2015年数学建模美赛埃博拉病毒 - 图文

The model of eradicating Ebola

In order to construct an effective model, the following factors need to be taken into consideration: the propagation of the disease, the demand of drugs, the transportation system and the producing speed of the drug. We first applied the SIR model to stimulate how the disease propagated and by assuming different cure rates, we got the demand of the drug when the disease propagated. Then, considering the situations of the epidemic, population and traffic of three countries in West Africa, we made suitable delivering systems for these countries.

In terms of the propagation of the disease, we searched for statistics and applied the SIR model to calculate the daily contact rate. Also, considering that the producing speed of drugs would increase due to economies of scale, we started from the current situation of the epidemic and increased the cure rate gradually. According to the calculation of MATLAB, we stimulated how the disease would propagate after effective drugs came out and the result was that the disease would be under control after fifty days.

With respect to the demand of the drug, because the supply of the drug would gradually increase as the production capacity strengthening, the cure rate would also increase. Combining the effect of the decrease in the number of patients and that of the increase in cure rate, the demand of the drug is supposed to go up and then go down.

As for the delivery system and the place of delivery, we took Sierra Leone as an example. Taking the population distribution, the situation of the epidemic and the traffic situation into consideration, we set the capital city Freetown as the chief trading place. After drugs were delivered to Freetown, most drugs would be distributed to those western coastal areas with a dense population and severe epidemic situations and the remaining drugs would be delivered to other places of the country.

Key words: Ebola SIR Model Drug Delivery Demand of the Drug

Non-technical Letter

According to the statistics of WHO, the cumulative cases has been reaching 22460 in the three countries in west Africa (Guinea, Liberia, Sierra Leone) until February 1, 2015. And the death toll has been reaching 8968 people. The morbidity increases nearly a week. Although only a few countries and regions suffer the disease, the world medical association has developed a new medication could stop Ebola and cure patients whose disease is not advanced to response the serious disease.

From March 21, 2014, Guinea, Liberia, Sierra Leone suffered from the disease one by one. Under the effective prevention interventions, the daily contact number of infected people has decreased. However the number of infected people is increasing.

To optimize the eradication of Ebola, or at least its current strain, we estimate that the recovery rate every day will reach 0.2 from 0.05 considering the speed of manufacturing of the vaccine and the treatment level. The total quantity of the medicine needed is close to 35000. Under this speed of medicine supply and treatment, the disease will be controlled in 50 days.

Focus on Sierra Leone for example, since the western area based on the capital Freetown is overcrowded and the disease of the western area is serious, the medicine provided by world medical association will be delivered in Freetown. Then the medicine will be allotted again based on population density and the condition of disease.

In fact, the most effective way to prevent the further spread of Ebola is effective isolation of the infected people, reducing the probability that susceptible populations contact with patients. The transmission speed, the range, the strength of Ebola depend on quantities of the infected persons and susceptible persons, and effective contact between the two parts which could be affected by exposure level, pathogenic species, the quantity of excreted pathogens, resistance of the susceptible.

Ebola virus is the most serious outbreak of the last 40 years, is a common challenge all the world as well. Currently, the fight situation against the epidemic is still very grim. As we all know, economic level and medical standard of the West African region is behindhand, the current state has overstepped their capabilities to fight with Ebola alone. We appeal to all countries for assisting the countries that are under the attack of Ebola, help them strengthen health systems and auxiliary infrastructure further.

Contents:

1. Introduction……………………………………………………………………1

1.1. Background………………………………………………………………….1

2. Model 1—Ebola Virus Propagation Model…………………………...1

2.1 Model Assumptions…………………………………………………………..1 2.2 Model Constitution…………………………………………………………...1 2.3 Numeric Calculation………………………………………………………….2 2.4 Analysis of Phase Trajectory Figure………………………………………….4 2.5 Conclusion……………………………………………………………………5

3. Model 2—Medicine Supply Model……………………………………...6

3.1 The demand of medicine……………………………………………………...6 3.2 Medicine Delivery System……………………………………………………7 3.2.1Drug distribution proportion………………………………………..……….7 3.2.2Methods of the Medicine Delivery……………………………………..……7

4. Sensitivity Analysis and Improvements………………………………....8

4.1 Sensitivity Analysis……………………………………………………………8 4.2 Improvements………………………………………………………………….8

5. Model Evaluation……………………………………………………………..9

5.1 strengths.......................................................................................................................9 5.2 weaknesses………………………………………………………………………9

6. Reference..............................................................................................................9

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1. Introduction

1.1Background

West Africa is hit by the most unprecedented outbreak of Ebola virus caused by the most lethal strain from Ebola virus family. The World Health Organization (WHO) declared it as an International Medical Emergency. As of 31st August 2014, the numbers of Ebola cases are 3685 with 1841 deaths reported from Liberia, Guinea, Senegal, Sierra Leona and Nigeria. WHO director general said that the actual numbers of cases are more than the reported cases.

