Discrete-time Non-Standard Finite Difference schemes for antimicrobial resistance models

Antimicrobial resistance (AMR) remains one of the most pressing global health challenges, with significant implications for human, animal, and environmental health. While numerous mathematical models have been developed to describe the dynamics of AMR, most are formulated in continuous time. In contrast, discrete-time models, particularly those based on Non-Standard Finite Difference (NSFD) schemes, offer important advantages, such as preserving key dynamical properties including nonnegativity, equilibrium points, and stability for arbitrary time steps. In this work, we analyze a family of discrete-time models for intra-host AMR dynamics, derived from continuous-time formulations via NSFD discretization. In particular, we consider four NSFD-based numerical schemes and investigate their qualitative properties. Moreover, we evaluate the performance of the discrete-time models through numerical simulations under various scenarios and conduct a comparative analysis of the four schemes from a numerical perspective. Additionally, we use one of the proposed schemes to construct a discrete-time representation of a more complex AMR model, which incorporates both mutation and horizontal gene transfer via plasmids. This modeling framework not only fills a methodological gap in the study of AMR dynamics, but also provides a foundation for computer simulations in several contexts where discrete-time analysis is more suitable.