Using dde23 to solve delay differential equations that contain integrals.

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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!

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