An efficient numerical scheme for fractional host–parasite hyperparasite interaction model

In this paper, we analyse the unique characteristics of hyperparasites and discharge incidents in the initial stage of parasite populations. If hyperparasites are effectively developed in a population, they can play a crucial role in controlling host–parasite interactions. First, we expanded the integer-order host–parasite–hyperparasite model by using different fractional-order operators. We then examined the uniqueness and existence of the solutions of the non-integer order host–parasite–hyperparasite model. We inspected the stability of the model using the Ulam–Hyers stability theorem and employed a numerical technique to find a solution to the host–parasite–hyperparasite model using the fractional operator. Finally, we discussed the graphical results with the help of the Toufik–Atangana (T–A) numerical scheme. To examine the host–parasite–hyperparasite models and approximate results, we employed the Caputo fractional operator and the Atangana–Baleanu (A–B) fractional operator. The numerical results demonstrate that every important aspect of the model is preserved by the anticipated numerical method, which also provides an understandable solution for the fractional problem. The findings of this study bear significant implications for the theory and methodology of biological control of plant diseases associated with hyperparasites. It sheds light on the ecology of biological invasions, which is a subject of great importance in today's world. This research provides valuable insights that can design effective strategies to combat plant diseases and prevent the spread of invasive species.