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University of Florida
MMB
HOMEWORK IV
Due: April 4, 2012
Name:
ID #:
Instructor:
Directions:
You have until 5:00 p.m. on the due date to answer the
following questions. You must show all your work as neatly and clearly as
possible and indicate the Fnal answer clearly. You may use any books and
you can work together but each of you must submit a homework.
Problem
Possible
Points
1
5
2
5
All
10
Total
20
1
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View Full Document (1) Malaria is an infectious disease transmitted by mosquitos. Susceptible human gets
infected when bitted by an infectious mosquito; susceptible mosquito gets infected
when it bites an infectious human. Let
I
H
(
t
) be the number of infected humans at
time
t
and
I
V
(
t
) be the number of infected mosquitos. If
M
the total humber of
mosquitos and
H
is the total number of humans (both assumed constant), then the
number of susceptible mosquitos is
M

I
V
and the number of susceptible humans
is
H

I
H
. Then the dynamics of the number of infected mosquitos and infected
humans is given by
(1)
I
′
V
(
t
) =
βI
H
(
M

I
V
)

gI
V
I
′
H
(
t
) =
αI
V
(
H

I
H
)

rI
H
where
β
=
ab
is the transmission rate from infected human to susceptible mosquito
and
α
=
ac
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This note was uploaded on 03/20/2012 for the course MAP 4484 taught by Professor Martcheva,m during the Spring '08 term at University of Florida.
 Spring '08
 Martcheva,M

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