










































  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 
 
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. 

MODELS FOR  
PREDICTING GLOBAL 

PLASTIC WASTE  

YUEXING HAO, 
GLENN SHAFER (FACULTY ADVISOR) 

 
 
 

✵ ABSTRACT  

For more than half a century, plastic prod-
ucts have been a part of people’s lives. When plastic 
waste is thrown into nature, it can cause a sequence 
of dangerous effects. Previous researchers esti-
mated that global plastic waste in 2020 will be more 
than 400 million tons. To reduce plastic waste, they 
built scientific models to analyze the sources of plas-
tic and provided solutions for regenerating these 
plastic wastes. However, their models are static and 
inaccurate, which may cause some false predictions. 
In this paper, we first observe the distribution of the 
real-world plastic waste data. Then, we build simple 
exponential growth model and logistics model to 
match these data. By testing different models on our 
plots, we discover that the SELF-ADAPTIVE MODEL is the 
best to describe and correctly predict our future 
plastic waste production, as this model combines 
the benefits of SIMPLE EXPONENTIAL GROWTH MODEL and 
the LOGISTIC MODEL. The self-Adaptive model has the 
potential to minimize the error rate and make the 
predictions more accurate. Based on this model, we 
can develop more accurate and informative solu-
tions for the real-world plastic problems.  
 

1 INTRODUCTION 
Plastic waste became a serious problem in 

the 21st century. According to data from 2017, sci-
entists estimate that human beings produced 
around 8300 million metric tons (Mt) of virgin plas-
tics. As of 2015, approximately 6300 Mt of plastic 
waste had been generated. Of this waste, only 

around 9% had been recycled[1]. Most plastic prod-
ucts are sent directly to landfills or make their way to 
the ocean. It may take one hundred to thousands of 
years for plastic products to decompose, and the 
available places for landfill waste are becoming 
fewer and fewer[2,3]. Therefore, we should prevent 
this global crisis from becoming more serious. 

In this paper, we will introduce three models 
and find the model best suited for better prediction 
making. Based on the previous data, we will consider 
more factors and make the model more adaptive to 
the real-world situations. There are some research-
ers who modeled past plastic consumption and pre-
dicted the future. However, our model will be more 
accurate and have better data visualization.  

 

2 METHODOLOGY 
To estimate the maximum levels of single-

use or disposable plastic product waste, we should 
first know the constraints and extent. The constraints 
are the EFFICIENCY of the natural environment or the 
waste disposal companies at processing plastic pol-
lution. If their efficiency of disposing plastic products 
is higher than the rate of people producing plastic 
waste, there will be no plastic pollution at all. There-
fore, we consider the constraint to be the availability 
of processing plastic waste. The extent is the RANGE of 
our plastic waste, since our plastic waste cannot in-
crease to infinity. We should set an upper bound and 
lower bound for the weight of our waste. 

The hard part of this problem is that if na-
tions and governments do not accurately know their 
nation’s total production of plastic waste, it increases 
the difficulty of managing single-use plastic waste 
comprehensively. The composition of modern plas-
tic waste is complex because the waste may contain 
both single-use and multi-use plastics. However, we 
can estimate the disposable plastics product usage 
by finding the characteristics of plastics waste’s his-
torical change. Then, based on this trend, we can 
predict the quantity change of plastic waste in the fu-
ture.  

In addition, there emerges another difficult 
aspect of this problem: there are many influencing 
factors regarding the generation of plastic waste. 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

There is no simple pattern or law that can be deter-
mined by looking at the data. We should, therefore, 
develop a model which does not need a typical data 
distribution law and use less theoretical calculations 
that can still make an accurate prediction. That is to 
say, we may not need to add much mathematical 
functions or calculations inside the model, but the 
model can adaptive the different situations by itself. 
Therefore, in this paper, we employ the SELF-ADAPTIVE 

MODEL to estimate and analyze the data on plastic 
waste production over the past 5 to 10 years, and 
then predict its production in the next 30 years. It is 
called a self-adaptive model because this model 
does not have specific relationships among factors 
in a system. We cannot clearly indicate the relation-
ships between the factors in the data, such as the in-
fluences of countries’ rules, population density, lev-
els of development. Thus, it is a good choice to use 
the self-adaptive model for this problem.   

 

3 BUILDING PLASTIC POLLUTION MODELS 
In this part, we first define plastic pollution 

into seven kinds of waste: Textiles, Transportation, 
Packaging, Electronic, Consumer Products, Indus-
trial Machinery, Building & Construction. These dif-
ferent kinds of waste will be considered as different 
variables. Currently, plastic packaging is the greatest 
source of primary plastic production. Because of the 
rapid development of online shopping and delivery 
services, the demand for plastic has increased rap-
idly in just a few years. Thus, we can find some con-
nections between these variables and the total 
amount of plastic waste[2].  

