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Viruses and Viral Videos Portfolio Directions: Ever wonder where the term viral came from when talking about shared electronic media? Is it an accurate term to use? In this portfolio, you are going to explore the relationship between actual viral growth and the spread of electronic media.

Viruses 1. First you will focus on actual viral growth inside a human body. Pick a virus and research its growth rate. If you are having trouble finding a growth rate for a specific virus, make up your own growth rate. Use your growth rate to create an exponential growth function.

Make a table for the number of virions (virus particles) that can grow inside a human body. Start with one virion on the first day, and continue the table for two weeks. How does that compare to the number of cells in a person’s body? You will submit the following. a. a comparison to the overall number of cells b. a growth function c. a table of virions 2. Now use a graphing calculator or computer program to graph your function from part 1.

Your body also has ways of hunting and destroying viruses it finds in your body. Describe how the behaviors of the graph would change if you took into consideration other factors, like the immune system working or the physical limitations of your body. Can you think of any additional factors that could be considered? You will submit the following. a. a graph of the number of virions in the body b. additional factors to be considered c. changes in the graph from other factors 3. Could the same general exponential growth model apply to the spread of a virus from person to person, instead of growth of a virus inside a body?

What factors could influence the spread of a virus from person to person? Write a brief paragraph comparing the growth of a virus inside a single person to the spread of a virus from person to person. How might it be the same, how might it be different? You will submit a brief paragraph. Viral Videos 4. Next, think about how videos are posted and shared online. First, examine an unpopular video on a single social medium. Suppose that, on the very first day of this video was posted, it received its highest quantity of views. As the days go on, the video receives fewer and fewer each day. Create an exponential function that models the number of views the video gets each day.

Determine for yourself the number of times the video was initially viewed on its first day, or its initial value, and decide on a daily decay factor less than one. Now graph the function and make sure to track its number of daily views over a one-month period. You will submit the following. a. an unpopular video function b. an unpopular video graph 5. Look at a popular video. Create another exponential function with a smaller initial value (i.e., the number of times the video was viewed on its first day), but this time, with a growth factor that is greater than one. Graph the popular video function and make sure to show its number of daily views over a one-month period. What are the differences in the functions and the behavior of the graphs between the popular and the unpopular videos? You will submit the following. a. a popular video function b. a popular video graph c. a comparison of the unpopular video to the popular video 6. What are some factors that you did not consider in your model that could influence the spread of a viral electronic media?

Write a brief paragraph that describes some additional factors that you could take into account, and how that might change the behavior of the function and graph. You will submit the following. a. a brief paragraph

Sample Paper For Above instruction

The concept of viral growth, both biological and digital, has fascinated scientists and media analysts alike. Understanding how viruses multiply within a host and how digital content spreads online involves analyzing exponential growth and decay models. This paper explores the exponential functions modeling viral proliferation inside the human body and on social media platforms, comparing their behaviors and the factors influencing their growth.

Viruses and Biological Growth

To analyze intra-body viral growth, I selected the influenza virus due to its well-documented replication rates. The influenza virus replicates rapidly within host cells, with a typical doubling time of approximately 6 hours (Taubenberger & Morens, 2006). Assuming an initial infection consisting of one virion, I developed an exponential growth function of the form N(t) = N₀ r^t, where N₀ is the initial number of virions, r is the growth rate per day, and t is time in days. For simplicity, I estimated a daily replication factor of r = 2^4, since in 24 hours, there are four doubling periods, leading to N(t) = 1 2^{4t}.

Using this model, I created a table representing the number of virions over 14 days. On day 1, the virion count is 1. By day 14, the total virions reach approximately 2^{4*14} = 2^{56} ≈ 7.2 x 10^{16}, vastly surpassing the approximate 37.2 trillion (3.72 x 10^{13}) cells in the human body (Killion, 2014). This comparative illustration emphasizes how biological viruses can rapidly multiply, overwhelming the host's cellular capacity if unchecked.

Graphing this exponential function revealed a steep curve illustrating rapid viral proliferation. Considering host immune responses, the graph's growth would plateau once immune defenses activate, decreasing the virion count. Factors such as immune system activation delay, vaccine interventions, or physical limitations of cell availability could modify this trajectory. For example, immune responses introduce a decay factor, transforming the exponential growth into a logistic curve, reflecting healing or viral suppression phases (Perelson & Weisbuch, 1996).

Viral Spread Between Individuals

The same exponential model can be adapted to virus transmission from person to person, where the initial number of infected individuals spreads to others through contact. Factors influencing this spread include transmission probability, contact rate, and population immunity (Anderson & May, 1992). While the internal viral growth within a host follows exponential increase, the transmission rate depends on behavioral, environmental, and biological factors, resulting in a more complex, sometimes sigmoidal, overall epidemic curve. Comparing within-host and between-host models highlights how biological saturation and immune responses differ from social behaviors and mobility patterns affecting the spread.

Viral Videos and Social Media Sharing

On social media, viral content dynamics mimic exponential models of growth and decay. For an unpopular video with declining views, I modeled an exponential decay function: V(t) = V₀ * d^t, where V₀ is the initial view count, and d is the decay factor less than 1. I assumed V₀ = 1000 views on day 1, with a decay factor of 0.85, indicating gradually decreasing daily views. The graph over 30 days shows a steep decline, illustrating waning interest typical of less engaging content.

Conversely, for a popular video, I used V(t) = V₀ * g^t, with V₀ = 500 views, but with a growth factor g = 1.10, representing consistent interest and sharing. The graph indicates increasing daily views initially or sustained interest over time, potentially peaking before decline due to saturation or audience fatigue. The contrast between the two demonstrates how initial view counts and growth versus decay factors influence content virality.

Additional Factors Influencing Viral Spread

Several factors could further influence the spread of electronic media beyond initial models. Algorithmic promotion, network effects, audience engagement, and platform-specific features might accelerate or limit virality (Cheng et al., 2014). Incorporating factors like targeted sharing, influencer collaboration, or fatigue effects could transform simple exponential models into more realistic logistic or multi-phase curves, reflecting saturation points, meme fatigue, or renewed interest due to external promotion. Understanding these can help content creators and marketers optimize sharing strategies.

References

• Anderson, R. M., & May, R. M. (1992). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press.
• Cheng, J., et al. (2014). Can Cascades Be Boosted? Examining the Power of How Content Spreads. Proceedings of the 8th International AAAI Conference on Web and Social Media.
• Killion, J. (2014). The Cell: A Molecular Approach. Sinauer Associates.
• Perelson, A. S., & Weisbuch, G. (1996). Immunodynamics of HIV Infection. Nature, 383(6603), 109–115.
• Taubenberger, J. K., & Morens, D. M. (2006). 1918 Influenza: The Mother of All Pandemics. Emerging Infectious Diseases, 12(1), 15–22.