Guinea, Sierra Leone and Liberia are the poorest countries of the world with scruffy healthcare system. Even their hospitals lack the basic public health facilities and they are facing the terrible Ebola epidemic.

2. Model 1—Ebola Virus Propagation Model

Ebola virus is mainly spread through blood and excreta of patients, and we build our model according to its propagation mechanism. Once cured, Ebola virus patient has a strong immunity, so, the people who have recovered are neither healthy (susceptible) nor patient (infective), they have dropped out infected system. In this case, situation is much complicated, so the following will be a detailed analysis of the modeling progress.

2.1 Model Assumptions:

● The total number of population N is constant. We don’t consider the born and death of people, and no migration of population, so people can be divided into three parts: the healthy, the infected and the removed recovered from Ebola disease. At time t, the proportion of three parts in the total population N were referred as s(t), i(t) and r(t).

● The average number of a patient contacts per day is a constant effective λ, λ is called daily contact rate. When patients have effective contact with the healthy, it makes the healthy people infect and become patients.

● The proportion of cured patients everyday in total number of patients is a constant effectiveμ, μ is called daily cured rate. Patients cured and recovered from the disease will not infect Ebola again.

● The contact number in the infectious period σ=λ/μ. 2.2 Model Constitution

According to assumption one, it is apparent that:

s(t)+i(t)+r(t)=1 (1)

According to assumption two and three, a patient can make λs(t) healthy people into patients per day, because the number of patients is Ni(t), so the number of infected healthy people isλN s(t)i(t), and λNsi is the increasing rate of patients, hence we have:

diN??Nsi??Ni (2) dt As to the recovered and immune people, we have

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dr??Ni (3) dt We assume that at the beginning, proportion of the healthy and patients are s0(s0>0) and i0(i0>0) (we might as well define r0=0), and according to equations (1), (2) and (3), we get the equation of SIR model:

N?di??si??i，i?0??i0??dt (4) ?ds????si,s?0??s0??dt The analytical solution of equation (4) can’t be obtained, so we first make

numerical calculation. 2.3 Numeric Calculation

In order to work out the analytical solution of equation (4), we have to figure out precise value of each parameter. Firstly, we need to figure out the value of daily contact rate λ. We find some necessary data in WHO official website, which include the population of Ebola severest three countries: Guinea, Sierra Leone and Liberia is 21.6 million and the number of infected people every once in a while. So we can get the proportion of the healthy and the infected, the number of new infected per day and the daily contact rate in the table below:

Table 1

time interval 0 13 19 62 32 11 9 7 10 9 12 9 12 7 5 6 7 7 7 7

proportion of health/% 0.9999963 0.99999338 0.9999888 0.99997227 0.99993875 0.99992079 0.99990153 0.99981741 0.99972949 0.99966866 0.99954116 0.99937315 0.9993487 0.99926384 0.99920782 0.99917093 0.99904111 0.99899588 0.99897884 0.99896019

proportion of infection/% 0.0000037 0.00000662 0.0000112 0.00002773 0.00006125 0.00007921 0.00009847 0.00018259 0.00027027 0.00033134 0.00045884 0.00062685 0.0006513 0.00073616 0.00079218 0.00082907 0.00095889 0.00100412 0.00102116 0.00103981

new infection per day

0.0 4.8 5.2 5.8 22.6 35.3 46.2 127.4 147.7 146.0 127.9 436.6 44.0 150.9 188.4 132.8 78.4 61.1 52.6 57.6

Contact number/λ — 0.0339 0.0215 0.0096 0.0171 0.0206 0.0217 0.0323 0.0253 0.0204 0.0129 0.0323 0.0031 0.0095 0.0110 0.0074 0.0038 0.0028 0.0024 0.0026

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According to the actual data, we can getλ at different time periods. As it clearly shown in the table, when the Ebola just out-broke, we figure out thatλ=0.0339, and it obtained its maximum value. With time pasted, the value of λ is becoming smaller and smaller, which indicates the patient contacted less people every day and less people were infected. This might because governments took some effective action to control and prevent the spread of the disease, the patients were separated from the healthy people. To simplify our model, we don’t take separation of patients into our consideration, and we ignore the condition that patients died of the virus. So, we determineλ=0.0339, because at the beginning of the virus out-broke, no external constrains obstruct the spread of the disease, it is an ideal environment for the virus, we takingλ=0.0339 will make our model more accurate.

