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Need this done with B or better. You fail me, you get a bad review. Need this completed ON TIME as well. Do a good job, you will get the best review ever! 🙂
Math project cal 1 Check the attachment. you can use any Microsoftoffice you want to solve the equations
TheSpread of SARS
In the Spring of 2003, SARS (Severe Acute Respiratory Syndrome) spread rapidly in several Asian countries and Canada. Predicting the course of the disease – how many people would be infected and how long it would last – was important to officials trying to minimize the impact of the disease.
Part I: SARS Predications for Hong Kong
This part compares three predications about the spread of SARS in Hong Kong. We measure time , in days since March 17, 2003, the data the World Health Organization (WHO) started to publish daily SARS reports. Let be the total number of cases reported in Hong Kong by day . on March 17, Hong Kong reported 95 cases.
The constants in the three differential equations whose predications are analyzed in this project were determined using WHO data available in March 2003. We compare predications from three models for June 12, 2003, the last day a new case was reported in Hong Kong.
1) A Linear Model. Suppose satisfies
Solve the differential equation and use your solution to predict the number of cases of SARS in Hong Kong by June 12 ().
2) An Exponential Model. Suppose satisfies
Solve the differential equation and use your solution to predict the number of cases of SARS in Hong Kong by June 12 ().
3) A Logistic Model. Suppose satisfies
a) Using a calculator or computer, sketch the slope field for this differential equation. Use and. What can you deduce about the solutions?
(HINT: Determine whether each equilibrium solution is stable or unstable).
b) Use Euler’s method with step size to estimate the number of cases of SARS in Hong Kong by June 12 () and the maximum number of SARS cases.
c) Consider the solution for the logistic equation is
Use this solution to predict the number of cases of SARS in Hong Kong by June 12 () and the maximum number of SARS cases.
d) Compare between the estimation value and predict value by June 12 () in part (b) and (c).
4) Comment on June 12 predications from the three models. What do each of the three models predict about the trend in the number of new cases each day?
5) To see how well the three models worked in practice, plot the total number of SARS cases reported in Hong Kong day (where is March 17,2003) in the table below and each one of the three solution curves. Comment on how well three models fit the data in the table.
|
0 |
5 |
12 |
19 |
26 |
33 |
40 |
47 |
54 |
61 |
68 |
75 |
81 |
87 |
|
95 |
222 |
470 |
800 |
1108 |
1358 |
1527 |
1621 |
1674 |
1710 |
1724 |
1739 |
1750 |
1755 |
6) Find and graph the daily increase in Hong Kong SARS cases from the above table. What trend do you see in the data? What does this trend suggest about which model fits the date best?
Part II: A SIR Model for SARS
This part analyzes the spread of SARS through interaction between susceptible and infected people.
The variables are , the number of susceptible people, , the number of infected people, and , the number removed (this group includes those in quarantine and those who die, as well as those who have recovered and acquired immunity). Time is in days since March 17, 2003, the date the World Health Organization (WHO) started to publish daily SARS reports. On March 17, 2003 Hong Kong reported 95 cases. In this model
and million, the population of Hong Kong in 2003. Estimates based on WHO data give .
1) What are and, the initial values of and ?
2) During March 2003, the value of was about 0.06. Using a calculator or computer, sketch the phase plane for this system of differential equations, and the solution trajectory corresponding to the initial conditions in (A). Use and.
3) What does your graph from (B) tell you about the total number of people infected over the course of the disease? (HINT: Determine how many susceptible people remain at the end of the epidemic and use this to calculate the number who got infected)
4) What is the threshold value? Show a calculation. Interpret the meaning of the threshold value.
5) During April, as public health officials worked to get the disease under control, people who had been in contact with the disease were quarantined. Explain why quarantining has the effect of raising the value of b.
6) Using the April value,, sketch the phase plane for this system of differential equations (use the same value of and the same ranges for the axes). What does your graph tell you about the total number of people infected over the course of the disease?
7) What is the threshold value now? Show a calculation and interpret the meaning of the threshold value.
8) Which parameter (or ) would be affected if most people began to use face-masks? Explain.
9) Which of the following policies, intended to prevent an epidemic and protect a city from an outbreak of SARS in a nearby region, would be most effective? Defend your reasoning.
a) Close off the city from contact with the infected region. Shut down roads, airports, trains, and other forms of direct contact.
b) Install a quarantine policy. Isolate anyone who has been in contact with a SARS patient or anyone who shows symptoms of SARS.
c) Have everyone wear face masks.
TheSpread of SARS
In the Spring of 2003, SARS (Severe Acute Respiratory Syndrome) spread rapidly in several Asian countries and Canada. Predicting the course of the disease – how many people would be infected and how long it would last – was important to officials trying to minimize the impact of the disease.
