Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у — 13ху — 68у where X represents susceptible individuals and y represents infected indi

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider a disease that propagates according to the system
dx
357 — Зху — 3х
dt
dy
= X
dt
х?у — 13ху — 68у
where X represents susceptible individuals and y represents infected individuals.
(a) Find all biologically meaningful equilibria.
Transcribed Image Text:Consider a disease that propagates according to the system dx 357 — Зху — 3х dt dy = X dt х?у — 13ху — 68у where X represents susceptible individuals and y represents infected individuals. (a) Find all biologically meaningful equilibria.
Classify each biologically meaningful equilibrium and determine its stability.
Draw the nullclines in the region X > 0, y > 0.
Draw the solution starting at(xo, yo) = (125, 1).
Describe in words what happens eventually.
Transcribed Image Text:Classify each biologically meaningful equilibrium and determine its stability. Draw the nullclines in the region X > 0, y > 0. Draw the solution starting at(xo, yo) = (125, 1). Describe in words what happens eventually.
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