A Nonstandard finite difference scheme for the tempered Caputo model of zika virus transmission

Abstract

This paper proposes a new epidemic transmission model based on the tempered Caputo fractional derivative, providing a novel framework for infectious disease dynamics that combines both biological accuracy and computational robustness. Theoretically, we rigorously prove the positivity and boundedness of model solutions and construct a new Lyapunov function to derive and verify the global asymptotic stability of the system equilibria. Secondly, to guarantee the positivity of numerical solutions, we develop a nonstandard finite difference (NSFD) discrete scheme for this fractional-order model and prove its stability. Finally, numerical simulations verify two merits: on the one hand, the fractional order not only determines the steady-state position of the system but also significantly regulates its convergence rate, enabling the accurate capture of transient dynamics neglected by traditional integer-order models; on the other hand, the proposed NSFD scheme is computationally effective.