Then we have to determine values of other parameters. Ebola is a very dangerous virus and it has caused devastating destruction. So we assume that at the beginning, Ebola disease can’t be cured, no effective measures can be taken to control the virus. In this conditionμ=0, Ebola virus will spread at a high speed.

Figure 2

Combined with the actual situation, we assume that at different time, the value ofλ is changing. We make every five days as an interval, and redefine the value of λ every five days. In the first five days, the disease was just out-broken, people had less conscience of the seriousness, and they lacked necessary action to protect themselves. What’s more, at the beginning, no effective drugs to treat patient, and the supply of medicine was not sufficient, so we define the daily cured rate μ=0.05. The next five days, people gradually realized that in their country has broken out a dangerous disease, they improved the awareness to protect themselves, and avoided contacting with the patient, so at this timeμ=0.1. In the third five days, government put a lot of effort to control and prevent the disease, patients were separated from the public, a lot of effort was put to research the virus and produce effective drugs, soμ=0.15. In the twentieth day and after, the whole world paid much attention to this disease and gave a lot of assistance to Africa countries, the disease was under control, the supply of

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medicine was sufficient, so more patients were cured, so we define the value of daily cured rate is constantμ=0.2.

We can get i0and s0 from Table 1: i0=0.00104, s0=0.99896. Then we use MATLAB to draw curves of i(t) and s(t).

Table 3

t 0 1 2 3 4 5 6

0.0010398 0.0010232 0.0010068 0.0009907 0.0009748 0.0009592 0.0008978 i(t)

0.9989602 0.9989253 0.9988909 0.9988571 0.9988238 0.9987911 0.9987596 s(t)

t 7 8 9 10 11 12 13

0.0008403 0.0007866 0.0007362 0.0006891 0.0006135 0.0005463 0.0004864 i(t)

0.9987302 0.9987027 0.9986769 0.9986528 0.9986308 0.9986112 0.9985937 s(t)

t 14 15 16 17 18 19 20

0.0004330 0.0003855 0.0003265 0.0002765 0.0002342 0.0001984 0.0001680 i(t)

0.9985782 0.9985643 0.9985523 0.9985421 0.9985335 0.9985262 0.9985200 s(t)

Figure 4

s(t) i(t)

From Figure 4 we can see that values of s(t) and i(t) change a little, s(t) changes from 0.99896 to 0.99849, and finally tends to a constant value. This means at last nobody was infected Ebola any more. This is conformed to real situation. After finding several people were died of Ebola virus, western Africa countries and WHO had paid highly attention to this problem. They took effective and instant action to control the spread of the disease. They separated the patient from the public and used the most advanced methods to treat the patient. In addition to this, these countries conducted a large investigation among suspicious people, making sure that the disease wouldn’t be infected in a large scale. Under these powerful action, Ebola virus didn’t spread, the number of infected people was increasing slowly, so the change of daily infected rateλ is very small, Analogously, the change of i(t) is small because of the same reason. Finally, the value of i(t) equals to zero, which indicates that Ebola virus was wiped out. But this is the result of our model, it is an ideal situation, and now this situation has not happened.

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2.4 Analysis of Phase Trajectory Figure

In order to analyze the general variation of s(t) and i(t), we need to draw i~s relationship figure. This i~s figure is called phase trajectory figure.

Based on the numeric calculation and observation of the figure, we can use phase trajectory line to analyze the character of s(t) and i(t).

The s~i plane is called phase plane, the domain of definition of phase trajectory line in the phase plane (s, i) ∈D is:

D???s,i?s?0,i?0,s?i?1?

We erasure dt in the equation (4), and noticing thatσ=λ/μ, we can get

di1??1,is?s0?i0 (5) ds?s We can easily figure out that the answer of equation (5) is:

i??s0?i0??s?1?lns (6) s0In the domain of definition D, the line that equation (6) displays is phase trajectory line, we can get the changes of s(t), i(t) and r(t).