To estimate the maximum mitigation levels 
for plastic waste without destroying the environment, 
we take the seven kinds of waste from different kinds 
of single-use or disposable plastic waste into ac-
count. Correspondingly, we consider each plastic 
waste factor’s weights, the resources to process, the 
total budget, and the cost of the environmental dam-
age it causes. We also set the damage levels for the 
environment to make our models more accurate. Af-
ter comparing each factor, we find the best combi-
nation to maximally mitigate the dangerous effects 
that plastic waste brings about.  

 

i. The Simple Exponential Growth Model 
Before the 21st century, from the 1960s to the 

1990s, the simple exponential growth model (also 
called as Malthusian Model) is a great model for de-
scribing the exponential growth of plastic waste[5]. 
The model could perfectly match with the data and 
creates great visualization.  

However, after fitting the data, we discov-
ered that plastic waste’s rate of increase is not as fast 
after 2000. This is because nations and governments, 
as intervention variables, have paid more attention 
on this global crisis and already taken some 
measures to prevent more plastic pollution. To show 
the intervention variables, we decided to switch our 
models to be more accurate.  

 

FIGURE 1: Global plastic production per year. As shown in 
the figure, plastic waste was largely static from 1950-1960. 
After this, plastic products became prevalent in humans’ 
lives, and plastic waste increased rapidly from 1960 on-
ward. There were some significant increases between the 
1970s and 2000s[4]. 

TO ESTIMATE THE MAXIMUM  
MITIGATION LEVELS FOR PLASTIC 

WASTE WITHOUT DESTROYING THE 

ENVIRONMENT, WE TAKE THE SEVEN 
KINDS OF WASTE FROM DIFFERENT 

KINDS OF SINGLE-USE OR DISPOSA-

BLE PLASTIC WASTE INTO ACCOUNT. 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

ii. The Logistic Model 
The logistic model was developed by Bel-

gian mathematician Pierre Verhulst[8]. He came up 
with this model’s idea by thinking about the rate of 
population increased may be limited. It may be af-
fected by many other factors, which may not always 
increase. We agree with the thoughts of Varhulst: the 
global plastic waste may not increase after reaching 
some points. Therefore, we used Logistic Model 
here. 

However, after 2015, we observe that the 
model’s coefficient is not a constant anymore. The 
curve’s rate of increase will change because of inter-
vention variables. That is to say, the model’s coeffi-
cient should be a flexible number. To make the co-
efficient adjustable, based on our Logistic model’s 
differential equation, we created another self-adap-
tive differential equation. 

 
iii. The Self-Adaptive Model 

Based on the differential equation from last 
section, we develop a more advanced model called 

a SELF-ADAPTATION model, for which the coefficients are 
flexible and easy to change. Some researchers call 
this kind of model a grey model, since it can be flex-
ible between black model or white model. Under 
this model, we create a self-adaptation differential 
equation, which can be easily adapted in different 
conditions. By employing this model, our predic-
tions are close to reality and the error is small.  

Since the simple exponential growth 
model’s predictions between 1950-1970 and Lo-
gistic model’s predictions before 2010 are accurate, 
we will employ both models in our new self-adaptive 
model. The coefficient of plastic waste before 2010 
is nearly static[4]. However, after 2010, when more 
countries and nations began to ban or limit the use 
of single-use or disposable plastic products, the co-
efficients of the plastic waste curve began to de-
crease. After 5-10 years, the self-adaptive model will 
change the coefficients, which makes it more adapt-
able to real-world data. 

After comparison of these models, we chose 
to employ a self-adaptive model as our main model 
to predict future plastic waste production.  
 

4 SELECTION OF THE MODELS 
The criteria of model’s selection are based 

on the accuracy of the models. (See APPENDIX 1) 

 Firstly, we started by building a SIMPLE EXPONENTIAL 

GROWTH model and trying to find a valuable result. 
Before the 21st century, around 1960s to 1990s, 
the Malthusian model is considered a great 
model for describing the exponential growth 
since the function is proportional to the speed to 
which the function grows.  

 However, after fitting the data, we discovered that 
the plastic waste’s increasing rate is not that fast 
anymore. This is due to the fact that nations and 
governments, as intervention variables, paid 
more attention on this global crisis and already 
took some measurements to prevent more plas-
tic pollutions. To show the intervention variables, 
we decided to switch our models to a more accu-
rate model.  

