Using dde23 to solve delay differential equations that contain integrals.

Hi there! I am looking to solve a system of delay differential equations, and within this system of DDEs there is an integral who integrand depends on variables of the system. For example:

,

where,

,

So as you can see the recruitment rates, and , depend on the integral of a fucntion that contains the other variable . Is dde23 capable of solving this? And, if so what is the best way to code this please?

Thank you so much in advance for your help!