Applications of Systems of Equations 477Use computer software to solve the following epidemic with inoculation
model
dS
dt = -.OlSI - .lSdIdt = .OlSI - 3I
dRdi= 3I + .lS
on the interval [O, 5] where t is in days for the initial conditions:
(i) So = 300, Io = 10 , Ro = (^0) (ii) So = 500, Io = 10, Ro = 0
In each case, display S, I, and Ron a single graph and display a phase-plane
graph of I versus S. Compare your results with the results of exercise l. Does
an epidemic occur in case (ii) as it did in exercise 1? What is limt_, 00 S(t) in
each case?
- A rapidly increasing number of infectives can frighten members of the
susceptible group and ~ause them to aggressively seek inoculation. So suppose
that the inoculation rate is proportional to the product of the number of
susceptibles and the number of infectives instead of simply proportional to the
number of susceptibles. In this case, a model for an epidemic with inoculation
is
dS
dt = - /3SI - aSI
dI
dt =/3SI-rIdRdi= rI +aSI
where a, /3, and r are positive constants.
Use computer software to solve the foll owing epidemic with inoculation
model
dS
dt = -.OlSI - .05SI
~~ = .OlSI - 3I
dR = 3I .05SI
dt +
on the interval [O, 5] where t is in days for the initial conditions: