Reference no: EM133949314
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.
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. Get expert-level assignment help in any subject.
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.
Task 1: Exploring the SEDIs model
Recommended reading resource: HELM 6: Matrices, pages 25-28.
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.
Find non-trivial expressions for the points where simultaneously. Provide an interpretation for what is happening in the network at this steady-state point.
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
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.
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:
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.
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.
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.
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.
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.
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.
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.