Visualization of Batik Patterns from Numerical Simulation of the SVEIQR Measles Model Using the Laplace Adomian Decomposition Method

Abstract

This study develops a fractional differential equation model of measles transmission using the Susceptible–Vaccinated–Exposed–Infected–Quarantined–Recovered (SVEIQR) framework, which incorporates the fractional Caputo derivative of order 0<q<=1.

The model captures the dynamic behavior of disease spread more accurately by considering memory effects inheret in fractional calculus. The system is analyzed theoretically to determine the existence and uniqueness of solutions,, equilibrium points, and basic reproduction numbers, and then solved numerically using the Laplace Adomian Decomposition Method (LADM), which combines Laplace transformation and Adomian decomposition to obtain approximate analytical solutions. Numerical simulations were perfomed for different fractional orders and parameter variations, showing that smaller fractional orders (q<1) introduce memory-dependent effects, producing smoother transitions between epidemiological compartments. Beyond its numerical results, this study presents an innovative visualization of the SVEIQR simulation data through batik-inspired patterns, where each motif, shape, and, color corresponds to specific epidemiological meanings. The resulting batik design transforms mathematical dynamics into an aesthetic representation, integrating scientific order with cultural symbolism. The five-petal flower pattern represents the five main epidemiological phases (S,V,E,I,R), while the central circle depicts quarantine (Q) as a stabilizing force between infection and recovery. Curving tendrils express nonlinear transitions, and leaf motifs symbolize regeneration andd healing. Through this integration of mathematics, biology, and traditional art, the research demonstrates how complex epidemiological phenomena can be communicated not only quantitatively but also through artistic and cultural perspectives, promoting an interdisciplinary understanding of epidemic dynamics.