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Consider the disease epidemics model from assignment 9, d.S rI - PSI, dt dI dt 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.

Consider the disease epidemics model from assignment 9, d.S rI - PSI, dt dI dt 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.

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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Consider the disease epidemics model from assignment 9, d.S dt dI dt - TI - PSI, PSI - rI, 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:Consider the disease epidemics model from assignment 9, d.S dt dI dt - TI - PSI, PSI - rI, 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.
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