Infection dynamics of rabbit and red fox with alternative prey

Abstract

In many countries, the decline in red foxes due to Rabbit hemorrhagic disease (RHD) in primary prey European rabbits is a significant concern. We proposed a four-compartment spatiotemporal rabbits-alternative prey-red fox eco-epidemiological model with mange disease and hunting in red foxes. The essential theoretical properties, such as existence, boundedness, stability, and bifurcation analysis, are executed. We have also conducted Turing instability and Higher-order stability analysis for the spatiotemporal model. Hopf bifurcation is shown at a critical value of hunting rate \(h=h_c\) using central manifold theory. Numerical simulation reveals that the present dynamic is chaotic for a mange disease transmission rate's threshold value \(\beta=\beta_+\), the most significant factor in the present dynamics. We can control the red fox population by controlling the mange contact rate despite RHD disease in European rabbits. Also, the model does not have diffusion-driven instability due to alternative prey, and if the system is linearly stable, it remains stable for higher-order.