The following ODES have been proposed as a model of an epidemic: ds -aSI dt dI aSI – rl dt dR rl dt where S = the susceptible individuals, I = 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 = 0.15/d. Develop time-series plots of all the state variables. Also generate a phaseplane plot of S versus / versus R.
The following ODES have been proposed as a model of an epidemic: ds -aSI dt dI aSI – rl dt dR rl dt where S = the susceptible individuals, I = 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 = 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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer the poin (a) with excel
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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