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1. Explain why there will be no disease spread if the initial susceptible amount s(0) is less than 1/c (the reciprocal of the contact number) 2. Suppose that a disease has a contact number of 4, and you have a vaccine with an efficacy 100% (which is not realistic). This means that every person who receives the vaccine, will be immune from contracting the disease. What percentage of the population would need to receive the vaccine in order to stop an epidemic from starting? 3. Suppose that a vaccine is developed with an efficacy of approximately 95%. What proportion of the population would need to receive the vaccine to prevent an epidemic spread?

1. Explain why there will be no disease spread if the initial susceptible amount s(0) is less than 1/c (the reciprocal of the contact number) 2. Suppose that a disease has a contact number of 4, and you have a vaccine with an efficacy 100% (which is not realistic). This means that every person who receives the vaccine, will be immune from contracting the disease. What percentage of the population would need to receive the vaccine in order to stop an epidemic from starting? 3. Suppose that a vaccine is developed with an efficacy of approximately 95%. What proportion of the population would need to receive the vaccine to prevent an epidemic spread?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A look at heard immunity: When we had the contact number from the part above, it tells us how many people will be infected by a single individual. We can also use information about contact numbers to estimate heard immunity numbers and vaccination efficacy. It turns out that the rate of infection is governed by only a few things. Lets take a look at the equation in more detail. di = ßs(t)i(t)- yi(t) dt Which we can factor and look at like this: di dt = (Bs(t)-y)i(t) It follows that i(t) will always be positive, and the rate of infection will be decided by the terms ßs (t) - y. 1. Explain why there will be no disease spread if the initial susceptible amount s(0) is less than 1/c (the reciprocal of the contact number) 2. Suppose that a disease has a contact number of 4, and you have a vaccine with an efficacy 100% (which is not realistic). This means that every person who receives the vaccine, will be immune from contracting the disease. What percentage of the population would need to receive the vaccine in order to stop an epidemic from starting? 3. Suppose that a vaccine is developed with an efficacy of approximately 95%. What proportion of the population would need to receive the vaccine to prevent an epidemic spread?
Transcribed Image Text:A look at heard immunity: When we had the contact number from the part above, it tells us how many people will be infected by a single individual. We can also use information about contact numbers to estimate heard immunity numbers and vaccination efficacy. It turns out that the rate of infection is governed by only a few things. Lets take a look at the equation in more detail. di = ßs(t)i(t)- yi(t) dt Which we can factor and look at like this: di dt = (Bs(t)-y)i(t) It follows that i(t) will always be positive, and the rate of infection will be decided by the terms ßs (t) - y. 1. Explain why there will be no disease spread if the initial susceptible amount s(0) is less than 1/c (the reciprocal of the contact number) 2. Suppose that a disease has a contact number of 4, and you have a vaccine with an efficacy 100% (which is not realistic). This means that every person who receives the vaccine, will be immune from contracting the disease. What percentage of the population would need to receive the vaccine in order to stop an epidemic from starting? 3. Suppose that a vaccine is developed with an efficacy of approximately 95%. What proportion of the population would need to receive the vaccine to prevent an epidemic spread?
This project will investigate the SIR model and use numeric methods to find solutions to the system of coupled, non-linear differential equations. We will work through the derivation of the model and some assumptions. You will need to use technology, in the form of a spreadsheet (Excel/Google Sheets) or computer code (C, C++, Python, Java, etc) to obtain approximate numeric solutions.
Transcribed Image Text:This project will investigate the SIR model and use numeric methods to find solutions to the system of coupled, non-linear differential equations. We will work through the derivation of the model and some assumptions. You will need to use technology, in the form of a spreadsheet (Excel/Google Sheets) or computer code (C, C++, Python, Java, etc) to obtain approximate numeric solutions.
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