Mathematical Modelling for Circular Prey-Predator Model

Abstract

The objective of the paper is to explore a unique concept involving cyclical relationships between prey(s) and predator(s) wherein stakeholders in a dynamic ecosystem can harm one another. The paper intends to highlight the possibility of an organism to shoulder both roles- as a prey and a predator with respect to the same organism(s) and environment, hence forming a cyclical relationship between all stakeholders in a given prey-predator ecosystem. The mathematical model hence developed makes use of conventional models, namely the SIR Epidemic Model and Prey Predator Model to show how two different mathematical models can be used together to model a situation in a more realistic way and gain meaningful inferences from it. The above mentioned conventional models have been clubbed together using basic mathematical modelling tools involving compartmental diagrams, differential equation generator, ODE & PDE solver, stability analysis solver, etc. These inferences drawn from the new model give an insight to theoretical results to combat present and future epidemics and maintain a balance in food webs in an ecosystem. The paper presents mathematical models for special cases (i.e. 2-way and 3-way models) and sums up with a general model (i.e. n+1-way model) to form a basis for future research and development. This will enable researchers to deal with more complex and real time issues like pandemic outbreaks, extinction of species, destabilized ecological cycles etc.