埃博拉病情的发展预测和最优药物运送系统的探究

何汶俊，于冰青，郭文敏，王菊平，郭东星(山西医科大学第二临床医学院，太原 0000;山西医科大学第一临床医学院;山西医科大学数学教研室;共同第一作者;通讯作者，E-mail:499898@6．com)

The Ebola epidemic，a severe public health challenge，has aroused widespread concerns all over the world from February 2014．Ebola virus disease is a zoonotic disease caused by Ebola virus．Ebola virus outbreaks have a case fatality rate of up to 90 percent．As of February 2015 the largest outbreak was ongoing，and the epidemic in West Africa centered in Guinea，Sierra Leone and Liberia．As of February 3rd，2015，this outbreak had reported 22 560 cases，resulting in 9 019 deaths［1］．Based on various transmissions and the highly pathogenic of virus，the EVD pose a serious public health challenge．However，as the topic in the MCM，the World Medical Association has announced that their new medication could stop Ebola and cure the patients whose disease is not advanced．Therefore，the problem was solved by establishing the SIR epidemic model and the TSP model．

1 Materials and Methods

1.1 Materials

The topic was chosen from the MCM contest problems—Eradicating Ebola and the Ebola map which indicated the infected districts in Guinea，Sierra Leone and the Liberia WHO on February 6th．The districts were marked and numbered on the map and their coordinates were listed．

1.2 Methods

The TSP Model The TSP model was established to get the shortest path of delivering drugs and the model was implemented successfully via Matlab7.0［3］．In this model，this paper chose the most serious outbreaks of the three countries，including Guinea，Liberia and Sierra Leone．Then，all the cities that have reported cases were found out up to February 6th，2015．As is shown in Figure 1，this paper numbered them and marked them on the map．The size of yellow range represents the severity of the epidemic．The lager the range is，the more serious the epidemic is．Moreover，this paper found the coordinates and measured them on the map(see Figure 1，Table 1 and Table 2 )．

These coordinates of the cities were found on the map from WHO，which had been marked on the map．Based on this，Table 1 was made．The X and Y position referred to the coordinates of cities．

Figure 1 The cities which have reported infectious cases［3］

Table 1 The districts and coordinates of the city numbers (km)

2 Results

The models were implemented successfully via Matlab7.0．

2.1 SIR Epidemic Model

This paper did numerical calculations by random sampling to estimate the s(t)and i(t)of the general variation．Simulation results were as follows．

Based on the simulated curves and the equations，the research came to the final conclusions as follows:

(1)Incorporating the influence of isolation，it was known that isolation was an effective measure of preventing the spread of disease．

(2)The higher the level of awareness of health and hygiene was，the smaller the rate of daily exposure was．

(3)A higher medical treatment level brought to a greater daily cure rate．

(4)Keeping up high medical standards was an effective way to control the spread of infectious diseases．

2.2 TSP Model

According to the TSP based on SA，these coordinates were run in the Matlab7.0．As a result，Figure 4 is the asymptotic convergence curve and Figure 5 shows the optimal route．

In order to make the delivery system efficient and feasible，the system was divided into four parts．First，this paper randomly chose a city as the distribution command center．The city has a certain economic foundation．Its function is to collect information and give feedback to other parts．Then，set the supply sides．The supply sides were districts which provided drugs and vaccine．Moreover，two cities(18 and 24)that the epidemic were the most two serious areas werechosen as the shortest route to be the logistics distribution center．This paper chose the highway transportation，which was the minimum cost way．From each logistics distribution center two trucks were dispatched．The two trucks from one center traveled on opposite directions along the shortest path．Until the four trucks traveled all cities without repeating，they came back to the initial departures．This system was very flexible．When a place suffered from a sudden circumstance，the system sent it the supplies preferentially．Moreover，the air transportation was considered when an emergency broke out［4］．

Figure 2 The relationship between i，s and t

Figure 3 The relationship of s and i

Figure 4 The asymptotic convergence curve

Figure 5 The optimal route

3 Discussion

This paper came to a conclusion that isolation was the most efficient measure of preventing the Ebola，which was similar to the results of other literature［2］．

As to the delivery system，by solving the problem of traveling salesman problem(TSP)based on simulated annealing(SA)，this research obtained an optimal solution—the shortest and most efficient path which cost the lowest．The model was flexible and efficient．Because of the few constrained initial conditions，the range of the application was large．Therefore，the result solved by this model was reasonable．

4 Conclusion

The SIR epidemic model predicted the development of the epidemic．Isolation is the most effective measure of preventing the spread of disease．Suspected patients should be isolated for observation;medical workers should wear protective equipments to work，if not strict disinfections，the equipments cannot be worn again;once monkeys in a natural region or laboratory show suspected symptoms，the whole monkeys in the same environment should be hunted．

From the traveling salesman problem based on simulated annealing，this research obtained an optimal solution—the shortest(2 521.717 5 km)and most efficient path．Based on the search，this paper built a delivery network and set Kerouane and Freetown as the Logistics Distribution Centers．According to the delivery system，other locations received the medicine one by one in sequence．

Step up publicity efforts and enhance the public awareness and education．People in West Africa should pay more attention to health problem，raise their medical standards and educate everyone;prohibit some inappropriate customs，such as kissing the dead in funerals and eating the fruit bats．

Only isolation combined with the shortest route of delivering drugs could prevent the Ebola Epidemic efficiently．

Acknowledgement:This paper was adapted from the topic C of the MCM which had won a“successful paticipant”prize．

［1］Wikipedia．Ebola virus disease［DB/OL］．https://en．wikipedia．org/wiki/Ebola-virus-disease．2015－02－07．

［2］Zhou Houqing，Xu Youzhuan．Mathematical model of Ebola virus infective numbers［J］．J Shaoyang Univ，2014(4):3－5．

［3］WHO．Cumulative cases and past 21 days new cases November 26，2014 ［DB/OL］．http://maps．who．int/SimpleViewer-WHO/?appid=3ada31510f2046d0939f0a1f362b24-1f．2015－02－06．

［4］Zheng Xuanyao．TSP Algorithm Based on Simulated Annealing Algorithm［D］．Hang zhou:Zhe Jiang University，2005:100－110．

［5］Gong Yawei．Research and implementation of emergency relief supplies optimal vehicle routing choice［D］．Wuhan:Wuhan University of Technology，2008:12．