Ecological Modelling of Two-Predator One-Prey Interactions with Holling Functional Responses and Disease Spread

Abstract

Infectious disease within predator–prey systems represents a critical but underexplored driver of ecological instability, with the potential to alter population persistence across trophic levels and contribute to biodiversity loss. This study develops an eco-epidemiological model of two-predator–one-prey interactions incorporating Holling type I and type IV functional responses and disease transmission from prey to predators through direct predation. The model is formulated as a system of five ordinary differential equations representing susceptible and infected prey, susceptible and infected first predator, and second predator populations. Four ecologically meaningful equilibrium states are identified, corresponding to total extinction, partial extinction, disease-free, and full coexistence, all of which are locally asymptotically stable under well-defined parametric conditions. Numerical simulations conducted in Maple reveal that the half-saturation constant governing predation on infected prey plays a dominant role in determining population persistence across trophic levels, while the direct disease transmission rate exerts a comparatively weaker effect. Importantly, increasing the half-saturation level can extend the period of multi-species coexistence but, beyond a critical threshold, precipitates the extinction of the first predator population. These findings offer a theoretical basis for understanding how disease-mediated trophic interactions govern the long-term stability of multi-species ecological systems, with implications for biodiversity conservation and the management of ecosystems affected by wildlife disease.