The Impact of Covid-19 on Italy
Samantha G, Kate H, Magdalena L, and Yuritzy V.
Roosevelt University, Chicago IL
April 13, 2020
Data
Model
Introduction
Discussion
References
The data was obtained by the publishers of the worldometer. Currently in Italy (April 5, 2020) there are 128,948 cases of Covid-19. New cases are reported daily so the numbers are always fluctuating. The numbers used to create the logistic and epidemic models are from March 1st, 2020 up to March 14th, 2020. The numbers can also be confirmed by the website WHO which is the World Health Organization. This organization has been main source of Covid-19 information. It is funded by the United Nations as well as the other international organizations.
Covid-19 is a virus that originated in China that has turned into a worldwide pandemic affecting around 2 million people. It has been theorized that it can spread from individual to individual through close contact. It has also been theorized that it can spread through respiratory droplets that are released when someone that is infected with the virus sneezes or coughs. The most common symptoms of the coronavirus are dry cough, fever, tiredness and in severe cases shortness of breath and difficulty breathing. In this project the research was focused on the spread of Covid-19 in Italy.
�Advantages:
One of the advantages is that is is ideal for ecological processes since this equation is dependent on density.
Another advantage of using a logistic model is because as it progresses an “s” shaped curve will appear because eventually the growth rate will level off.
Limitations:
One of the limitations of the model is that it does not account for the impact of external factors. This means that the model only focuses on the growth rate of the virus and not other factors that can influence a change in population.
Another limitation is that the growth rate will not always stay constant due to limiting resources. The growth rate will only increase if there are enough resources left for it to increase, otherwise the rate will reach carrying capacity and then begin to decay.
Another limiting factor as to the accuracy of projected is that due some limiting factors not all cases are being reported because of a lack of the number of test available to
hospitals and patients.
https://www.worldometers.info/coronavirus/country/italy/
https://sites.math.northwestern.edu/~mlerma/courses/math214-2-03f/notes/c2-logist.pdf
www.expii.com/t/differential-equation-for-logistic-growth-313.
The differential equation is dp/dt=kP(1-(P/K)) for the logistics model. The explicit solution is P= K/1+Ae^-kt, where A=K-Po/Po.
The parameters are important because there will be a carrying capacity which stands for the “K” value in the equation. When “P” is less than 0 that means that the population growth is maximal. When the population rate declines and P reaches 0 that means that P and K are equal. When the population is bigger than K that means that the population growth rate is negative.
Table 11
March 1-14 2020 | |
Day | Number of Cases |
0 | 1701 |
1 | 2,036 |
2 | 2,502 |
3 | 3,089 |
4 | 3,858 |
5 | 4,636 |
6 | 5,883 |
7 | 7,375 |
8 | 9,172 |
9 | 10,149 |
10 | 12,462 |
11 | 15,113 |
12 | 17,660 |
13 | 21,157 |
Graph 1 was produced using the logistics model approach. It demonstrates the projected number of cases that will be caused by the virus. This graph also shows when the number of cases will reach its peak as well when the numbers will begin to decrease. Since it is impossible to have a negative number of cases the graph will always show positive numbers or 0. It is important to state that the initial population of the graph is 1701.
Graph 1
Projected cases of Covid-19 in Italy
Logistic Curve vs. Epidemic Curve
In graph 2 there is the plotted data from Table 1 with the theoretical curve that estimates future cases. Below that there is the epidemic curve that shows the progression of the Covid-19 outbreak in Italy. In this graph the initial population is 1701 and the carrying capacity is 2,000,000.
The data as seen in table 1 shows the number of cases that were observed during the time period between March 1 to March 14 in Italy.
Graph 2
The Growth Rate of the logistic model
r=1/(2-0)*Log[2502/1701]
=1/2Log[278/189]
Data from time 0 to 2 from Table 1 were used to calculate the growth rate.