ENGF0003: Mathematical Modelling and Analysis I
Integrated Engineering Programme (IEP)
How do Fake News Spread in Social Media?
ENGF0003 Project (30%)
Information
Coursework Release Date: 17 November 2025, 14:00
Submission Deadline: 16 January 2026, 14:00
Estimated Coursework Return: 13 February 2026
Project Guidance
Read this document thoroughly before starting your work. Use the Moodle forum to ask questions about this coursework or to check answers given to your colleagues. Note that no questions posted after 9 January 2016 will be answered.
How is this project different to school homework?
In school you have been trained to solve mathematical problems that have a single correct solution and a small number of correct ways to solve them. However, we want to train you to deal with real-life engineering problems and to analyse them critically.
In this module, most of the problems you will encounter in your coursework and project have multiple correct solutions, which depend on the method that you choose and the way you explain both your solution and justify the decisions that you make.
Grade Breakdown
Your grade in this coursework can be a maximum of 100 points, awarded in two tasks.
§ 10 points awarded for Presentation and Communication, including adherence to page limits, the Formatting Checklist below, and criteria described in the Marking Criteria section at the end of this document. We expect that your presentation and communication will have improved since the ENGF0003 Coursework.
§ 90 points awarded for your work in Tasks 1 and 2 in this document, with criteria described in the Marking Criteria section at the end of this document. Task 1 is in the style. of traditional mathematics questions and will support you in preparing for Task 2, which is an open-ended design task.
Academic Integrity
Academic integrity means being transparent about your work. For the ENGF0003 project all the following rules apply:
§ Do not share and do not copy project solutions, figures, tables or MATLAB code from your peers.
§ Reference books, articles, or teaching resources that you used on the last page of your document. Read about how to reference someone else's work here, and how to avoid plagiarism here.
§ Do not publish assessment materials in external online forums or “homework help” websites such as Chegg, Course Hero, etc.
§ Do not paste assessment material into Generative Artificial Intelligence (GenAI) tools such as Co-Pilot, ChatGPT, Gemini, Claude, DeepSeek, etc. You are not allowed to use GenAI tools to completely or partially write the coursework for you. Read more about using GenAI here.
§ You are allowed to use GenAI in an assistive capability, such as helping you write code and proofreading your document, but you must run, check, and explain results by yourself.
§ Remember that GenAI is not completely reliable and can produce incorrect answers.
§ We routinely detect high similarity in AI-generated work across large cohorts.
Note: There are serious consequences for breaching UCL’s assessment regulations.
Formatting Checklist
Formatting and presentation will make up for 10% of your grades in this project. This project is marked anonymously, so do not write down your name or student number anywhere in your submission. Our online systems will automatically link your submission to your Moodle ID after the project is marked. You are required to type your answers in Microsoft Word or in LaTeX. Submit a single pdf file named ENGF0003Project.
Table 1. Formatting guidance for the ENGF0003 Project.
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What
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How
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q Use Heading styles.
q Apply page numbering.
q Use a sans serif font e.g. Arial, Calibri, Helvetica. (Not Times Roman).
q Use font size of 12 points.
q Use bullet points to break down long paragraphs.
q Number figures and tables throughout the document.
q Insert Captions for figures and tables.
q Use the Word Equation Editor for inserting equations.
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· To apply a style. to selected text:
Home tab, Styles group, choose one of the inbuilt Heading styles series, e.g. Heading 1, Heading 2.
· To insert page numbering:
Insert tab, Page Number.
· To number a figure or table, right-click it and select Insert Caption…
· To insert a caption for a figure or table, fill in the “Caption” field in Insert Caption…
· To insert an equation in Word, use the Insert tab then click on Equation.
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Background
Social media platforms such as Instagram, WhatsApp, and TikTok have revolutionised human communication and connection. From the emergence of memes – adaptable and humorous image templates that capitalise on and make fun of social norms – to emoji communication, social media has shaped much of the look and feel of popular culture and discourse over the last decade.
However, social media platforms have more recently started to be used as a source of news and information. According to research findings from the Reuters institute, more than half of people in the United States (US) get news from platforms such as Facebook and X (formerly Twitter). In the UK, an Ofcom’s News survey found that the number of adults consuming news from traditional sources such as TV is falling year-on-year. This survey also found generational differences in news consumption, where 88% of respondents between 16 and 24 years old reported getting their news from social media.
Figure 1. An AI-generated picture of late Pope Francis wearing a puffer jacket. Many people now know this image as "Balenciaga Pope", making reference to the similarities with the style. of the Spanish luxury fashion house.
Despite being designed to connect humans globally and facilitate communication, social media has also enabled the spread of “fake news”, false stories or narratives about a person, social group, or event. For example, in March 2023 an AI-generated photo of late Pope Francis rocking a puffer jacket went viral on social media (Figure 1). While many perceived the image to be a funny meme, others genuinely assumed it was a real photo.
Likewise, during the COVID-19 pandemic much misinformation was spread on social media. An example was a conspiracy theory that 5G internet technology was linked to the spread of coronavirus. TikTok videos from very popular accounts sharing the conspiracy were shared and viewed thousands of times, and the rumour was even endorsed by a number of celebrities.
