A study of general reaction-advection-diffusion equations describing dynamics between target, partaker, and inhibitor

This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and an inhibitor. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime hotspots in urban areas to shifts in public attitudes during critical events as individuals and control units move through space. We prove local and global existence of solutions under realistic assumptions and showcase the model through scenarios of protest intensity driven by demonstrators joining and mitigated by two different control managements. Numerical simulations highlight the resulting complex spatial patterns and temporal dynamics.