Part I: SARS Predications for Hong Kong
This part compares three predications about the spread of SARS in Hong Kong. We measure time , in days since March 17, 2003, the data the World Health Organization (WHO) started to publish daily SARS reports. Let be the total number of cases reported in Hong Kong by day . on March 17, Hong Kong reported 95 cases.
The constants in the three differential equations whose predications are analyzed in this project were determined using WHO data available in March 2003. We compare predications from three models for June 12, 2003, the last day a new case was reported in Hong Kong.
1) A Linear Model. Suppose satisfies
Solve the differential equation and use your solution to predict the number of cases of SARS in Hong Kong by June 12 ().
2) An Exponential Model. Suppose satisfies
Solve the differential equation and use your solution to predict the number of cases of SARS in Hong Kong by June 12 ().
3) A Logistic Model. Suppose satisfies
a) Using a calculator or computer, sketch the slope field for this differential equation. Use and. What can you deduce about the solutions?
(HINT: Determine whether each equilibrium solution is stable or unstable).
b) Use Euler’s method with step size to estimate the number of cases of SARS in Hong Kong by June 12 () and the maximum number of SARS cases.
c) Consider the solution for the logistic equation is
Use this solution to predict the number of cases of SARS in Hong Kong by June 12 () and the maximum number of SARS cases.
d) Compare between the estimation value and predict value by June 12 () in part (b) and (c).
4) Comment on June 12 predications from the three models. What do each of the three models predict about the trend in the number of new cases each day?
5) To see how well the three models worked in practice, plot the total number of SARS cases reported in Hong Kong day (where is March 17,2003) in the table below and each one of the three solution curves. Comment on how well three models fit the data in the table.
|
0 |
5 |
12 |
19 |
26 |
33 |
40 |
47 |
54 |
61 |
68 |
75 |
81 |
87 |
|
95 |
222 |
470 |
800 |
1108 |
1358 |
1527 |
1621 |
1674 |
1710 |
1724 |
1739 |
1750 |
1755 |
6) Find and graph the daily increase in Hong Kong SARS cases from the above table. What trend do you see in the data? What does this trend suggest about which model fits the date best?
Part II: A SIR Model for SARS
This part analyzes the spread of SARS through interaction between susceptible and infected people.
The variables are , the number of susceptible people, , the number of infected people, and , the number removed (this group includes those in quarantine and those who die, as well as those who have recovered and acquired immunity). Time is in days since March 17, 2003, the date the World Health Organization (WHO) started to publish daily SARS reports. On March 17, 2003 Hong Kong reported 95 cases. In this model
and million, the population of Hong Kong in 2003. Estimates based on WHO data give .
1) What are and, the initial values of and ?
2) During March 2003, the value of was about 0.06. Using a calculator or computer, sketch the phase plane for this system of differential equations, and the solution trajectory corresponding to the initial conditions in (A). Use and.
3) What does your graph from (B) tell you about the total number of people infected over the course of the disease? (HINT: Determine how many susceptible people remain at the end of the epidemic and use this to calculate the number who got infected)
4) What is the threshold value? Show a calculation. Interpret the meaning of the threshold value.
5) During April, as public health officials worked to get the disease under control, people who had been in contact with the disease were quarantined. Explain why quarantining has the effect of raising the value of b.
6) Using the April value,, sketch the phase plane for this system of differential equations (use the same value of and the same ranges for the axes). What does your graph tell you about the total number of people infected over the course of the disease?
7) What is the threshold value now? Show a calculation and interpret the meaning of the threshold value.
8) Which parameter (or ) would be affected if most people began to use face-masks? Explain.
9) Which of the following policies, intended to prevent an epidemic and protect a city from an outbreak of SARS in a nearby region, would be most effective? Defend your reasoning.
a) Close off the city from contact with the infected region. Shut down roads, airports, trains, and other forms of direct contact.
b) Install a quarantine policy. Isolate anyone who has been in contact with a SARS patient or anyone who shows symptoms of SARS.
c) Have everyone wear face masks.
FINALPROJECT INSTRUCTIONS
Math Writeup (50 points) is due at the beginning of class on Wednesday 12/04/2013
Individual work turned in answering all questions and showing all work for each one.
Written Paper (25 points)
o Introduce system: explain model equation and question asked
o Explain strategy suggested and why (verbal explanation supported with results)
o Include visuals representing your results/supporting your strategy
o Discuss assumptions and limitations of model, possible extensions of model, and suggested future
work.
• Final draft is due at the final exam day.
Presentation (25 points)
• 10-8 minutes total
• Use presentation software: Powerpoint, Prezi, etc.
• Brief explanation of written paper:
o Introduce project
o Explain the strategy you suggested and why
o Support your answer with the results of analysis (do not need to show how you got the
results, just need to know what they are and how they support your conclusion)
o Prepare a script and practice it!
• Presentation Zen
o Examples: http://sixminutes.dlugan.com/presentation-zen-slide-examples/
o More information: http://www.presentationzen.com