Problem
Fake news is a complex phenomenon because people do not necessarily need to believe it to share it. The UK House of Commons Library has published a resource in 2024 discussing factors contributing to the spread of fake news being as diverse as alignment with pre-existing beliefs and values, emotional responses, trust in the source of fake news, or even repeated exposure to them.
Social media amplifies the spread of fake news with fast publication of content, “likes and comments”, and peer-to-peer sharing, making it fundamentally different from the flow of information on traditional media such as newspapers, radio, and television where there are robust fact-checking systems to prevent and rectify inaccurate information.
Given that social media algorithms track user engagement and reward highly viral content, in this project you will study mathematical models originally developed to model the spread of contagious diseases to understand the spread of fake news in digital networks.
The SEDIS model
The SEDIS model, standing for susceptible (), exposed (), doubter () and infected () models individuals in a network where fake news has been spread. This model assumes conservation of the number of individuals in the network , such that . The SEDIS model is given by the following system of ordinary differential equations:
where and respectively represent the fraction of individuals in the total population that are susceptible, exposed, doubtful or infected by fake news.
The constants and are the transmission rates between states in units of [1/time]. Table 2 expands on the meaning of the model parameters.
Table 2. Parameter interpretations for SEDIS model in equations 1a - 1d.
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Parameter
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Interpretation
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Fraction of individuals susceptible to fake news
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Fraction of individuals exposed to fake news
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Fraction of individuals doubter of fake news
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Fraction of individuals that believe fake news (infected)
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Transition rate from susceptible to exposed state
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Transition rate from exposed to doubter
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Transition rate from exposed to infected
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Transition rate from exposed to susceptible
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Transition rate from doubtful to susceptible
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Transition rate from infected to susceptible
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Transition rate from doubtful to infected
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Figure 2 illustrates the model given in equations 1a – 1d.
The model states that as fake news spreads; the majority of the population is initially susceptible to believing it. Susceptible individuals become exposed to fake news with a ratio , and once the individual has been exposed to fake news there are three possibilities:
§ completely disregarding them and going back to being susceptible with rate ,
§ becoming doubtful of the fake news with rate ,
§ believing the fake news and becoming infected with rate .
Individuals that are doubtful might not believe the fake news and go back to being susceptible with rate or believe the fake news and become infected with rate . Infected individuals might eventually find out the truth and go back to being susceptible with rate .
Figure 2. Network schematic of the SEDIS model. Solid arrows represent forward steps in infection and dashed arrows represent recovery back to a susceptible state.
Task 1: Exploring the SEDIs model [30 marks]
[5 pages maximum]
Recommended reading resource: HELM 6: Matrices, pages 25-28.
A. [10 marks] Express the system of equations 1a – 1d in matrix form. and verify that the sum of any column in the matrix of coefficients is zero. Use linear algebra to demonstrate a mathematical interpretation for this fact and identify at least one assumption of this model that makes it unrealistic for real-life social networks.
B. [10 marks] Find non-trivial expressions for the points where simultaneously. Provide an interpretation for what is happening in the network at this steady-state point.
C. [10 marks] Show that 1a – 1d have strictly positive solutions for all and derive expressions for the lower bound of these solutions.
Task 2: The effect of doubters [60 marks]
[6 pages maximum]
Your task is to understand how the parameters and initial conditions associated with the doubter state influence the evolution of the infected state in time.
You will need to reflect on the mathematical results obtained in Task 1, as well as use MATLAB to solve the system of equations 1a – 1d algebraically and numerically for a wide range of conditions and parameters.
Once you have analysed your numerical results, discuss what they imply about the importance of doubters in a social network and explicitly connect your findings to your mathematical work in Task 1. Your work will be evaluated based on criteria set out in A and B below.
We suggest you dedicate up to 2 pages for Task 2.A and up to 4 pages for Task 2.B.
A. [30 marks] The clarity and rationale behind the design of a numerical study in MATLAB to address this problem.
This will involve clearly describing your plan of analysis, including an outline of parameter ranges and initial conditions, the methods and MATLAB functions you will use, and a justification for these choices. Please find specific guidance below:
i. Present a table outlining the range of parameters and initial conditions you chose to study in your model. Write up to two paragraphs discussing your rationale for choosing them.
ii. Create a flowchart/schematic to represent your methodology. Include the mathematical and computational methods you will use and describe how they are connected to one another.
iii. Describe your computational implementation in a short paragraph. Your goal is to write transparently so that someone reading your project could replicate it and check for themselves if the results are correct.
B. [30 marks] The quality of your results, as well as the way that you describe them in words and discuss them. This will involve displaying your results effectively and concisely in visual and numerical forms and providing concise and accurate written interpretations. Please find some guidance below:
i. Include one figure contrasting the solutions of the system across different initial conditions but with fixed transmission rates. Explain how the initial conditions affect the long-term behaviour of the solution.
ii. Include one figure displaying how varies according to the rates associated with the doubter state for two sets of initial conditions explored in part B.i. Discuss your results and describe the role of the doubter state in the model.
iii. Conclude your report with an appraisal in 2 to 3 paragraphs of the validity and limitations of this model. Use this appraisal to design and present the schematic of a model that would be more realistic. Summarise your proposed model in three bullet points.