Impact of herd shape and delay in a two strain prey–predator model

In the present study, a novel two-strain eco-epidemiological SIS-type model with mass-action incidence rates is developed. In this model, we assumed that only healthy prey form herds, which not only limits predator access but may also injure or kill predators. Basic reproduction numbers for both strains derived, demonstrate that, despite differing values, the system permits coexistence of both infection strains. The numerical simulation demonstrates that certain herd formation and predator mortality thresholds eliminate one strain while the other strain persists, implying they have an inhibitory effect on strain persistence. In some cases, one strain may dominate over the other, similar to observations in avian influenza virus dynamics. The dynamics are investigated both with and without delay. Bifurcation analysis of the model without delay reveals critical thresholds for herd shape and predator mortality, leading to stable limit cycles, collapse, or extinction. Generalized Hopf (GH) bifurcations are observed in the (k−e1) parameter space, along with associated limit points of cycles (LPC), revealing complex dynamics and bistability under two-strain infection. Introducing delay induces further instability through new Hopf bifurcations, highlighting the role of time lags in population stability. These results underscore the interplay of herd effects with two-strain infection, demonstrating coexistence and the destabilizing influence of delays.