Study of a symbiotic system with disease and delay

In the present paper, we study a model with two symbiotic species, where one of the species is subject to disease infection. We observe that for increasing mutualism, the system may become unbounded. We also perform sensitivity analysis to identify the sensitive parameters of the model. Further, we incorporate incubation delay in the disease transmission and investigate how the qualitative behavior of the system changes for the incubation delay. We analyze the model with the help of stability and bifurcation analysis. Taking time-delay as bifurcation parameter, Hopfbifurcation and direction of Hopf-bifurcation are investigated near the coexistence equilibrium point. We illustrate analytical findings through numerical simulations.