Existence of periodic solutions for periodic eco-epidemic models with disease in the prey

For an eco-epidemic model with disease in the prey and periodic coefficients it is conjectured in Niu et al. (2011) [5] that, when the infected prey is permanent, there is a positive periodic orbit that is globally asymptotically stable in the interior of (R+)3. In this paper we prove the existence part of the conjecture for a large family of periodic systems.