Explanation Calculation: Everyone is initially susceptible to the disease and that no one leaves the community while the epidemic is spreading. So, total population n is s ( t ) + i ( t ) + r ( t ) = n (1) Here, s ( t ) is the number of people in the community (measured in hundreds) who are susceptible to the disease but not yet infected with it, i ( t ) is the number of people who are infected with the disease, and r ( t ) the number of people who have recovered from the disease. The rate of change of change of the susceptible persons is proportional to the number of contacts between the number of people infected and the number of people who are susceptible to it. d s d t = − k 1 s i The rate of change of change of number of persons who have recovered is proportional to the number of people infected. d r d t = k 2 i Differentiate equation (1) with respect to t . d d t ( s + i + r ) = d d t ( n ) d s d t + d i d t + d r d t = 0 d i d t = − d s d t − d r d t Substitute − k 1 s i for d s d t and k 2 i for d r d t in above equation

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.9, Problem 17E

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To explain: the given system of differential equations is a reasonable mathematical model and to find a reasonable set of initial conditions.

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Chapter 2.9, Problem 16E

Chapter 2.9, Problem 18E

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Chapter 2 Solutions

Advanced Engineering Mathematics

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - Prob. 18E Ch. 2.2 - Prob. 19E Ch. 2.2 - Prob. 20E Ch. 2.2 - 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the given system of differential equations is a reasonable mathematical model and to find a reasonable set of initial conditions.

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Chapter 2 Solutions