（School of Physics and Electronic-Electrical Engineering， Ningxia University， Yinchuan 750021，China）

Abstract： Since December 2013，Ebola outbreak in west Africa again， and the year’s disease was the most serious Ebola serious， which arouse the global attention. We are consider that among the countries where outbreak Ebola disease， Nigeria has the most serious problem. So we choose Nigeria as our object， establish differential equation and take the initial value to calculate， expecting rate of change in the number of Ebola infections for the country from 2006 to 2015， in the absence of any additional drugs. Clearly giving the inspecting time， we can get the change of the number of healthy people and the patients.

Key words： Ebola； Develop drugs； Nigeria

1 Introduction

The deadly hemorrhagic fever Ebola was first discovered in 1976， and it has haunted the public imagination for twenty years， Since December 2013， an ongoing outbreak of Ebola in West Africa has infected at least 567 people in Guinea， Sierra Leone and Liberia， including 350 who died， according to the World Health Organization[1-3].

2 The Description of the Problem

Choose the country you believe to be most critical in terms of Ebola in Africa. Build a model to approximate the expected rate of change in the number of Ebola infections for the country from 2006 to 2025， in the absence of any additional drugs. Fully explain your model and the assumptions that underlie your model. In addition，， estimate the cost of US to deal with the crisis.

3 Building Models

Searching for the data， we know that there were 400 people infected by Ebola in 2006， and the total population in Nigeria is about 4.3 million. Comparing with other countries where there were Ebola cases， Nigeria’s problem was the most serious， so we choose Nigeria to be most critical in terms of Ebola in Africa， and establish differential equation model， studying the expected rate of change in the number of Ebola infections for the country from 2006 to 2025。

3.1 The Foundation of Model

According to the assumption， every person can infect s（t） susceptible into patient， because the total number of patient is Ni（t），every year there areNi（t）s（t） susceptible infected， so Nis is the increasing rate of number of patients Ni，the rate of dead for each year is ，so：

（1）

Because the reduction of susceptible equals to the susceptible infected every year， so：

（2）

And also

s（t）+i（t）+r（t）=1 （3）

the proportion of patient in the initial time（t=0）is ，the proportion of susceptible is

（4）

，

After the analysis ，，

According to the equation（3），we get the result as follows：

3.2 Analysis of the Result

According to the result， Nigeria is infected by Ebola virus， in the initial time， which is 2006， there were 400 people infected， almost accounting for 0.1% of the total population. When there weren’t drugs to cure the disease， the illness seriously deteriorated.

The change of the susceptible as the dotted line in figure1shows， the number constantly decrease， and finally it maintain a constant at lower than10%， the reason is because the susceptible infected by the patient， the number will constantly decrease.

From 2006 to 2015， the change of the number of the patient as the solid line in figure 1shows， the number increase at first， then it decreases. The reason is that the patient will infect the susceptible， resulting in the increasing of the number of the patient. On the other hand， the patient will die， so the number will decrease again. From 2006 to 2013， because there are many susceptible and less patients， the susceptible infected increase， and the patients who die have a small number. Which means， the rate of the increasing number patients is greater than the decreasing number of the patients， so the number of patients increase？ From 2013 to 2015， the proportion of the susceptible decrease and the number of patients increase， during this period， the rate of the people dying is greater than the susceptible infected， so the number of patients decrease.

Around 2013， the number of patients is of the most number， at this time ， the rate of susceptible infected is the biggest， so among the change of the number of the susceptible， around the middle of 2013， the curve of the susceptible is of the steepest， which means， the number is the fastest declined.

4 Conclusions

we choose Nigeria as our object， establish differential equation model， approximate the expected rate of change in the number of Ebola infections for the country from 2006 to 2015， in the absence of any additional drugs. Clearly giving the change of the healthy people and the patient as the change of time during the inspecting time. And estimate the cost of US to deal with the crisis.

References

[1] Zhang Fa， Li Lu， Xuan Hui-yu . Survey of transmission models of infectious diseases. System s Engineering-Theory & Practice. Vol.31 ， No .9 SePt.2011.

[2] Liming-jing ，Zhang zhen-ji. Applications of Matlab in Mathematical Model of the Economy. China traffic Forum . Vol.3 ， No .7 Nove.2013.

[3] Cao Zhi-dong，Zeng Da-jun，Zheng Xiao-long. Characteristics of SARS popular with law of spatio-temporalpropagation. China Science： Earth Science. The sixth period Vol.40.2011.