A Meshless Radial Basis Function Approach for a Spatiotemporal Model of SARS-CoV-2 Immune Response and Tissue-Level Thermoregulatory Dynamics

This work presents a spatially explicit 19-variable reaction–diffusion model for within-host SARS-CoV-2 dynamics that integrates viral kinetics, innate and adaptive immune responses, cytokine regulation, antibody production, and tissue-level thermoregulatory dynamics. Adaptive immune recruitment is described through smooth sigmoidal activation functions, whereas pro-inflammatory cytokines are controlled by Michaelis–Menten-type saturation with IL-10 feedback. The thermoregulatory component is formulated as a downstream tissue-level inflammatory readout driven by bounded virus-dependent pyrogenic forcing, homeostatic relaxation, and effective thermal diffusion. The system is solved using a meshless multiquadric radial basis function collocation method based on Kansa’s formulation. Numerical simulations reproduce the qualitative progression of acute infection, including early viral expansion, innate immune activation, delayed adaptive recruitment, and immune-mediated clearance. Spatial analysis reveals heterogeneous tissue-level patterns, such as localized viral foci, antibody depletion near the infection center, delayed cytotoxic effector coverage, and transient thermal gradients. The proposed framework provides a biologically interpretable and computationally flexible approach for investigating the spatiotemporal organization of within-host SARS-CoV-2 immune dynamics, while remaining a mechanistic modeling study rather than a patient-specific clinical predictor.