Delayed Parasitism and Population Cycles in Mosquito–Water Mite Systems

Abstract

This study uses a delay differential equation (DDE) model that takes into account both parasitism and predation effects to examine the dynamic interactions between water mites and mosquito populations. The proposed DDE model uniquely captures the dual ecological role of water mites as both parasites and predators of mosquitoes through biologically motivated nonlinear interactions. To account for parasitism’s biological lag and its effect on water mite reproduction, the model adds a time delay. In order to ensure biologically meaningful solutions, mathematical analysis verifies the system’s positivity and boundedness. The model performs stability analysis at a variety of delay conditions and locates a biologically viable equilibrium point. At a critical point of delay, a Hopf bifurcation occurs and marks the beginning of long-term oscillations of the population dynamics. Numerical simulations are used to create time-domain plots and phase space diagrams that demonstrate how the system responds without a delay, below the delay threshold, at the critical point and exceeding it. Under the findings, a small delay results in the creation of the asymptotic stability, and a large delay results in the creation of the periodic solutions as well as population cycles. The analysis of the significance of time delays in the establishment of ecological balance between the parasite and host species is brought into the limelight of the study. It further emphasizes that the study establishes the existence and uniqueness of the biologically feasible equilibrium, investigates delay-induced stability switching and Hopf bifurcation, and examines the influence of developmental delay on the long-term population dynamics. The modeling approach also serves as a natural foundation of future ecological studies that incorporate time-dependent interactions by providing an understanding of biological control measures and population management in aquatic ecosystems.