A Delayed Host-Parasite Model with Partial Host Cover and Parasite Harvesting

Abstract

This paper improves and investigates a delayed host parasite communication model that encompasses partial host cover and parasite harvesting. The partial cover represents a constant fraction of the host population that is temporarily shielded from parasitic attack due to behavioural, spatial, or physiological refuge. The delay accounts for the time lag in the parasites growing process or infection transmission. A system of nonlinear delay differential equations formulated to describe the population dynamics. The equilibria and their stability are examined, and analytical conditions for the occurrence of the Hopf bifurcation are derived. The results show that intensifying time delay can dislocate the positive equilibrium, ahead to periodic oscillations, whereas increasing host cover or harvesting strength has a steadying influence. The numerical simulations back up the theory and show just how complicated these systems can get. We see stable coexistence, ongoing oscillations, and even points where everything collapses. This study really shines a light on how delayed reactions, safe zones, and different harvesting strategies shape the long-term behaviour of host parasite relationships, passive implications for sustainable management and biological control.