Modeling of dengue epidemics using Runge-Kutta and Euler-Maruyama methods in the SIR-SI formulation

Abstract

Dengue epidemics exhibit inherent stochasticity in transmission dynamics that introduces fluctuations in local population structures and contact patterns. This leads to heterogeneity in transmission,  and consequently variability of the dengue spread. Hence, in this study, we explored the influence of this randomness on the dynamics of dengue using the SIR-SI framework. We then solved its system of equations using the Euler-Maruyama method that captures the stochastic variability and then compared it to 4^th-order Runge-Kutta approach that approximate the deterministic solution. Our findings show that both approach follows qualitatively nearly the same path, with 93-99% similarity for {S_h, I_h, R_h, I_v}, despite some variability due to the inclusion of noise. However, the induced dispersion of trajectories using stochastic approach reveal that S_h, I_h, and I_v's ensembles fluctuate at earlier times, while S_v and R_h at later times.