& Epidemics. A model for the spread of contagious diseases is obtained by assuming that the rate of spread is proportional to the number of contacts between infected and noninfected persons, who are assumed to move freely among each other. Set up the model. Find the equilibrium solutions and indicate their stability or instability. Solve the ODE. Find the limit of the proportion of infected persons as t→0 and explain what it means.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Epidemics. A model for the spread of contagious
diseases is obtained by assuming that the rate of spread
is proportional to the number of contacts between
infected and noninfected persons, who are assumed to
move freely among each other. Set up the model. Find
the equilibrium solutions and indicate their stability or
instability. Solve the ODE. Find the limit of the
proportion of infected persons as 1→x and explain
what it means.
Transcribed Image Text:Epidemics. A model for the spread of contagious diseases is obtained by assuming that the rate of spread is proportional to the number of contacts between infected and noninfected persons, who are assumed to move freely among each other. Set up the model. Find the equilibrium solutions and indicate their stability or instability. Solve the ODE. Find the limit of the proportion of infected persons as 1→x and explain what it means.
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