Uncorrected Proof Research Paper Computational Methods for Differential Equations http://cmde.tabrizu.ac.ir Vol. *, No. *, *, pp. 1-15 DOI:10.22034/cmde.2025.64960.2960 Fractional Prey-Predator Model in Biological Pest Control Ram Pratap Chauhan 1 , Ravikant Singh 2 , and Srinivasarao Thota 1,∗ 1 Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh–522503, India. 2 Department of Mathematics, Amity School of Engineering and Technology, Amity University, Gwalior, Madhya Pradesh–474020, India. Abstract In developing countries, the agricultural industry is pivotal in economic development and sustaining rural liveli- hoods. However, one of the major challenges to achieving food security globally is crop losses due to pests. Pest control is a vital practice for safeguarding crops; it is often complicated by the need to balance pest reduction with the associated costs of operations, as well as the potential impacts on the environment and human health. This delicate balance is crucial for sustainable agriculture and long-term food security. In this paper, a mathematical model is developed to quantify the complex biological processes involved in the biological control of pests through prey-predator mechanisms. We provide trajectory analysis in the research discussion analysis. Keywords. Fractional derivative, Prey-predator, Biological pest, Food Security, Stability. 2010 Mathematics Subject Classification. 92D45, 37N25, 34D20. 1. Introduction The nature of the affected crop defines the nature of the impacts. Damage to food crops can lead reduced food availability, which may also reduce the economic sector. The severity of these initial impacts depends on the intensity and duration of the disease outbreak. These primary effects can also trigger further consequences: epidemics on food crops may result in a shortage in supply to storage systems, a decline in exports, or an inconsistent supply of food to markets. These outcomes are often a reflection of the socioeconomic conditions and market structures at various scales [22]. Food security is increasingly threatened by various factors worldwide. Among the most significant risks, especially in developing countries, are food damage caused by plant diseases and pests [9]. Pests are organisms that disrupt human activities or cause damage, loss, or irritation to crops, stored products, and livestock. In agriculture, pest control is predominantly reliant on chemical insecticides. However, this approach has several drawbacks, including diminished effectiveness over time due to pests developing resistance, adverse impacts on beneficial insect populations, and the disruption of natural pest control systems. Such disruptions can lead to the destruction of pests’ natural enemies, the emergence of more destructive pest outbreaks, and the accumulation of chemical residues in crops. As global population growth heightens the need for effective pest management, developing sustainable techniques becomes crucial. Educating farmers about agricultural practices and pest control methods is equally important to enhance these efforts [23]. Effective pest control strategies have a profound societal impact, making it essential to adopt integrated approaches. The use of natural predators, in combination with the judicious application of chemical pesticides, is strongly recommended for managing pest populations. Biological control [21], in particular, is defined as the use of parasitoids, predators, or pathogens to maintain the population density of a target organism at levels lower than would occur in the absence of these natural enemies. Mathematical models are being utilized more frequently to analyze agricultural issues, especially in the context of pest and natural enemy interactions. By employing simulation tools, these models enhance the understanding of system dynamics, offering researchers a comprehensive view of the environment. This capability allows them to Received: 10 December 2024; Accepted: 22 May 2025. ∗ Corresponding author. Email: srinithota@ymail.com, t srinivasarao@av.amrita.edu. 1