FIGURE 2: The Logistic Model for fitting the real-world data. 
This plot shows that our logistic model is perfectly suited 
to the real data, where the x-axis represents the year, and 
the y-axis represents plastic production. Compared to our 
previous model, the logistic model is closer to the real-
word data from 1960 to 2015. 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

 Secondly, we built a LOGISTICS model. The logistics 
model matches with our real data from 1960-
2015. However, after 2015, we found out that the 
model’s coefficient is not a constant anymore. 
The increasing rate will also change because the 
intervention variables. That is to say, the model’s 
coefficient should be a flexible number. To make 
the coefficient adjustable, based on our Logistics 
model’s differential equation, we created another 
self-adaptive differential equation.  

 Lastly, we move our eyes to the SELF-ADAPTIVE 

model, in which the coefficients are flexible and 
easy to change. Using this model, we created a 
self-adaptation differential equation. By employ-
ing this model, our predictions and the reality are 
similar, and the error is small.  

Therefore, after comparisons, we chose to employ 
the self-adaptive model as our main model to pre-
dict the future plastic waste productions.  
 

5 RESULTS 
To examine the accuracy and efficiency of 

our models, we compared each year’s plastic waste 
and the data calculated from each model. All these 
three models' error rates are low in the beginning 
before the 21st century[4]. Then, depending on the 
different functions, each model has some deviation 
from the real-world data. By graphing all the models 
(FIGURE 3), we can  easily see the differences between 
the models and the best model for future prediction. 
Therefore, we concluded that the self-adaptive 
model is the most accurate one, performing much 
better than the simple exponential growth model or 
logistic model.  

The strength of our model is that we take 
three models and use them to continue to improve 
the accuracy of our model. We built up the first sim-
ple exponential growth model, which gave us a gen-
eral idea about the trend of plastic waste. Based on 
the prediction model, we came up with another Lo-
gistic model. By employing the Logistic model, the 
results perfectly match our data. We then tried to use 
Logistic model to predict our future data; however, 
the results deviated from the prediction data. We fig-
ured out that the problem might be the coefficients 

of our Logistic model, which should not be a con-
stant. Since the coefficients are flexibly changing, we 
switched our model to a self-adaptive model.  
 

6 DISCUSSION 
There are a number of plastic waste preven-

tion techniques, which can commonly be summa-
rized as the 4 Rs: reduce, reuse, recycle, and recover. 
Before, people summarized this technique as 3Rs, 

FIGURE 3: The prediction of different models. In this figure, 
we can visually compare the prediction results of these 
three models. Blue dots represent real-world data[4], and 
while yellow dots represent prediction data made by pre-
vious researchers[5]. We can clearly see that a blue linear 
line of a trend. This line just shows a trend of the future 
plastic waste but has no meaning to the predictions. The 
simple exponential growth model (RED) provides a great 
example of the maximum level of plastic pollution that the 
system can handle. It could perfectly suit current data, but 
not future data. The logistics model (PURPLE) shows the ex-
ponential growth of the prediction. After 2030, the logis-
tics model deviates with the real-world data. The self-
adaptive model (GREEN) displays the flexible curve which 
suits not only the current data, but also future data. By us-
ing a self-adaptive model, our predictions can be more de-
tailed and precise. 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

which did not include recovery[6]. However, more 
and more people are realizing that it is not enough 
to recycle. They also need to reduce and reuse recy-
cled plastics.  

The total population of the above 15 coun-
tries are around 5 billion, including the development 
and developed countries. From figure 4, we find out 
that developing countries usually produce less plas-
tic waste than developed countries. All nations are 
responsible for managing their waste production. 
For example, the countries above the trend should 
make more actions to prevent increasing plastic 
waste further. Governments can design laws to pre-
vent highly plastic polluting companies from pro-
ducing single-use or disposable plastics. They can 

also reduce taxes for those companies that have 
plastic recycling technology and produce multiple-
use or biodegrade plastic products. These actions 
could limit single-use or disposable plastic produc-
tion. Moreover, they would provide a cleaner and 
healthier plastic cycle.  

Since plastic pollution has become a global 
crisis, governments, companies, and human beings 
have realized the urgency of recycling plastic prod-
ucts and reducing single-use or disposable plastic. 
In our self-adaptive model, we predict that the rate 
of increase of plastic waste in 2030 and 2040 will be 
much slower than the previous year’s rates∎ 

 

FIGURE 4: The relationship between GDP and Plastic Waste. We choose 15 countries from different regions and development 
levels[4]. The sizes of the circles represent the total plastic waste of that country. We can conclude from the graph that when 
GDP goes up, plastic waste per year also increases. In the other word, the total plastic wastes have some connections with the 
country’s degree of development. 



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

7 REFERENCE 
[1] Geyer, R., Jambeck, J. R., & Law, K. L. (2017). Production, use, 

and fate of all plastics ever made. Science Advances, 3(7), 
e1700782.  

