone3.4063hNMC of Nigeria
Figure 5. Each flight duration between medical centers
? Data comes from WHO.
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From Figure 5, it could be inferred that you could reach every health center in the shortest time. For example, it takes only 0.9362h to fly from NMC of Liberia to TMC, which also suggests the epidemic situation in Liberia is the most serious. Given that the shorter distance is, the more serious epidemic situation is, Mali looks not bad relatively.
Besides, in this model, even if the two medical centers are far apart and aircraft cannot fly directly, filling up the aircraft tank near the medical center then taking off is a good idea, too
4.2.3 Strengths and Weaknesses
● Strengths: The traditional medical system is that various countries sent their medical team to
implement aid to Africa, and there is no efficient mechanism of communication between the various medical teams, which usually results in a waste of medical resources management, let alone concentrate all the rational allocation of resources.
The establishment of better medical center means we found the most efficient and shortest approach to deliver supplies by Tree-like structure and unified international medical resources allocated by TMC and NMC based on EL.
● Weaknesses: Putting aside political prejudices and narrow nationalism will be the difficult part in the application of this model.
4.3 Shortest Logistics Distance
Given the difficulties of political and economic factors, our team provide a program to design the shortest path for material distribution, which is an easy way. Almost all of the current medical system should apply this simple and efficient program to their rescue work.
Table 6. Logistics locations.
ID 1/21 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Logs_Name Conakry Kissidougou Nzerekore Logs Hub SKD/MLB FLB Harper Food distribution site Gbarnga WFP Warehouse Freeport Monrovia (?) WFP Warehouse Voinjama WFP Warehouse/office Zwedru FLB Gbarnga FLB Voinjama FLB Zwedru FLB Buchanan Monrovia Airport Facility Freetown Port Loko Kenema Makeni Kailahun Cntry_Name Guinea Guinea Guinea Liberia Liberia Liberia Liberia Liberia Liberia Liberia Liberia Liberia Liberia Liberia Sierra Leone Sierra Leone Sierra Leone Sierra Leone Sierra Leone Status Open Open Open Open Planned Open Open Open Open Open Open Open Planned Open Open Under Construction Open Open Open Latitude 9.579252 9.183333 7.75 6.25602941 4.37651223 6.987378 6.3403196 8.417957 6.074801 7.006217 8.31724023 6.093141 5.87915 6.2373605 8.484444 8.766667 7.863215 8.881667 8.277222 Longitude -13.619759 -10.1 -8.816667 -10.7004164 -7.70347312 -9.464531 -10.7929706 -9.748569 -8.130976 -9.566275 -9.77234039 -8.124531 -10.020161 -10.353631 -13.234444 -12.7875 -11.195717 -12.044167 -10.573889 Note: The data comes from UNMEER; we consider all labs regardless of status.
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