● At any case, the patient will disappear at last, that is i∞=0

● The final proportion of the uninfected healthy people is s∞, we define i=0 in the equation (6), so s∞is the answer of equation

s0?i0?s??1?lns??0 s0● If s0<1/σ, i(t) is monotone decrease and finally drops to 0, s(t) is monotone decrease to its minimum s∞ . 2.5 Conclusion

According to our analysis and calculation, the number of patients is constantly decrease, and in the fiftieth day after the virus broke out, we figure out that the patients will drop to 24 people, compared with the beginning of the disease, the number of patients is more than 20000, so we can draw the conclusion that we have

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already successfully controlled the disease, the virus didn’t spread in a large range. If we continue conducting some effective action, such as separating the patient, propagating the information about avoid the virus, Ebola disease will be completely wiped out in the next few weeks.

3. Model 2—Medicine Supply Model

3.1 The demand of medicine

The world medicine association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced. That is to say, as long as the supply of medicine is sufficient, all the patients could be cured. Next step our goal is to figure out the demand of medicine every day.

To solve this question, we assume that one unit medicine could cure one patient, and according to model one, we have calculated the number of patients and daily cured rate, so the quantity of daily demand medicine can be calculated. We define that daily needed quantity of medicine is Q.

Q=N*s(t)*μ

The result is shown in the Table 5 below.

Figure 5

The changes of medicine demand are shown in the figure 5.We can see that in the first four days, demands of medicine slightly declined. Because at the beginning, the effective medicine has been developed, and the daily cured rate was relatively low, the virus wasn’t wide spread, the number of infected people was small, so the demand wasn’t very high. However, in the next few days, the demand was abruptly increased, almost doubled the demand in the fourth day. With more people were infected the Ebola virus, they needed more medicine to treat their diseases. Another reason is that the daily cured rate increased, which means more medicine was used to mitigate patients’ symptom and pains. The next six days, the demand of medicine was showing a wavy change, because of the intervention of governments. They put more effort to control the virus in case it was spread in a large range, and more medicine was manufactured, hospitals tried their best to treat the Ebola patient. After the fifteenth day, the demand of medicine was constantly dropping, and finally dropped to near

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zero, which indicates the virus was under control, more and more people were cured, and very few people were infected Ebola virus, and at last Ebola virus was wiped out, medicine was scarcely needed. 3.2 Medicine Delivery System

3.2.1Drug distribution proportion

Good delivery system is based on the distribution of population, the condition of disease, the condition of traffic. There we take Sierra Leone for example. We find the data about the population of every province and the number of infected people. According to the initial data, we calculate the rate of infections, rate of population density. Combined with this two rates, we get the final drug distribution proportion. This table is the result about drug distribution proportion.

Table 6

district Northern Province Eastern Province Southern Province Western Area

rate of infections

37.57% 16.30% 6.89% 39.24%

rate of population density rate of medicine

13.27% 20.91% 14.82% 51.01%

25.42% 18.61% 10.85% 45.12%

Rate of infections means the rate of infected people in every district to the total infected people in the country. Rate of population density means the population density in every district compared to the sum of population density. Rate of medicine equals to the average of rate of infections and rate of population density. That is the proportion of drug distribution.

As we can see from the table, the western area where the capital is needs 45.12% of the drug. However, western area covers the area of less than 10% compare to the total land area. And the condition of disease is as follow:

Figure 7

3.2.2Methods of the Medicine Delivery

Because the railway and road system of Sierra Leone are defective and out-dated, the medicine was firstly delivered to the capital city Freetown, then by the air transportation delivering to other airports. Afterwards, the medicine was delivered to

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the medical center in the Ebola serious area. The situation of airports in Sierra Leone is shown in the table below:

Table 8 1 2 3 4 5 6 7 8 9 10 Airport Bo Airport Bonthe Airport Daru Airport Gbangbatok Airport Hastings Airport Kabala Airport Kenema Airport Lungi International Airport Sierra Leone Airport Yengema Airport Location Bo Bonthe Daru Gbangbatok Freetown Kabala Kenema Freetown Sierra Leone Yengema Size Small Small Small Small Small Small Small Medium Small Small 4. Sensitivity Analysis and Improvements

4.1 Sensitivity Analysis

Model one we use SIR model to simulate the development of Ebola virus, and through two variables λ(daily infected rate) and μ(daily cured rate) to describe the situation of the disease. We can figure out the number of healthy people and infected people every day, there are many factors affecting the changes of healthy and infected number. For the convenience of calculation, we ignore the death of patients, and assume the total population is constant, and the daily cured rate is defined by ourselves, and the disparity between real value and the calculated one may be obvious. What’s more, we assume the medicine is very effective, all of the patients take the medicine will be cured, and we don’t consider the time of treatment, these problems could make our model have some drawbacks and less accuracy. 4.2 Improvements