[2] Jambeck, J. R., Geyer, R., Wilcox, C., Siegler, T. R., Perryman, 
M., Andrady, A., … & Law, K. L. (2015). Science, 347(6223), 
768-771. 

[3] Li, W. C., Tse, H. F., & Fok, L. (2016). Plastic waste in the ma-
rine environment: A review of sources, occurrence and ef-
fects. Science of the Total Environment, 566, 333-349. 

[4] Hannah Ritchie and Max Roser (2020). Plastic Pollution. Pub-
lished online at OurWorldInData.org.  

[5] Eriksen, M., Lebreton, L. C., Carson, H. S., Thiel, M., Moore, 
C. J., Borerro, J. C., ... & Reisser, J. (2014). Plastic pollution in 
the world's oceans: more than 5 trillion plastic pieces weigh-
ing over 250,000 tons afloat at sea. PloS one, 9(12), e111913. 

[6] Lebreton, L., Andrady, A. (2019).  Future scenarios of global 
plastic waste generation and disposal. Palgrave Commun 5. 

[7] Cramer, J.S. (2002) The Origins of Logistics Regression. 
Chapter 9 of Logit Models from Economics and Other Fields, 
Cambridge University Press. 

 
 
 
 

  



  ARESTY  RUTGERS UNDERGRADUATE RESEARCH JOURNAL, VOLUME I, ISSUE II 
 
 
 

 

8 SUPPLEMENTARY TABLES 
 
 

 
 
 
 
9 SEE ALSO 

HTTPS://PREZI.COM/VIEW/BJDEXJKYPKMAV4ZXQ2TZ/ 

YEAR 
PLASTIC WASTES 

(TONNES) 
SIMPLE EXPONENTIAL 

GROWTH MODEL ERROR (%) 
LOGISTICS 

MODEL ERROR (%) 
SELF-ADAPTIVE 

MODEL ERROR (%) 

1960 
1970 
1980 
1990 
1995 
2000 
2005 

8,000 
35,000 
70,027 

120,383 
152,068 
213,209 
263,002 

- 
35,110 
70,069 

120,443 
151,099 
213,028 
263,799 

- 
0.3143 
0.0599 
0.0498 
-0.6372 
-0.0849 
0.0303 

- 
35,069 
70,090 

120,409 
152,430 
213,790 
262,997 

- 
0.1971 
0.0899 
0.0216 
0.2381 
0.2725 
-0.0019 

 

- 
34,980 
70,431 

120,011 
151,995 
213,563 
263,503 

- 
-0.0571 
0.0769 
-0.0390 
-0.0480 
0.1717 
0.1905 

2010 
2011 
2012 
2013 

… 
2017 
2018 
2019 

313,000 
325,089 
338,797 
352,642 

… 
368,782 
398,603 
442,488 

320,263 
329,994 
380,863 
423,569 

… 
457,592 
482,905 
540,000 

2.3204 
1.5088 

12.4163 
20.1130 

… 
24.0820 
21.1494 
22.0372 

320,067 
324,989 
339,002 
353,059 

… 
369,728 
399,766 
444,050 

0.2257 
-0.0308 
0.0605 
0.1183 

… 
0.2565 
0.2918 
0.3530 

313,067 
325,209 
338,997 
352,368 

… 
368,597 
398,645 
442,766 

0.2578 
0.03690.0

590 
-0.0777 

… 
-0.0501 
0.0105 
0.0628 

2020 
2021 
2022 
2023 
2024 
2025 

… 

486,323 
510,360 
546,085 
584,311 
625,213 
668,978 

… 

589,670 
600,678 
634,335 
669,895 
700,000 
724,330 

… 

21.2507 
17.6970 
16.1605 
14.6470 
11.9618 
8.2741 

… 

487,982 
513,480 
546,999 
582,994 
624,785 
670,012 

… 

0.3411 
0.6113 
0.1673 
-0.0543 
-0.6846 
0.1546 

… 

486,373 
510,299 
546,327 
583,994 
625,869 
668,321 

… 

0.0461 
0.0623 
0.0443 
-0.0542 
0.0105 
-0.0982 

… 

2030 715,806 768,450 7.3545 715,949 0.1997 624,330 0.0529 

2040 876,893 1000,785 14.1285 879,323 0.2771 823,780 0.0947 

2050 1,275,997 1,868,544 46.4379 1,276,544 0.4264 1,276,544 0.0426 

SUPPLEMENTAL TABLE 1: The Comparison of Total Plastic Wastes and its Simulation based on three models 

https://prezi.com/view/BJdeXjKyPkmaV4zXq2tz/

