This paper mainly studies the eradication of the Ebola virus, proposing a scientific system, including three modules for the eradication of Ebola virus. Firstly, we build a basic model combined with nonlinear incidence rate and maximum treatment capacity. Secondly, we use the dynamic programming method and the Dijkstra Algorithm to set up MS (storage) and several delivery locations in West Africa. Finally, we apply the previous results to calculate the total cost, production cost, storage cost, and shortage cost.
The Ebola virus large outbreaks in Africa began in 2014. The high number of people infected and the high mortality caused widespread concern in the world. Ebola virus disease shocked the world in 1976. It turned up for the first time in two cases that began the epidemic at the same time [
Now the spread of Ebola virus has caused wide public concern all over the world. In order to make drugs and vaccine exert the greatest effect which can effectively cure patients, we propose a scientific system, including three modules for the eradication of Ebola virus. First, we build a basic model combined with nonlinear incidence rate and maximum treatment capacity. Then, we use the dynamic programming method and the Dijkstra Algorithm to set up MS (storage) and several delivery locations in West Africa. Finally, we apply the previous results to calculate the total cost, production cost, storage cost, and shortage cost.
We established a practical, sensitive, useful model. For other manuscripts, we find that iteration, Floyd algorithm, and genetic algorithm are used to optimize the eradication of Ebola. Meanwhile, in our model, we consider not only the disease propagation speed and the drugs required quantity and the impact of transportation on the treatment but also the design of a distribution optimization feasible transmission system [
Considering the production and distribution of drugs and local medical infrastructure, we build a basic epidemic model with maximum treatment capacity. How to restrain the spread of Ebola virus is shown in the following five steps.
Build the epidemic model with nonlinear incidence rate and maximum treatment capacity.
The total population changes because of the birth rate and natural death rate and is classified into
Build the improved SEIQT epidemic model.
Utilize the equivalent system of equations to figure out the basic reproduction number
Analyze the stability.
In most of classical epidemic models, the incidence rate is assumed to be
We assume that there is no birth rate or natural death rate and the total population is fixed. The process of modeling is shown in Figure
Overview of epidemic model.
Build simultaneous differential equations:
From
At the same time, the function
First of all, we must introduce the concept of basic reproductive rate. The basic reproduction number (sometimes called basic reproductive ratio and denoted by
To analyze the spread rate of Ebola, we collect the data of population and total cases and deaths in Guinea, Liberia, and Sierra Leone from May 27 to November 28 in 2014; see Table
The number
Area  Guinea  Liberia  Sierra Leone  

Month  Population  Total cases  Total deaths  Population  Total cases  Total deaths  Population  Total cases  Total deaths 
May 27, 2014  11.2 million  281  186  4.3 million  12  9  6.1 million  16  5 
June 24, 2014  11.2 million  390  270  4.3 million  51  34  6.1 million  158  34 
July 27, 2014  11.2 million  460  339  4.3 million  329  156  6.1 million  533  233 
August 26, 2014  11.2 million  648  430  4.3 million  1378  694  6.1 million  1026  422 
September 25, 2014  11.2 million  1103  668  4.3 million  3564  1922  6.1 million  2120  561 
October 24, 2014  11.2 million  1598  981  4.3 million  6253  2704  6.1 million  4017  1341 
November 23, 2014  11.2 million  2134  1260  4.3 million  7168  3016  6.1 million  6599  1398 
December 28, 2014  11.2 million  2597  1607  4.3 million  7862  3384  6.1 million  9004  2582 
Based on the data in Table
Total cases of three states in 2014.
Total cases and deaths in Guinea.
Total cases and deaths in Sierra Leone.
Total cases and deaths in Liberia.
To fight against Ebola, infectious individuals tend to be isolated to control the spread of the disease, so as to form a separate group known as isolators. We introduce isolators
Overview of improved epidemic model.
Also build simultaneous differential equations:
We can find that
Motivated by the works of Du and Xu [
We obtain the expression of
Therefore, decreasing the basic reproduction number is one of the effective ways to eradicate Ebola or control the development of epidemic [
Increase the value of
Decrease the value of
Increase the value of
This model is to establish how to distribute drugs quickly and reasonably. The aim of the first day is acquiring initial data of each infected district, according to the number of the infected people of each district to distribute drugs [
The pictorial diagram of the model is given in Figure
The pictorial diagram of the model.
First, we use two matrixes which contain the information of MS roads’ and each of the area roads’ level data:
The velocity combined with the road level factors can be calculated:
We can also get the distance between the MS and each area:
After that, we can obtain shortest time data of each routine. Assume that
Then we figure out the best routine by using dynamic programming. We design the transport time between area
When the routine contains one area road,
When the routine contains two area roads,
When the routine contains zero area roads,
Next we get the shortest transport time between arbitrary area and destination:
Finally, we can use Dijkstra Matrix Algorithm to get the shortest time on the routine between every two areas:
The shortest time between MS and every destination can be figured out:
The parameter
According to the model preparation, we can easily know that
According to our previously established model, we select the Ivory Coast in an area (9 in densely populated areas, a drug storage station) for data simulation. Limited by lack of data search, part of the data (population, prevalence, drug and vaccine production, and storage efficiency) in accordance with the reality of the situation is assumed; see figure position distribution and geographic condition (Figure
An area of Ivory Coast.
According to the map information, we use the transport model to calculate the data. We can get the shortest time by the MS transport of drugs and vaccines to 9 of this densely populated area with Table
The shortest time of the transport line.
Destination  1  2  3  4  5  6  7  8  9 


