Stability and bifurcations analysis in an ecoepidemic system with prey group defense and two infectious routes

In this paper, we explore an ecoepidemic model of a prey–predator type in which the prey population is infected by an SI type disease with two infectious routes (horizontal and vertical). Specifically, we consider that both susceptible and infected preys have emergent carrying capacities, which implies that both preys are involved in intraspecific and interclass competitions. In addition, we assume that the susceptible prey gathers together to defend the predator. It is found that the proposed system exhibits abundant dynamics and admits nine equilibria: three boundary equilibria, three plane equilibria, and three interior equilibria. At least one of the three populations can be eliminated from the ecosystem based on the stability of the previous two types of equilibria. According to the stability of the interior equilibria, the given ecosystem can allow the coexistence of susceptible prey–infected prey–predator. We then investigate the stability and direction of Hopf bifurcation. A sensitivity analysis is also conducted to show the effects of the six parameters which are relevant to the emergent carrying capacity and infectious routes on the studied system. Numerical simulations are conducted to verify our theoretical conclusions.