My Learning Goal
For my IB Personal Project, my learning goal will be to explore and expand my knowledge in mathematical models that predict the propagation of biological viruses of a controlled location, by analyzing certain variables that would hypothetically make up to predict the spread of a virus. In terms of global contexts, I will be looking at Scientific and Technical Innovation, and it’s influence in the mathematical ambit of algorithmic model production; analyzing how certain mathematical calculations possess a presence in a real-life scenario. I will learn how to determine certain values of the variables present in the model. Furthermore, I will have to learn how to mathematically progress in the different stages of the mathematical model’s production. In addition, I will have to learn how to create an interactive website that can show the mathematical model in a more visually represented ambit. The scientific innovation will be shown by looking into how these mathematical models have influenced the response of governments to biological hazards present in the nation throughout the years recorded in history. This information will be gathered through the study of published papers that explain different models that predict, and by looking into practical ways to easily comprehend the function of these models and the reasoning behind any component present in the formula of the model.
The main goal will be to personally understand the way a mathematical model functions and the reason behind why it works. This is an import goal because I hope that my mathematical skills are high enough to comprehend difficult topics, and overall set a challenge for myself by exploring a more relevant mathematical topic in a daily life context. Furthermore, I will have to investigate how viruses like covid-19, could’ve been better handled by taking into consideration how to reduce the variables in relation to the model of prediction that I have determined. I have investigated the θ-SEIHRD model, a prediction tool used specifically during the covid pandemic, and I’ve come up with the conclusion that a model like the SIR model will be suitable in the hopes of achieving my personal goals and by exceeding the success criteria that sets the boundaries of what I will achieve. To meet the success criteria, I will have to potentially interview individuals that possess knowledge related to the understanding of the mathematical algorithms. I would hope to receive advice from some primary sources, like mathematicians that worked on the discovery of the model, to further increase my knowledge on the topic. Lastly, I would like to develop a skill in producing interactive things utilizing a computer as the machine of production; this would help me build the skills necessary to build a good resume.
As I was choosing the topics for my personal project, I knew from the start that I wanted to figure out a way to connect mathematics to a relevant topic in the present, therefore I thought about what was happening as of right now and I came up with the conclusion that I was going to connect math’s with the covid pandemic. This decision is related to my fascination for biological viruses and how they have impacted different societies. As I progressed in the covid pandemic, questions on how a virus could spread so profoundly came to my knowledge. These questions led to me wonder on how big pandemics could potentially get if the variables were set to certain values. In addition, this resonated with me as I experienced the pandemic on my skin as I grew up a minute part of my childhood, during the presence of a biological virus global quarantine, and I have always had a great wonder in some of the hardest formulas in mathematics.
My relationship with mathematics has been an important thing in me since a very early age. The first instance I remember thinking about mathematics as a concept was when I was in grade 4, and the teacher was explaining the concept of multiplication to the class; and although I found it easy to comprehend, it fascinated me how numbers had a specific relationship between each other that permit for such operations to happen. Since that day I’ve had my scholastic interest pointed towards the understanding of mathematics, looking at many movies and documentaries that explore different secrets and theories that have never been solved in mathematics. Looking into an algorithm and producing a product that explains how the model is able to come up with certain values will serve as concrete evidence for myself that I am able to work and produce with mathematical formulas This passion laying deep in me, deepened even further during quarantine, where I found myself only enjoying the math’s homework more than the other assignments that I had to complete for school. Since a very young age I’ve always kept it clear, even for my parents, that I was going to do something related to mathematics later in life, and differently from other of my peers, this passion has only grown other the years and hasn’t dialed down like some other people experienced. During my time in MYP, I have been able to explore different sections of mathematics and further understand my preferences in the subject. I have also decided that due to my growing interest in mathematics, I believe that studying it at university would help me reach the goals that I have set myself to accomplish in my professional life. I believe that other the course of my personal project I will be able to either prove or disprove my passion for mathematics by presenting myself something that could be interpreted as too hard for my capabilities. Throughout this process I would like to learn how certain things are interconnected and how when in collaboration can function to provide an individual with values that could describe a real-life scenario. This knowledge will help me fabricate better skills at interpreting and understanding different formulas in general and further help me in my career.
