The existence of a positive periodic solution for
{
d
H
(
t
)
d
t
=
r
(
t
)
H
(
t
)
[
1
−
H
(
t
−
τ
(
t
)
)
K
(
t
)
]
−
α
(
t
)
H
(
t
)
P
(
t
)
,
d
P
(
t
)
d
t
=
−
b
(
t
)
P
(
t
)
+
β
(
t
)
P
(
t
)
H
(
t
−
σ
(
t
)
)
\begin{equation*} \begin {cases} \frac {\mathrm {d}H(t)}{\mathrm {d}t}=r(t)H(t) \left [1-\frac {H(t-\tau (t))}{K(t)}\right ] -\alpha (t)H(t) P(t),\ \frac {\mathrm {d}P(t)}{\mathrm {d}t}=-b(t)P(t)+\beta (t)P(t)H(t-\sigma (t)) \end{cases} \end{equation*}
is established, where
r
r
,
K
K
,
α
\alpha
,
b
b
,
β
\beta
are positive periodic continuous functions with period
ω
>
0
\omega >0
, and
τ
\tau
,
σ
\sigma
are periodic continuous functions with period
ω
\omega
.