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(a) If a single infectious individual enters the city at t = 0, compute the progression of the epidemic until the number of infected individuals falls below 10. Use the following parameters: a = 0.002/(person-week) and r = %3D 0.15/d. Develop time-series plots of all the state variables. Also generate a phaseplane plot of S versus / versus R.

(a) If a single infectious individual enters the city at t = 0, compute the progression of the epidemic until the number of infected individuals falls below 10. Use the following parameters: a = 0.002/(person-week) and r = %3D 0.15/d. Develop time-series plots of all the state variables. Also generate a phaseplane plot of S versus / versus R.

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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The following ODES have been proposed as a model of an epidemic: ds = -aSI dt dI = aSI dt - rl dR = rl dt where S = the susceptible individuals, / = the infected, R = the recovered, a = the infection rate, and r = the recovery rate. A city has 10,000 %3D people, all of whom are susceptible. (a) If a single infectious individual enters the city at t = 0, compute the progression of the epidemic until the number of infected individuals falls below 10. Use the following parameters: a = 0.002/(person-week) and r = %3D 0.15/d. Develop time-series plots of all the state variables. Also generate a phaseplane plot of S versus / versus R. (b) Suppose that after recovery, there is a loss of immunity that causes recovered individuals to become susceptible. This reinfection mechanism can be computed as pR, where p = the reinfection rate. Modify the model to include this mechanism and repeat the computations in (a) using p = 0.015/d.
Transcribed Image Text:The following ODES have been proposed as a model of an epidemic: ds = -aSI dt dI = aSI dt - rl dR = rl dt where S = the susceptible individuals, / = the infected, R = the recovered, a = the infection rate, and r = the recovery rate. A city has 10,000 %3D people, all of whom are susceptible. (a) If a single infectious individual enters the city at t = 0, compute the progression of the epidemic until the number of infected individuals falls below 10. Use the following parameters: a = 0.002/(person-week) and r = %3D 0.15/d. Develop time-series plots of all the state variables. Also generate a phaseplane plot of S versus / versus R. (b) Suppose that after recovery, there is a loss of immunity that causes recovered individuals to become susceptible. This reinfection mechanism can be computed as pR, where p = the reinfection rate. Modify the model to include this mechanism and repeat the computations in (a) using p = 0.015/d.
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