A Nonlocal Aggregation–Diffusion Model with Adaptive Perception Kernels for Descriptive Norm Dynamics

This paper presents a partial differential equation (PDE)-based auto-aggregation model for simulating descriptive norm dynamics in autonomous multi-agent systems, capturing convergence and violation through nonlocal perception kernels and external potential fields. Extending classical transport equations, the framework represents opinion popularity as a continuous distribution, enabling direct interactions without Bayesian guessing of beliefs. Using azithromycin and prednisolone as illustrative treatment features from a real-world coronavirus disease 2019 (COVID-19) dataset, the numerical experiments exhibit reduced local perception-to-target discrepancy under target-based updating, redistribution and the formation of a new unimodal density under fact-informed updates with potential guidance, and persistent multiple peaks without target-based fitting or an external potential field. Quantitative evaluation uses population-weighted local perception-to-target Wasserstein distance estimates for the selected treatment dimensions.