(a) Explanation Given: The population of the community is 700. It is visited by an outsider who carries influenza. After 6 weeks 300 people are uninfected. Calculation: Consider t as the time ( in days ) and y as the number of individuals infected at time t . The rate of spread of the disease satisfies the following logistic equation. d y d t = k ( 1 − y N ) y The general solution of the above differential equation is as follows: y = N 1 + b e − k t ...... ( 1 ) It is given that an outsider carries influenza. After 6 weeks 300 people are uninfected. Therefore, the conditions are as follows: y ( 0 ) = 1 y ( 6 ) = 400 Substitute 700 for N 0 for t and 1 for y in equation ( 1 ) to obtain the value of b . 1 = 700 1 + b e − k ( 0 ) 1 = 700 1 + b b + 1 = 700 b = 699 Substitute 700 for N , 699 for b , 6 for t and 400 for y in equation ( 1 ) to obtain the value of k . 400 = 700 1 + b e − k ( 6 ) 400 = 700 1 + b e − 6 k 1 + 699 e − 6 k = 700 400 699 e − 6 k = 7 4 − 1 Further simplify the above equation (b) To determine The number of people still uninfected after 7 weeks. (c) To determine The maximum infection rate will occur.

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Differential Equations

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Chapter 10, Problem 64RE

(a)

To determine

The equation for the number of people uninfected at time t.

(b)

To determine

The number of people still uninfected after 7 weeks.

(c)

To determine

The maximum infection rate will occur.

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Chapter 10, Problem 63RE

Chapter 10, Problem 65RE

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Chapter 10 Solutions

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

Ch. 10.1 - Find all solutions of the differential equation . Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Prob. 4YT Ch. 10.1 - Prob. 1WE Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 5WE Ch. 10.1 - Find the general solution for each differential...

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The equation for the number of people uninfected at time t .

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The equation for the number of people uninfected at time t.

The number of people still uninfected after 7 weeks.

The maximum infection rate will occur.

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Chapter 10 Solutions