My Product Goal
To demonstrate my learning goal, I intend to create a product that will synthesize my deep passion for mathematics in an interactive map. This product will serve to be a visual representation of how different countries might experience a virus spreading, showing to a viewer how changing the values, like the infected individuals, the recovered, and the immune individuals would change the amount of people that get infected by the virus. By the end of the personal project, I aspire to have a map that can do all the things listed above and potentially have even more functions. I took inspiration to creating this as my product from a game that I played once I was younger, called Plague. Inc, a game that shows the map of the world and makes the gamer decide where to start an outbreak of a biological virus and even synthetic viruses. I have always believed the game to being quite interesting as it demonstrated how different factors, like airport functionality and water transport would affect the timing where people were infected by the virus. Unfortunately, the game doesn’t serve to demonstrate a realistic scenario as it has no ties with any models of prediction. Differently from the game, my product aims at demonstrating the way one of these models function and doesn’t aim to lie to the viewer. I am conscious that I won’t be including too many variables to the map as it won’t reflect the real factors present in the model.
To complete my project, research, testing, and interviews must be conducted. The research aspect of the project is one to follow intensively, as I will have to be sure of the values that I will be computing in my project. It is also important because as a mathematician myself, I tend to be more accurate in calculations once I know myself what each number represents in the formula, this is because having a visual relationship between the numbers and real concept makes the values obtained by the model have a meaning, and once these values have a meaning, it is far more intriguing for the mathematician to investigate the values and come up with questions related to it. Testing should be conducted during this personal project as I will have to test the product to see if it agrees with the values obtained manually by solving the model’s formula. Testing the model will also serve to deepen my understanding of the relationship between each factor and will enhance my explanation during the presentation of the product that will occur at the completion of my personal project. I will achieve my goals by analyzing various sources and seeing the model throughout different points of view. I will learn how to implement my mathematical understanding in simplified concepts that can be easily taught to anyone. The interviews that I will be conducting will serve to demonstrate the viewer that I went to the extent of figuring out who came up with these models of prediction and interviewing them to gather information that was left out of published papers revolving the formulas.
I think that creating an interactive map of the model will satisfy and achieve my goal by demonstrating my understandings of mathematics through a visual product for any type of audience. This project will also demonstrate my personal growth as it will show how an individual like me, can practically teach himself a complicated topic and how despite my age I am able to comprehend mathematics that is far ahead of my year group.
Product Success Criteria
When creating the success criteria for my project I had to remind myself that the purpose of my project was to study how virus spread following an algorithm. After looking into the model that I want to study. I now know that my success criteria are possible, but it will be a serious challenge on a comprehensive point of view of my life. I looked at many examples of and I realized the standards that I should expect should consider that I am a beginner in this field, I realized that a short algorithm would be easier considering that many studies have been published since coronavirus.
For my success criteria I will have two categories to focus on: website production skill and expressing my knowledge of mathematics. In terms of website production skill, I will have to create criteria for the design (aesthetics of the map), the calculations (making sure it’s accurate based on the model, and the functionality (the interactive map working). When looking at expressing my knowledge in mathematics, I will want my criteria to focus on the accuracy of the formula that I will input in the map. Therefore, I will assess my ability to expose a complicated topic in an easy manner and how much I am able to comprehend of the mathematics behind the model.
Primary ATL Skill Used to Accomplish the Learning Goal: Research Skills
To achieve my learning goal of developing a mathematical model predicting the propagation of biological viruses in a controlled location, an extensive research process was paramount. This endeavor required delving deep into both the theoretical underpinnings of epidemiological modeling and the practical aspects of implementing these models through digital tools. My approach was multifaceted, involving a thorough investigation into existing mathematical models, particularly focusing on the θ-SEIHRD and SIR models, which are crucial for understanding virus spread dynamics.
