Effect of multiple gestation delays in a prey–predator food chain system with infected class of prey

Abstract

This article investigates a tri-trophic food chain model with the epidemic at the bottom level (prey) and gestation delays for the next two levels( the intermediate predator and top predator). The steady states' positivity, boundedness, existence, and stability have been analyzed. The study of Hopf bifurcation has been carried out for different steady states. It is shown that when the gestation delay for intermediate predator τ 1 is absent, the interior equilibrium is locally stable for gestation delays of top predators τ 2 ∈ (0, τ + 20 ) and performs Hopf bifurcation for all τ 2 > τ + 20 . Further, in the presence both the delay τ 1 and τ 2 , the system becomes unstable when τ 1 , τ 2 crosses their critical values τ ++ 10 , τ ++ 20