In this paper, a fifth-order adaptive self-modeling network model is introduced to describe epigenetic regulation in T2-high asthma. These five orders of adaptivity and their interlevel interaction were modelled as a higher-order adaptive dynamical system according to the self-modeling network modeling principle. They cover epigenetic changes, gene expression, mRNA production, enzyme production, and physiological structures. Simulations demonstrate how extreme allergen exposure induces IFNG promoter methylation, downregulates Th1 differentiation, and causes a Th1/Th2 imbalance leading to persistent asthma symptoms. A second simulation introduces epigenetic therapy that demethylates the IFNG promoter, restoring the Th1/Th2 balance and reducing symptoms. These findings demonstrate how high-order adaptive networks can capture cascading biological regulation and provide a framework for exploring epigenetic-based therapy for asthma.