ATL Skills Used in Planning: Research
My rearch process was divided into two main sections: Epidemiological and Mathematical Research, and Technical Skills in Digital Implementation. This involved a deep dive into scientific literature to understand the variables and equations that form the backbone of virus propagation models. I explored numerous academic papers, textbooks, and online resources to grasp the theoretical aspects of these models and their real-world applicability, especially in the context of the COVID-19 pandemic.
Given my goal to translate these complex models into an interactive map, I had to concurrently learn about web development technologies and tools. This required engaging with online courses on platforms like YouTube tutorials to acquire skills in coding, web design, and the use of specific software tools necessary for creating an interactive and user-friendly digital product.
Research Methodology
ATL Skills Used in Product: Self-Management Skills
Working on my personal project to figure out how viruses spread using math was really important. I had to be good at managing myself, which meant I needed to be organized and make sure I used my time well. I had to plan everything out from the start to the end.
When I started planning my project, I made a detailed plan that outlined every step I needed to take. But, as I soon found out, creating a model to predict how viruses spread is no easy feat! So, I set aside time to learn everything there is to know about math and how it affects the spread of viruses. My plan was well-organized, but I also knew I needed to be flexible because sometimes research can take unexpected turns. Being able to adapt my plans was crucial.
Even though I had a plan ready, there were still surprises along the way. One example of this is when I was required to develop a website in order to make my study accessible. I had no prior experience doing this, so I had to educate myself on how to create websites and learn how to design them. I made adjustments to my strategy in order to create room for this new information.
In terms of both my academic and personal life, this project presented me with a significant challenge. As I progressed, I made sure to keep myself motivated by setting a series of smaller goals for myself. Despite the fact that things were quite difficult, I was able to keep going and I feel like I was making progress because of these modest goals being achieved . There were times where I felt like I couldn’t handle everything that I had to do, but I was aware that I had to learn and understand how to deal with my stress. Even though working with mathematics, and medical science was a lot to handle, I was determined to do everything I was capable of and more. I had the goal of making my website more than just random data scattered throughtout a page; I wanted it to be a learning resource that could assist others in need, in comprehending the process by which viruses are transmitted.
The production of the map was an important part of my project, although it was a challenge to ensure that it was both user friendly and visually appealing. In order to demonstrate how viruses spread, I wanted people to be able to use the map and see how the numbers worked together with a relation to reveal the pattern. I put the map through a series of tests to ensure that it was compatible with a wide range of devices and computers. With every test, I gained more knowledge of the requirements necessary to make it accurate. It took a lot of effort, but in the end, it was well worth it to see how much the map was able to assist others in comprehending how viruses are transmitted.
When it was all finished up, the project demonstrated all of the various skills that I had learned. My ability to handle a large project from an idea to something that is actually real was demonstrated by the finished map, which was not simply about mathematics. It required a combination of clever thinking, computer abilities, and creative solutions, and I was able to do all of this by maintaining focus and commitment.
Reflection: Impact on My Learning
My journey through my IB Personal Project has been an extremely educational & transforming experience, challenging the limits of my intellectual curiosity and skill set. I am grateful for the opportunity to have embarked on this adventure. Specifically, as part of the realm of scientific and technological innovation, this project has been an influence for my personal development and education. Its main objective was on the investigation of mathematical models that predict the spread of biological viruses. By venturing into the intricate area of epidemiological models, such as the SIR and θ-SEIHRD models, my objective was to use these mathematical tools to better understand and demonstrate the trends of virus propagation inside a controlled environment. My interest in mathematics worked along with the relevance of pandemic response methods through the building of an interactive map that depicted these relationships. This was a further challenge and expansion of my capabilities.
A determined link of my long-standing passion with mathematics and a strong interest in real world application of mathematical to understand biological events, was something I always aspired to investigate. The project was an ambitious opportunity for me to combine these two interests. I have been intrigued by mathematics ever since I was a kid because it provides an opportunity through which some of the complexities of the world can be understood. This project gave me the opportunity to investigate how abstract mathematical theories and models convert into tools for the benefit of society, particularly in the context of global health crises such as the COVID-19 epidemic.
