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2. A simple mathematical model in epidemiology for the spread of a disease assumes that the rate at which the disease spreads is jointly proportional to the number of infected people and the number of uninfected people. Suppose that there are a total of N people in the population, of whom No are infected initially. Show that the number of infected people after t weeks, x(t), is given by a) x(t) = N- No 1+ -kNt No where k is a nositive constant

2. A simple mathematical model in epidemiology for the spread of a disease assumes that the rate at which the disease spreads is jointly proportional to the number of infected people and the number of uninfected people. Suppose that there are a total of N people in the population, of whom No are infected initially. Show that the number of infected people after t weeks, x(t), is given by a) x(t) = N- No 1+ -kNt No where k is a nositive constant

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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2. A simple mathematical model in epidemiology for the spread of a disease assumes that the rate at which the disease spreads is jointly proportional to the number of infected people and the number of uninfected people. Suppose that there are a total of N people in the population, of whom No are infected initially. Show that the number of infected people after t weeks, x(t), is given by a) N x(t) = N- No le No 1+ -kNt where k is a positive constant.
Transcribed Image Text:2. A simple mathematical model in epidemiology for the spread of a disease assumes that the rate at which the disease spreads is jointly proportional to the number of infected people and the number of uninfected people. Suppose that there are a total of N people in the population, of whom No are infected initially. Show that the number of infected people after t weeks, x(t), is given by a) N x(t) = N- No le No 1+ -kNt where k is a positive constant.
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