For model one, according to analysis before, two measures can be taken to restrain the spread of the disease, one is improving health and medical level, in the other words is dropping the daily contact rate λ and improving daily cured rate μ; the other method is herd immunity, that is improving the original rate of the removed r0. We can see that in the SIR model, σ=λ/μ is a very important parameter. In reality, the value of λ and μ is difficult to estimate, but when an infectious disease is over,

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we can get the value of s0 and s∞, and we neglect the parameter i0because of its small value, so we can have the result of σ:

??lns0?lns? (7)

s0?s? We can use the change of σ to analyze the development of the disease instead of λ and μ.

5. Model Evaluation

5.1 Strengths

● Model is simple and easy to understand, and we innovatively define the suspicious degree, making us to carry out a quantitative analysis of suspects.

●Processes the data and make a variety of charts, simple and intuitive shortcuts

●Model established in this paper and the actual closely, give full consideration to the different stages of the reality of the situation, so that the model is more realistic 5.2 Weaknesses

● In order to make the calculation is simple in the model, so that the results obtained are more ideal, ignoring the minor factors.

●For some data, we carried out a number of necessary treatment, which will bring some errors.

6. Reference:

[1]. Xuan Zhou, Junquan Song, Xuejun Wu. Introduction and Improvement of Mathematical Contest in Modeling[M]. Zhejiang:ZHEJIANG UNIVERSITY PRESS.2012.Page 201 to 205.

[2]. Qiyuan Jiang, Jinxing Xie, Jun Ye. Mathematical Model[M].Beijing:HIGHER EDUCATION PRESS.2011.Page 136 to 145.

[3]. Ebola Situation Report[DB/OL],http://apps.who.int/ebola/ [4]. Sierra Leone—Provinces and

districts[EB/OL].http://schools-wikipedia.org/wp/s/Sierra Leone.htm

[5].HongqingZhou,ZhuanXu. A Mathematical Model of Ebola Virus Infection Numbers [A].

[6].Themap of Sierra Leone[Z/OL].http://www.onegreen.net/maps/HTML/49248.html

Appendix:

BasicMatlabprogram： >>function y=ill(t,x) a=0.0339;b=0.2;

y=[a*x(1)*x(2)-b*x(1),-a*x(1)*x(2)]';

ts=0:100

x0=[0.00103981,0.99896019]; [t,x]=ode45('ill',ts,x0); [t,x] plot(t,x(:,1)),grid on; plot(t,x(:,2)),grid on; plot(x(:,1),(:,2)),grid on;

Data recording:

Detailed data of Table 1: time proportion proportion New in fections new infections Contact interval of health ofinfection at period of time per day number /% /% /λ 0 13 19 62 32 11 9 14 7 7 10 9 9 12 9 12 7 7 0.9999963 0.9999888 0.0000037 0.0000112 0 63 99 357 724 388 416 925 892 422 1477 1314 1219 1535 3929 528 1045 1056 0.0 4.8 5.2 5.8 22.6 35.3 46.2 66.1 127.4 60.3 147.7 146.0 135.4 127.9 436.6 44.0 149.3 150.9 — 0.0339 0.0215 0.0096 0.0171 0.0206 0.0217 0.0217 0.0323 0.0138 0.0253 0.0204 0.0162 0.0129 0.0323 0.0031 0.0099 0.0095 0.99999338 0.00000662 0.99997227 0.00002773 0.99993875 0.00006125 0.99992079 0.00007921 0.99990153 0.00009847 0.9998587 0.0001413 0.99981741 0.00018259 0.99979787 0.00020213 0.99972949 0.00027027 0.99966866 0.00033134 0.99961222 0.00038778 0.99954116 0.00045884 0.99937315 0.00062685 0.9993487 0.0006513 0.99930032 0.00069968 0.99926384 0.00073616

5 6 7 7 7 7 7 7 7 7 0.99920782 0.00079218 0.99917093 0.00082907 0.99914032 0.00085968 0.99914032 0.00085968 0.99906616 0.00093384 0.99904111 0.00095889 0.99901569 0.00098431 0.99899588 0.00100412 0.99897884 0.00102116 0.99896019 0.00103981 942 797 661 801 801 549 549 428 368 403 188.4 132.8 94.4 114.4 114.4 78.4 78.4 61.1 52.6 57.6 0.0110 0.0074 0.0051 0.0062 0.0057 0.0038 0.0037 0.0028 0.0024 0.0026

