308 Infectious Disease Modeling
considering subpopulations of males and females. We will develop such a
model by studying the dynamics of gonorrhea.
Gonorrhea is caused by a bacterial infection that is spread through sexual
contact. The CDC estimates that approximately 650,000 cases of gonorrhea
occur each year in the United States, making it a common sexually transmitted
disease. Within a few days of infection, men usually develop symptoms such
as a burning sensation when urinating, a yellowish discharge from the penis,
and painful or swollen testicles. Women typically have milder initial symp-
toms, which can be mistaken for a bladder infection. If untreated, however,
women may develop pelvic inflammatory disease, which can lead to infertil-
ity. Babies born to infected woman may get the infection, which can cause
blindness and be life-threatening. Untreated men may also become infertile
or be left with urethral scarring. Fortunately, antibiotic treatment is effective,
though penicillin is no longer used since resistant strains have developed.
Once cured, an individual is unfortunately at risk of recontracting the illness;
no immunity results from an infection.
While an infected female may be asymptomatic, she may still pass on the
infection to a sexual partner. Moreover, it is reasonable to assume that the
average time from infection to treatment might be longer for females than
males, because females may be unaware of their infected state for a longer
period. In addition, data indicate that, in heterosexual intercourse between
infected and susceptible individuals, a new infection is roughly twice as likely
to result if the male is the infective rather than the female.
Because of these sex differences, to begin modeling gonorrhea, we divide
the human population into two groups: females and males. Within the two
groups, we have two subclasses: susceptible females S
f
t
and infective females
I
f
t
, and susceptible males S
m
t
and infective males I
m
t
. Because gonorrhea is
curable, but the treatment offers no immunity from further infection, there
are no removed classes.
As before, we will assume that populations remain constant, S
f
+ I
f
=
N
f
, S
m
+ I
m
= N
m
, and the total population under study is N = N
f
+ N
m
.
If we assume, for modeling purposes, that gonorrhea is only spread through
heterosexual contact, then we will need a transmission coefficient α
f
to mea-
sure the rate at which gonorrhea is spread from men to women and a transmis-
sion coefficient α
m
for the spread from women to men. Similarly, this model
requires two removal rates γ
f
and γ
m
, one for each sex.
From the description of gonorrhea, should α
f
or α
m
be larger? Should
γ
f
or γ
m
be larger?