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d.S dt dI dt = TI - PSI, pSI – TI, where I represents individuals who are infected with some virus and S rep- resents individuals who are susceptible to infection. This time we will not assume conservation of individuals. (a) Find any critical points associated with this system. (b) Calculate the linearized system near a critical point. (c) Determine the stability of the critical point as a function of the parame- ters p and r. (d) State values of p and/or r where you would expect the nature of the

d.S dt dI dt = TI - PSI, pSI – TI, where I represents individuals who are infected with some virus and S rep- resents individuals who are susceptible to infection. This time we will not assume conservation of individuals. (a) Find any critical points associated with this system. (b) Calculate the linearized system near a critical point. (c) Determine the stability of the critical point as a function of the parame- ters p and r. (d) State values of p and/or r where you would expect the nature of the

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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ds dt dI dt = TI - PSI, pSI - TI, where I represents individuals who are infected with some virus and S rep- resents individuals who are susceptible to infection. This time we will not assume conservation of individuals. (a) Find any critical points associated with this system. (b) Calculate the linearized system near a critical point. (c) Determine the stability of the critical point as a function of the parame- ters p and r. (d) State values of p and/or r where you would expect the nature of the critical point (s) to change.
Transcribed Image Text:ds dt dI dt = TI - PSI, pSI - TI, where I represents individuals who are infected with some virus and S rep- resents individuals who are susceptible to infection. This time we will not assume conservation of individuals. (a) Find any critical points associated with this system. (b) Calculate the linearized system near a critical point. (c) Determine the stability of the critical point as a function of the parame- ters p and r. (d) State values of p and/or r where you would expect the nature of the critical point (s) to change.
Expert Solution
Step 1: Conceptual Introduction

The system of differential equations given describes a simplified model of disease spread.

The variable I represents the number of infected individuals, and S represents the number of susceptible individuals.

The term rI represents the rate at which infected individuals recover or die, and the term pSI represents the rate at which susceptible individuals get infected.

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