第三届“认证杯”数学中国
数学建模国际赛
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我们的参赛队号为：1032
我们选择的题目是： C 题
参赛队员 (签名) ：
队员 1：李振
队员 2：耿伟
队员 3：孟峰
参赛队教练员 (签名)： 无
第三届“认证杯”数学中国
数学建模国际赛
编 号 专 用 页
参赛队伍的参赛队号：（请各个参赛队提前填写好）：1032
竞赛统一编号（由竞赛组委会送至评委团前编号）：
竞赛评阅编号（由竞赛评委团评阅前进行编号）：
Team #1032 Page 1 of 25
THE ANALYSIS OF EBOLA VIRUS
Zhen Li Wei Geng Feng Meng
Shandong University of Science and Technology, Qing Dao, China
Abstract:
According to the question, we study the Ebola virus in each aspect. We check the data on
the Internet about Ebola virus outbreak in Africa. Compare with different country`s case of
illness ,rate of death and others factors which affected most serious. Finding the internal
information and the characteristic of problem is not very obvious to us, in other words ,part of
them is unknown to us. Then we find the different mathematical model to solve it. Using the
data we collect to draw the rate curve and predict it`s change in the future.
Focusing on the task#1, we find the finical of America`s costs in different aspects.
Predicting the economic development in drugs for cure Ebola virus. And forecast how much
America will spend to deal with the crisis. Collecting the informations about virus in Africa.
Connected the economy, virus and so many factors, finding the suitable country. Using gray
prediction model and GM(1,1) model to build the codes in MATLAB then draw the curve of
different factors.
Task#2 is refer to the Polynomial regression curve fitting and we use the Logistic
regression model to solve it. We are fitting the different data them together. Through the two
models we predict the probability for drugs development. At last, we analyze the result from
the Ebola virus. We study at the influence factor of drugs research. Finding the main
influence resource is the virus development spreed, rate of death, deathrate of change. Fitting
three factors into the curve of change.
Focusing on task#3, we build the "reward" policy model describe it impersonality in
every aspect of "reward" policy. After that, on the basis of result of development divided offer
us a new innovate "reward" policy. It excites the company to create bigger social benefit. And
make "reward" policy become better.
In task#4, in line accordance of every company`s scheme dealing with risks of drugs
development and different costs. Through the task assignment model, lower the cost and the
risks of drug development. Making a better optimal assignment to increase the effective of
work.
Key words:
Gray Prediction Model, GM(1,1)Model, Logistic regression model, Generalized Linear
Model, Probabilistic Models, “reward” policy model, Innovative Incentives, Tasking
Matching Model
Team #1032 Page 2 of 25
Contents
1.Introduction.........................................................................................................................3
1.1 The problem itself...............................................................................................................3
1.2 What we faced the annoyance in problems........................................................................4
1.3 Operational research...........................................................................................................4
1.4 Probability theory...............................................................................................................5
2. The Description of Problem............................................................................................5
2.1 The physical truth of Democratic Republic of Congo........................................................5
3. Basis Models........................................................................................................................5
3.1 Gray Prediction Model........................................................................................................5
3.1.1 The Foundation of Gray Prediction Model................................................................5
3.1.2 Gray generating sequence..........................................................................................6
3.1.3 GM(1,1)Model...........................................................................................................7
3.1.2.1 The Foundation of GM(1,1) Model..............................................................7
3.1.4 Analysis of the problem and use the model into result answering............................8
3.1.5 Assumptions(in task#1).............................................................................................8
3.1.6 Solution and Result(in task#1)..................................................................................8
3.2 Logistic Model..................................................................................................................11
3.2.1 The Foundation of Logistic Model............................................................................11
3.3 Polynomial regression curve fitting..................................................................................11
3.3.1 The Foundation of Polynomial regression curve fitting..........................................11
3.3.2 Assumptions(in task#2)...........................................................................................12
3.3.3 The analysis of the problem(in task#2) ...................................................................12
3.3.4 Solution and Result(in task#2).................................................................................13
3.3.5 Analysis of the Result(in task#2).............................................................................15
3.4 On the basis budget prediction assumption model...........................................................15
3.4.1 Assumptions(in task#3)...........................................................................................15
3.4.2 Solution and Result(in task#3)................................................................................15
3.4.3 Analysis of the Result(in task#3).............................................................................17
3.5 On the basis of task matching (allocation) models...........................................................17
3.5.1 The Foundation of task matching Model.................................................................17
3.5.2 Assumptions(in task#4)...........................................................................................17
3.5.3 Solution and Result(in task#4).................................................................................17
4. References..........................................................................................................................22
5. Appendix............................................................................................................................23
5.1 chart(used in the task#2).................................................................................................23
Team #1032 Page 3 of 25
I. Introduction
In order to indicate the origin of Ebola virus problems, the following background is
worth mentioning.
1.1 The problem itself
The deadly hemorrhagic fever Ebola was first discovered in 1976, and it has haunted the
public imagination for twenty years, ever since the publication of Richard Preston’s “The Hot
Zone.” Yet, in all that time, no drug has ever been approved to treat the disease. Since
December 2013, an ongoing outbreak of Ebola in West Africahas infected at least 567 people
in Guinea, Sierra Leone and Liberia, including 350 who died, according to the World Health
Organization. The outbreak appears to be the largest in history, surpassing the 425 cases that
occurred in an Ebola outbreak in Uganda in 2000. People with Ebola are treated with only
general therapies meant to support the ill patient. They might be given fluids (Ebola patients
are frequently dehydrated), or treatments aimed at maintaining blood pressure and oxygen
levels, and treating infections if they develop, according to the Centers for Disease Control
and Prevention. (Supplies of the experimental drug administered to two American patients
have already run out.) The lack of an Ebola treatment is disturbing. But, given the way drug
development is funded, it’s also predictable.
When pharmaceutical companies are deciding where to direct their R & D money, they
naturally assess the potential market for a drug candidate. That means that they have an
incentive to target diseases that affect wealthier people (above all, people in the developed
world), who can afford to pay a lot. They have an incentive to make drugs that many people
will take. And they have an incentive to make drugs that people will take regularly for a long
time—drugs like statins.
This system does a reasonable job of getting Westerners the drugs they want (albeit often
at high prices). But it also leads to enormous underinvestment in certain kinds of diseases and
certain categories of drugs. Diseases that mostly affect poor people in poor countries aren’t a
research priority, because it’s unlikely that those markets will ever provide a decent return. So
diseases like malaria and tuberculosis, which together kill two million people a year, have
received less attention from pharmaceutical companies than high cholesterol. Then, there’s
what the World Health Organization calls “neglected tropical diseases,” such as Chagas
disease and dengue; they affect more than a billion people and kill as many as half a million a
year. One study found that of the more than fifteen hundred drugs that came to market
between 1975 and 2004 just ten were targeted at these maladies. And when a disease’s
victims are both poor and not very numerous that’s a double whammy. On both scores, a drug
for Ebola looks like a bad investment: so far, the disease has appeared only in poor countries
and has affected a relatively small number of people.
It’s not just developing nations that the system disserves, however. In recent years, the
rise of drug-resistant microbes has made the antibiotics we use less effective and has
increased the risk that an infectious disease could get out of control. What people in the West
need, health officials agree, is new drugs that we can keep in reserve against an outbreak that
regular antibiotics can’t contain. Yet, over the past thirty years, the supply of new antibiotics
has slowed to a trickle. “Antibiotic resistance really has the potential to make everything
about the way we live different,” Kevin Outterson, a co-director of the Health Law program at
