Effect of disease-selective predation on prey infected by contact and external sources

Abstract

We propose and analyze a simple mathematical model for susceptible prey (S)-infected prey (I)-predator (P) interaction, where the susceptible prey population (S) is infected directly from external sources as well as through contact with infected class (I) and the predator completely avoids consuming the infected prey. The model is analyzed to obtain different thresholds of the key parameters under which the system exhibits stability around the biologically feasible equilibria. Through numerical simulations we display the effects of external infection and the infection through contact on the system dynamics in the absence as well as in the presence of the predator. We compare the system dynamics when infection occurs only through contact, with that when it occurs through contact and external sources. Our analysis demonstrates that under a disease-selective predation, stability and oscillations of the system is determined by two key parameters: the external infection rate and the force of infection through contact. Due to the introduction of external infection, the predator and the prey population show limit-cycle oscillations over a range parametric values. We suggest that while predicting the dynamics of such an eco-epidemiological system, the modes of infection and the infection rates might be carefully investigated.