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Consider a disease that propagates according to the system dx 357 — Зху — Зх dt - dy = x²y – 13xy – 68y dt - where X represents susceptible individuals and y represents infected individuals. (a) Find all biologically meaningful equilibria. (b) Show that J(x, y), the Jacobian matrix of this system, is given by — Зу — 3 -3x J = 2ху — 13у x² – 13x – 68 - (c) For each of the biologically meaningful equilibria from (a), find the eigenvalues of the Jacobian matrix.

Consider a disease that propagates according to the system dx 357 — Зху — Зх dt - dy = x²y – 13xy – 68y dt - where X represents susceptible individuals and y represents infected individuals. (a) Find all biologically meaningful equilibria. (b) Show that J(x, y), the Jacobian matrix of this system, is given by — Зу — 3 -3x J = 2ху — 13у x² – 13x – 68 - (c) For each of the biologically meaningful equilibria from (a), find the eigenvalues of the Jacobian matrix.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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Consider a disease that propagates according to the system dx 357 — Зху — 3х dt dy = x²y – 13xy – 68y dt where X represents susceptible individuals and y represents infected individuals. (a) Find all biologically meaningful equilibria. (b) Show that J(x, y), the Jacobian matrix of this system, is given by | -3y – 3 -3x J = 2ху — 13у х2 — 13х (c) For each of the biologically meaningful equilibria from (a), find the eigenvalues of the Jacobian matrix.
Transcribed Image Text:Consider a disease that propagates according to the system dx 357 — Зху — 3х dt dy = x²y – 13xy – 68y dt where X represents susceptible individuals and y represents infected individuals. (a) Find all biologically meaningful equilibria. (b) Show that J(x, y), the Jacobian matrix of this system, is given by | -3y – 3 -3x J = 2ху — 13у х2 — 13х (c) For each of the biologically meaningful equilibria from (a), find the eigenvalues of the Jacobian matrix.
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