Predicted Growth Patterns of the Coronavirus (COVID-19)

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2)

Author: Ashlyn Kawakami, Benson Yu

from Dr. Ham's Math 5B Honor class

Graph for Number of Individuals Infected by COVID-19 per Day

1. Growth Rate:

P1: (7, 6058) P2: (14, 24545)
6058 = y(0) e^k(7) 24545 = y(0) e^k(14)
y(0) = 6058 / e^7k y(0) = 24545 / e^14k
6058 / e^7k = 24545 / e^14k
6058e^7k = 24545
k = 0.200

2. Based on the data, COVID-19 will have infected approximately 570,000 individuals within a month and the earth's entire human population within a year. Without interference or attempts to stop the rapidly spreading virus , it is completely possible for the number of COVID-19 infections to mimic the data in Model 1. 550

Graph for Number of Deaths Due to COVID-19 per Day

3. Growth Rate:
P1: (7, 132) P2: (14, 492)
132 = y(0) e^k(7) 492= y(0) e^k(14)
y(0) = 132 / e^7k y(0) = 492 / e^14k
132 / e^7k = 492 / e^14k
132e^7k = 492
k = 0.188

4. Based on the data, COVID-19 will have killed approximately 9,300 individuals within a month and the entire world’s human population within a year. This is accurate since viruses can spread rapidly if efforts are not made to stop further infection.

Graph for Number of Individuals Infected by COVID-19 per Day

5. When comparing the estimated data of Model 1 to the actual data in Model 3, it can be observed that Model 1 represents a major overestimate. The growth rate of Model 1 is much greater than the growth rate of Model 3 because it does not take into account various external factors that could slow the spread of the virus. These include an increase in personal hygiene, self-quarantine, and general precaution.

6. Model 3 shows a decrease in the growth rate of the virus around day 25 which was most likely due to an increase in personal and public hygiene. Media coverage of the virus sent the world into a cleanliness frenzy which explains the sudden slow of the virus between day 20 and day 40.

Graph for Number of Deaths Due to COVID-19 Per Day

7. When we compare Model 4 with Model 2, we can clearly see that there are discrepancies in the data. We can see that the amount of predicted deaths in Model 2 is way higher than the actual number of deaths shown in Model 4. The probable cause of this discrepancy is probably due to the rise of precautions made to counteract the disease. These precautions can mean a decrease in interaction between individuals on a daily basis, closing borders, applying the techniques disclosed by the CDC, and the stopping of community faculties such as schools and factories. This means that as the number of newly infected individuals decreases, the number of deaths also decreases.

8. It is quite unordinary to see the decrease in deaths, but then have it grow exponentially again. A possible explanation for this phenomenon might be because the growth rate of the deaths of the coronavirus did not decrease; it was just temporarily delayed.

9. The number of deaths due to the coronavirus is directly dependent on the number of infections which means that Model 4 is directly influenced by Model 3. Their correlation is not abnormal and their tendencies to increase and decrease are strikingly similar.

Conclusion

1. SARS coronavirus (SARS-CoV) was discovered in 2003 and claimed the lives of eight-hundred people. This virus affected twenty-six countries and infected around eight-thousand. The outbreak affected travel, commerce, and health of individuals for around one year.

Two Histograms to represent probable cases of SARS

2. By looking at Model 3 and Model 4, we concluded that the disease will continue to spread until around late June or early July, which means that the apex of the coronavirus outbreak will take place around that time. The disease will not be fully contained until around November at the earliest, which means that Coachella will probably be further delayed.

3. Due to the rapid growth of coronavirus, we suggest that all schools, including Pasadena City College, transfer their courses online. The best course of action for PCC is to keep all students and faculty at home. This will decrease the probability of the spread of coronavirus.