Batik Motifs from SEIT Mathematical Modeling as a Representation of the Spread of Non-Genetic Diabetes

Abstract

This study develops an interdisciplinary approach between mathematics, health, and batik art by utilizing the SEIT (Susceptible Exposed Infected Treatment) model as the basis for creating visual motifs. The SEIT model, which was previously used to model the spread of non-genetic diabetes, was reviewed and transformed into a geometric representation that can be visualized in the form of mathematical batik motifs. Each compartment in the model Susceptible (S), Exposed (E), Infected (I), and Treatment (T) is represented through interconnected pattern elements, reflecting the dynamics of population transition from a healthy state to the treatment stage. Mathematical analysis using a system of differential equations shows two conditions of stability, namely disease-free equilibrium and endemic equilibrium, with the basic reproduction number (R₀) as the main indicator. Based on the model parameters, a value of R₀ = 0.09 was obtained, indicating that the system is in a stable condition and disease spread tends to decline. These parameter values were then translated into symmetrical and repetitive patterns in batik motifs, symbolizing the balance between biological and social factors in the control of chronic diseases. The resulting batik motif features geometric elements in the form of a green circle (S) as a symbol of healthy life, a yellow half-moon (E) as the exposure phase, a brick-red triangle (I) as a warning sign of infection, and a blue lotus flower (T) symbolizing the process of treatment and recovery. These four shapes are connected by winding curved lines like a river flow, reflecting the continuous transition of the population in the SEIT system. Additional ornaments in the form of mathematical symbols such as  reinforce the scientific character of the design, while also serving as a reminder that batik patterns can also contain profound scientific concepts. Through the integration of mathematical modeling and batik art, this research not only provides innovation in understanding the dynamics of non-communicable diseases but also enriches Indonesia's cultural heritage by combining scientific value and visual aesthetics. The results are expected to serve as an educational and inspirational medium that demonstrates that mathematics is not limited to numbers and formulas but can also give rise to beauty, balance, and meaning in artistic expression.