多因素量化国家脆弱性的数学建模与案例研究资源-CSDN文库

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Team # 93840 Page 1 of 19

Motivated to measure a country's stability quantitatively and more accurately, our team

builds a mathematical framework to identify the current status of a country. In the paper, we

introduce a composite index processing comprehensive datasets that consist of di erent factors

including economy, politics, demographics and climate change.

With the composite measure, we build a dynamic system simulating the uctuation of the

market as a result of the variations in di erent sectors. This system not only describes the current

fragility of a country facing potential alternation in social and environmental factors, but also it

predicts the equilibrium states that the country would approach overtime.

Moreover, we propose a bifurcation plot that depicts the tipping points between three states

of a country in terms of its fragility: stable state, vulnerable state, and fragile state. We then

further apply our model and bifurcation plot in real-life case analyses with three selected

countries, Syria, Cuba and New Zealand.

After calibrating parameters and comparing di erent factors in each country, we nd out that

climate conditions play a signi cant role in Syria's fragile state due to factors such as limited

water resources and food supply. We also nd that factors of droughts and occurrence of natural

disasters in Cuba caused huge market losses and Cuba would reach the tipping point under

appropriate human intervention.

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Team # 93840 Page 2 of 19

1 Introduction

Climate change includes increased droughts, shrinking glaciers, temperature rise and sea

level rise. Despite a scienti c consensus on global warming, climate change denial and doubts

still exist and the impacts of climate change and the extent to which it is caused by humans are

suspected. In our paper, we build a mathematical framework to determine a country's fragility

with a composite measure considering multiple factors including economic, political and

demographic indicators and climate change. In section 6, we select three countries, Syria, Cuba

and New Zealand to do case studies and further analyze the idea of tipping points in the speci c

contexts. In section 7, we examine the e ects of human intervention and estimate the total cost of

intervention based on our model and research. In section 8, we discuss our limitations and

strengths, consider the scenarios for smaller \states" and larger \states", and talk about potential

future research on this topic and our framework.

2 Assumptions

Our framework measures the market impacts of di erent factors such as climate change,

economic status, political stability and demographic pro les in the unit of US dollars

because we think it is more e cient to quantify and examine the extent of e ects.

We de ne the state as a country for consistency and data collection purpose.

We assume all data we obtain are trustworthy since all of sources are reliable. Thus, we are

con dent that our metrics can re ect the accurate condition.

3 Framework

3.1 De ning Fragility

Before devising our model, we rst de ne three possible states of a country: stable state,

vulnerable state, and fragile state.

Stable state A stable country should be less likely to be in uenced by the incidents such as

economic downturns, natural disasters, or political instability. Even if there is a crisis, a stable

country can quickly recover and return to its equilibrium state.

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Team # 93840 Page 3 of 19

Vulnerable state A vulnerable country is more susceptible then a stable country to the

changes in the economy, politics, demographics and climate. A damaging event could cause the

country leave its current state and gradually become a fragile state; a favorable event could, on

the contrary, lead the country approach to the stable state.

Fragile state A fragile country is the currently experiencing uctuations in economy and

politics. It does not possess a strong economy or a well-regulated society. As a result, any small

turbulence could bring large impacts on all factors. Moreover, even if the country manages to

recover from these disturbances, it can only resume to its previous fragile state.

3.2 The Model

To quantify a country's fragility, we use a dynamic system, in terms of money (M), to

estimate the impacts of changes in di erent factors on a country. However, we believe that money

is not the sole predictor of the fragility of a country. Thus, in our model, we incorporate factors

including economy, politics, demographics and climate.

M = f(E; P; D; C)

(1)

Here, M is a function of E; P; D; and C, where M represents the market impact of those factors,

and E, P , D, C are the economic, political, demographical and climate change metrics

respectively. In this way, we could comprehensively analyze a country's capability to combat

unexpected events categorized under di erent sectors. We achieve this simulation by studying

how the variation in one parameter would in uence the overall fragility of the society.

Further developing our model, we realize that the derivative of M is an autonomous function,

that is growth rate of the market is not dependent on time. Yet, the growth rate of the market is

described as the positive impact minus the negative impact.

growth rate = positive($) negative($)

(2)

The positive impact considers the natural growth of the market itself accompanied with a limited

capacity which varies depending on the parameters. The negative impact is composed of human

intervention, disturbing climate change and other unfavorable variation in the

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Team # 93840

Page 4 of 19

parameters that we have de ned.

′

(M) = m

M(1

); g

′

(M) =

(3)

+ M

Inspired by the outbreak system by Ludwig et al. (1978), we obtain the functions above. p

′

(M)

represents the market growth with limited capacity, where m

describes the growth rate, m

represents the maximum of market capacity, and k is a scale factor that measures how economy,

politics, demographics and climate change would a ect the actual limit of the market. To come up

with the value of k, we use a composite index consisting of metrics in economy, politics,

demographics and climate change. g

′

(M) represents the negative impact that could potentially

slow down the market growth. In the early development stage, M is small and the negative

market impact would only show signs. However, when the market exceeds a critical level A, the

negative impact would turn on quickly. This happens when the harmful events have built up to

an extent that they cause a chain of reactions and the impact would nally reach to its limitation B.

Therefore, we have the whole model:

= m

M(1

)

(4)

+ M

In order for us to examine the model more easily, we have converted the function into a

dimensionless form so that there are only two parameters, r and s.

Next step, we de ne all parameters and the techniques of processing relevant data.

4 Metrics for Assessing Fragility

Our metrics are similar to indicators used in the Fragile States Index. But, instead of rating

those factors, we target to collect both quantitative and qualitative data by coun-try and by year.

Besides, our metrics will be more concise because we nd that there are some overlapping

variables in FSI. For example, both Factionalized Elites of the Cohesion indicators and Uneven

Development in Economic indicators have considered the wealth dis-tribution and tries to assess

the equality of wealth (Marshall and Cole, 2017). In the end, using RStudio, we process all the

datasets and obtain a composite index.

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Team # 93840 Page 5 of 19

4.1 Climate Change

Climate change is expected to have negative impacts on human societies and economies,

which may bring huge economic losses.

Occurrence of natural disasters

EM-DAT contains data on the occurrence and e ects of di erent types of natural disasters

worldwide from 1900 to present. However, the data is not publicly available. So we use

probabilistic risk results provided by UNISDR. The probabilistic risk results provide

results of an estimate of probable loss levels in a country based on historic events. This

data is useful because it considers damages caused by small, moderate and severe events

and obtains a robust metric for risking ranking and comparison.

Deforestation

Food and Agriculture Organization (FAO) contains comprehensive forestry datasets such

as forest coverage, reforestation, burned forest and economic value of the country's

forestry value. Among them, we select the annual Tree cover loss rate by country with unit

of hectare to re ect the deforestation rate as part of climate change.

Droughts/ oods

We use Precipitation Anomaly from World Bank to re ect occurrence of both droughts

and oods. This dataset includes historical monthly precipitation worldwide from 1900

to present.

Rising sea levels/shrinking glaciers

Although sea level rise is a major component of global climate change, it is not a typical

question for all countries. Since rising sea level and green house e ects are tightly related,

we only consider temperature rises instead of rising sea level.

Rising temperatures

We retrieve historical temperature data from World Bank. This data is called Global

Historical Climatology Network version 2 station monthly mean temperatures and station

metadata created by U.S. National Climatic Data Center. This dataset contains quality-

controlled, adjusted monthly mean temperature in unit of degree Celsius.

4.2 Economical Metrics

The economic meta-metrics considers factors related to economic decline within a country.

Except for the economic factors listed below, we have also considered unequal development

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