Throughout the course of this project, I was able to considerably improve my capabilities in a range of Approaches to Learning (ATL) skills. A key one of these was my ability to conduct research. My understanding of the theoretical foundations of epidemiological models as well as the practical aspects of digital application grew because of my participation in a thorough course of study, during which I investigated a wide variety of materials, ranging from academic papers to computer tutorials. This extensive study not only increased the size and complexity of my knowledge, but it also broadened the range of sources that I dealt with. The utilization of a wide range of research methods contributed to the enhancement of my project by supplying me with a solid foundation upon which I could construct my interactive map.
Furthermore, the ability to regulate myself was very necessary to successfully navigate the complexities of this task. My ability to efficiently manage time, set goals that are attainable, and react to unexpected problems was refined via the process of bringing my vision to reality, which needed rigorous planning and focused execution of many things. To construct a product, it was necessary to master software navigation, coding, and web development abilities from the ground up. I had to force myself out of my comfort zone and learn new technical abilities to complete this component of the project, which included a particularly difficult but ultimately gratifying challenge. Not only did the repeated steps of designing, testing, and refining the map boost my technical abilities, but it also improved my problem-solving skills. This was because I had to traverse the tight balance between precision, convenience, and visual appeal.
Moreover, the initiative had a significant influence on both my personal development and my academic progress. The experience confirmed my enthusiasm for mathematics and the applications of mathematics, strengthened my confidence in my ability to solve difficult issues, and solidified my intention to continue mathematics in further education and beyond. Lucidity, conciseness, and audience engagement are abilities that are extremely essential in both academic and daily life. The task of presenting complicated mathematical concepts in a way that is accessible brought to light the relevance of these talents, that I will need to further develop during the two years of DP ahead of me.
Reflecting on this process, I am filled with an overwhelming sense of satisfaction for what I have achieved. Not only did the project give me the opportunity to investigate a subject that holds not only profound personal but also global significance, but it also helped me make significant progress in both my physical and mental abilities. The building of the interactive map is an important milestone in both my academic and personal development. It is a demonstration of the strength of mathematical modeling in comprehending and adjusting to biological viruses, and it is a tribute to the power of mathematical simulation. I am thankful for the fundamental experiences that this project has provided, which have fueled my passion for mathematics and its ability to make important contributions to society. As I look ahead to future challenges and learning opportunities, I am appreciative for the contributions that this project has made.
Upon the completion of my product, I decided to create a survey that I forwarded to a couple of friends and family members, in order to receive a general review of my product. Looking at the data, I noticed how out of the 11 people that submitted a response, all of them found my interactive map of their liking. Some of the likings of my product where reffered to the clean design of my map, the color palette that I utilized to color-coat the nations, and most impartantly, the search function of the map was higly praised upon; making me even more enthusiastic of my product due to the fact that coding for the search function of the website was one of the hardest things that I had to do during the process. Overall, these responses gave me the confirmation of succeeding my my success criteria.
In addition, I decided to ask what I should improve in my map to make it even better. Some of the replies that I received suggested to add more interractive elements, like info boxes, to simplify even more the content present on the map. Another major suggestion that I receive was to improve the responsiveness of the website on mobile devices. This minor issue could be due to the fact that the website has a limited ram usage because of the domain plan that is set for that specific adress.
Lastly, I asked what they would rate my product out of 8, and most of the responses were 7, having 60% of 10 people give me that response. This, as aforementioned, further proves that I was successful in the creation of my product, while still having some room for improvement that will be handled in the future.
In general, my product met all the necessary criteria that I set myself to succeed and become a product that I am proud of and something that I enjoyed creating. This process was an eye opening experience for me as it gave me a vague insight of what I aspire doing at university. I had to deal with stress and handle my time like I never had to before in my academic career. Meeting the finalization of my product, I have now gained skills in website development, and a better understanding in how a numerical concept lkike mathematics, can be applied to a real life context, like the one of biological viruses. Before this process I truly felt unsure if my passion for mathematics was something totally real, but after this experience, and the feedback that I received from teachers, friends, and family; I am now sure that this passion of mine wasn’t only a figment, but more something of genuine, and something that I am sure will challenge me mentally in the future, bringing me joy and other formative experiences like this one.