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# Solved: PROBLEM 16E(a) In , explain why it is sufficient ISBN: 9781111827052 44

## Solution for problem 16E Chapter 3.3

A First Course in Differential Equations with Modeling Applications | 10th Edition

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Problem 16E

PROBLEM 16E

(a) In Problem 15, explain why it is sufficient to analyze only (b) Suppose k1 = 0.2, k2 = 0.7, and n = 10. Choose various values of i(0) = i0, 0 < i0 < 10. Use a numerical solver to determine what the model predicts about the epidemic in the two cases s0 > k2/k1 and s0 k2/k1. In the case of an epidemic, estimate the number of people who are eventually infected.

Reference: Problem 15

SIR Model Acommunicable disease is spread throughout a small community, with a fixed population of n people, by contact between infected individuals and people who are susceptible to the disease. Suppose that everyone is initially susceptible to the disease and that no one leaves the community while the epidemic is spreading. At time t, let s(t), i(t), and r(t) denote, in turn, the number of people in the community (measured in hundreds) who are susceptible to the disease but not yet infected with it, the number of people who are infected with the disease, and the number of people who have recovered from the disease. Explain why the system of differential equations where k1 (called the infection rate) and k2 (called the removal rate) are positive constants, is a reasonable mathematical model, commonly called a SIR model, for the spread of the epidemic throughout the community. Give plausible initial conditions associated with this system of equations.

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##### ISBN: 9781111827052

Since the solution to 16E from 3.3 chapter was answered, more than 283 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. This full solution covers the following key subjects: disease, people, epidemic, community, model. This expansive textbook survival guide covers 109 chapters, and 4053 solutions. The full step-by-step solution to problem: 16E from chapter: 3.3 was answered by , our top Calculus solution expert on 07/17/17, 09:41AM. The answer to “(a) In 15, explain why it is sufficient to analyze only (b) Suppose k1 = 0.2, k2 = 0.7, and n = 10. Choose various values of i(0) = i0, 0 < i0 < 10. Use a numerical solver to determine what the model predicts about the epidemic in the two cases s0 > k2/k1 and s0 k2/k1. In the case of an epidemic, estimate the number of people who are eventually infected.Reference: SIR Model Acommunicable disease is spread throughout a small community, with a fixed population of n people, by contact between infected individuals and people who are susceptible to the disease. Suppose that everyone is initially susceptible to the disease and that no one leaves the community while the epidemic is spreading. At time t, let s(t), i(t), and r(t) denote, in turn, the number of people in the community (measured in hundreds) who are susceptible to the disease but not yet infected with it, the number of people who are infected with the disease, and the number of people who have recovered from the disease. Explain why the system of differential equations where k1 (called the infection rate) and k2 (called the removal rate) are positive constants, is a reasonable mathematical model, commonly called a SIR model, for the spread of the epidemic throughout the community. Give plausible initial conditions associated with this system of equations.” is broken down into a number of easy to follow steps, and 229 words.

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