Detailed data of Table 3 and Figure 4： t/day i 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.00103981 0.00102316642901013 0.00100678807840512 0.000990670759500238 0.000974810348560671 0.000959202785833016 0.000897812263961328 0.000840349967987889 0.000786564647943243 0.000736221110535207 0.000689099194662761 0.000613536145331262 0.000546258563639528 0.000486358030159459 0.000433025708102361 0.000385541430314833 s 0.99896019 λ 0.05 0.05 x 1122.9948 1105.019743 0.998925260274163 0.998890890858391 0.99885707278534 0.998823797230521 0.998791055510049 0.998759629105913 0.998730214953287 0.998702684180303 0.998676916171759 0.998652798039722 0.998630773112218 0.998611163739899 0.998593704971626 0.998578160923393 0.998564321588228 0.05 1087.331125 0.05 1069.92442 0.05 1052.795176 0.05 2071.878017 0.1 0.1 0.1 0.1 0.1 1939.27449 1815.155931 1698.97964 1590.237599 2232.681391 0.15 1987.857111 0.15 1769.877746 0.15 1575.800018 0.15 1403.003294 0.15 1665.538979

16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 0.000326522803194833 0.000276524757700488 0.000234190073204331 0.000198354202974809 0.000167990890587151 0.000142267048513734 0.000120492636797839 0.000102054102458839 0.998552297149039 0.998542110696561 0.998533485653142 0.998526184714197 0.998519998763799 0.998514758053685 0.998510321985987 0.998506565549964 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 1410.57851 1194.586953 1011.701116 856.8901569 725.7206473 614.5936496 520.528191 440.8737226 373.3654233 316.2044903 267.8184648 226.8216289 192.0891055 162.6891731 137.7933896 116.6938775 98.82841797 83.70553732 70.8921291 60.03661375 50.84778302 43.06670871 36.47214531 30.88837283 26.16178262 8.64271813147248e-05 0.99850338192991 7.31954838669551e-05 6.1995014996132e-05 5.2505006689096e-05 4.44650707065251e-05 3.76595308026266e-05 3.18966179526099e-05 2.70124716405719e-05 2.28769486031412e-05 1.93762817874903e-05 1.64102150684292e-05 1.38973642942416e-05 1.17703201425963e-05 9.96914553387301e-06 8.44262622827315e-06 7.15008630285132e-06 6.05596819973069e-06 0.998500686290367 0.998498404471604 0.99849647112175 0.998494833191077 0.998493446739497 0.998492272697839 0.998491277682991 0.998490435181157 0.998489722014915 0.998489117759465 0.998488605834785 0.998488172507912 0.998487805568192 0.99848749458205 0.998487231262836 0.998487008366639

42 43 44 45 46 47 48 49 50 51 5.12893718622922e-06 4.34355693023827e-06 3.67875889630616e-06 3.11580997802901e-06 2.63870336756512e-06 2.23472597258083e-06 0.998486819509846 0.998486659510489 0.998486524076426 0.998486409391299 0.998486312194157 0.998486229895059 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 22.15700864 18.76416594 15.89223843 13.46029911 11.39919855 9.654016202 8.176742325 6.925158686 5.865014608 4.96724847 1.8927644271255e-06 0.998486160229962 1.60304599206071e-06 1.35764227037617e-06 1.14982603466862e-06 0.998486101207942 0.998486051213808 0.998486008877073

Population and Infected People in Different District of Sierra Leone: Aggregate Aggregate District Bombali District Koinadugu District Port Loko District Tonkolili District Kambia District Kenema District Kono District Kailahun District Area/km2 7985 12121 5719 7003 3108 35936 6053 5641 3859 15553 Eastern Province Northern Province Province Population 408390 265758 455746 347197 270462 1747553 497948 335401 358190 1191539 Number of Infections 990 104 1334 449 151 3028 502 247 565 1314

Aggregate Bo District Bonthe District Pujehun District Moyamba District Western Area Urban District Western Area Rural District 5474 3468 4105 6902 19949 3568 Western Area 4175 7743 79181 463668 129947 228392 260910 1082917 1272873 314 5 31 205 555 2041 Southern Province Aggregate Total 174249 1447122 5469131 1121 3162 8059

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