Hours  1.04375  0.985417  1.516667  3.650417  3.750417  2.770833  1.754167  2.34375  3.079167 
The most efficient routine is in Table
The most efficient routine.
Destination  1  2  3  4  5  6  7 

Routine 







Based on the data in each region, the initial drug inventory is 5000 units. In this inventory, 2000 units are available every day and 3000 units are used to make vaccines. Besides, 4000 units can be transported when the virus infection coefficient
Transport schedule on the first day.
City  Population  Patients  Drugs  Vaccine 

1  511154  112  41  471 
2  12211  11  5  14 
3  121233  0  0  132 
4  56454  0  0  55 
5  64441  1  1  63 
6  2023756  2133  767  1930 
7  68782  12  65  161 
8  124144  0  0  291 
9  468444  0  0  457 
Transport schedule when the epidemic is controlled.
City  Population  Patients  Drugs  Vaccine 

1  511154  131  48  495 
2  12211  11  5  14 
3  121233  0  0  139 
4  56454  0  0  68 
5  64441  0  0  79 
6  2023756  1683  662  2513 
7  68782  4  663  348 
8  124144  0  0  700 
9  468444  0  0  3337 
From the simulation results, we spend a total of 42 days on complete control of the epidemic. The number of infections in the region is not on the increase. Then the supplies of vaccine and drug need to be sustained.
The parameter
In this section, we will find what kind of storage solution can make the minimum total cost. Given the drug in the corresponding point of storage, we set up the storage model, then we integrate transport vaccine and drugs production costs, and we can get the minimum total cost solution.
Combining with the general economic ordering quantity model, we should not only consider the relationship between the transport from the pharmaceutical production department to storage and the affected areas needing drugs but also allow the inventory shortage situation. The rate of transport of drugs is
Storage capacity of the model with allowed shortages.
We suppose that a cycle length of time for storage is
By analysis, OC, CC, and SC can be given as
So the average total cost per unit of time can be obtained as
From Figure
Restoring data, each length of time can be given as
After obtaining the sum cost of the average fee, storage fee, and loss fee in the unit of time, the final total cost can be obtained after adding the corresponding medicine manufacturing cost and transportation cost.
In summary, we can enlarge the drugs and vaccine supply to control the epidemic. As we can see, the index of
The authors declare that there is no conflict of interests regarding the publication of this paper.
The work was supported in part by the Natural Science Foundation of Anhui Province of China under Grant no. KJ2013B105, the Natural Science Foundation for the Higher Education Institutions of Anhui Province of China under Grant no. KJ2015A331, the National Natural Science Foundation of China, no. 11301001, the Excellent Youth Scholars Foundation, and the Natural Science Foundation of Anhui Province of China under Grant no. 2013SQRL030ZD.