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 without 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, aligned 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 (α_{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. Key features include biocompatibility assessments, optimized antigen dosing, LNP stability evaluations, lymphatic trafficking kinetics, and strategies to mitigate immunological interference in multivalent formulations, with explicit delineation of potential biases, confounders, and alternative hypotheses. A sophisticated ordinary differential equation (ODE) system models the temporal dynamics of discrete dosing via a pharmacokinetically parameterized antigen input function A(t), incorporating maternal antibody attenuation. This ODE framework is extended to broader autoimmune diseases, including rheumatoid arthritis and type 1 diabetes, enabling cross-disease insights and therapeutic generalizations. Bayesian inference calibrates the model against data from the LEAP and EAT trials using a bridging parameter ϕ, validated through an exhaustive suite of sensitivity analyses: local, one-at-a-time (OAT), and global variance-based (Sobol') methods, augmented by Morris screening and eFAST for convergence assurance. The proposal includes a WHO-aligned cost-benefit analysis with 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 work integrates immunology, systems biology, and translational science to advance equitable global prophylaxis, while transparently articulating epistemological boundaries and empirical refutability criteria, establishing it as a paradigm for rigorous interdisciplinary scholarship.