A Three-Dose Prophylactic Vaccine Against Food Allergy in Early Childhood: A Mechanistic, Bayesian, and Falsifiable Conceptual Framework with Extended ODE Modeling for Autoimmune Diseases and Comprehensive Global Sensitivity Analysis

Food allergy (FA) afflicts approximately 8% of children globally, posing a substantial public health challenge devoid of approved prophylactic measures. This manuscript presents a meticulously constructed, preclinically substantiated, and rigorously falsifiable framework for a three-dose prophylactic vaccine administered at 2, 4, and 12 months of age, harmonized with the World Health Organization's Expanded Program on Immunization (EPI). The vaccine incorporates hypoallergenic peptides from principal allergens—peanut (Ara h 2), egg (ovomucoid, Gal d 1), and milk ($ \alpha_{s1} $-casein)—encapsulated in GE11-functionalized lipid nanoparticles (LNPs) and adjuvanted with Pam3Cys and monophosphoryl lipid A (MPLA) to induce regulatory T cell (Treg)-mediated tolerance. Salient features encompass biocompatibility assessments, optimized antigen dosing, LNP stability evaluations, lymphatic trafficking kinetics, and strategies to avert immunological interference in multivalent configurations, with explicit delineation of potential biases, confounders, and alternative hypotheses. A sophisticated ordinary differential equation (ODE) system delineates the temporal dynamics of discrete dosing through a pharmacokinetically parameterized antigen input function \( A(t) \), incorporating maternal antibody attenuation. This ODE framework is extended to model broader autoimmune diseases, including rheumatoid arthritis and type 1 diabetes, facilitating cross-disease insights and therapeutic generalizations. Bayesian inference calibrates the model against data from the LEAP and EAT trials via a bridging parameter \( \phi \), with validation through an exhaustive suite of sensitivity analyses: local, one-at-a-time (OAT), and global variance-based (Sobol') methodologies, augmented by Morris screening and eFAST for convergence assurance. The proposal is consummated with a WHO-aligned cost-benefit analysis incorporating probabilistic sensitivity, a phased clinical roadmap (Phases I--III) with power calculations and interim analyses, and supplementary materials comprising mathematical derivations, computational implementations, raw simulation datasets, and uncertainty propagation analyses. This unfunded conceptual opus amalgamates immunology, systems biology, and translational science to propel equitable global prophylaxis, while transparently articulating epistemological boundaries and empirical refutability criteria, positioning it as a paradigm for Nobel-caliber interdisciplinary scholarship.