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<p>In this study, we have analyzed the dynamic behavior of a fractional-order predator–prey model with disease in the prey using the Caputo derivative. There are three components in this prey–predator model at time <i>t</i>: an infected prey, a susceptible prey, and a predator. The fractional-order model addresses the complexities of non-local interactions and memory effects by using fractional derivatives. Our study examined the local stability at equilibrium points and the residual error of the proposed fractional eco-epidemiological model. The non-integer eco-epidemiological model has been numerically studied and behaviorally analyzed using phase portraits and bifurcation plots, as well as time series diagrams with the Caputo derivative. Additionally, we have described the sensitivity analysis for the parameters of prey–predator model. This non-integer prey–predator model is solved numerically using the Bernoulli polynomial-based wavelets method and the Adam–Bashforth technique with Caputo derivative. Numerical simulations were carried out using MATLAB programming. Our simulations enable us to demonstrate the elegance of fractional derivatives in eco-epidemiology.</p>

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Numerical analysis of the prey–predator model with Bernoulli wavelet and Adams–Bashforth schemes

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Ajay Kumar,
  • Dhirendra Bahuguna

摘要

In this study, we have analyzed the dynamic behavior of a fractional-order predator–prey model with disease in the prey using the Caputo derivative. There are three components in this prey–predator model at time t: an infected prey, a susceptible prey, and a predator. The fractional-order model addresses the complexities of non-local interactions and memory effects by using fractional derivatives. Our study examined the local stability at equilibrium points and the residual error of the proposed fractional eco-epidemiological model. The non-integer eco-epidemiological model has been numerically studied and behaviorally analyzed using phase portraits and bifurcation plots, as well as time series diagrams with the Caputo derivative. Additionally, we have described the sensitivity analysis for the parameters of prey–predator model. This non-integer prey–predator model is solved numerically using the Bernoulli polynomial-based wavelets method and the Adam–Bashforth technique with Caputo derivative. Numerical simulations were carried out using MATLAB programming. Our simulations enable us to demonstrate the elegance of fractional derivatives in eco-epidemiology.