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Updated: Aug 14, 2025

Visualizing Dengue Virus through Alexa Fluor Labeling
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Stochastic Bayesian Runge-Kutta method for dengue dynamic mapping.

Mukhsar1, Gusti Ngurah Adhi Wibawa1, Andi Tenriawaru2

  • 1Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Halu Oleo Kendari, Indonesia.

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|January 9, 2023
PubMed
Summary

This study introduces a Bayesian stochastic model to understand Dengue Hemorrhagic Fever (DHF) transmission dynamics. The four-order Runge-Kutta method proved most accurate for modeling DHF spread in Indonesia.

Keywords:
BayesianEulerFour order Runge-KuttaSIR-SI modeStochastic

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A Murine Model of Dengue Virus-induced Acute Viral Encephalitis-like Disease
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Area of Science:

  • Epidemiology and Biostatistics
  • Mathematical Modeling of Infectious Diseases
  • Public Health Entomology

Background:

  • Dengue Hemorrhagic Fever (DHF) remains a significant global health threat, particularly in tropical regions, exacerbated by environmental and socioeconomic changes.
  • Understanding the complex transmission dynamics between human hosts and mosquito vectors is crucial for effective disease control.
  • Stochastic processes within Bayesian statistical frameworks offer a robust approach to modeling infectious disease spread.

Purpose of the Study:

  • To develop and evaluate a Bayesian stochastic SIR-SI model for simulating Dengue Hemorrhagic Fever (DHF) transmission dynamics.
  • To compare the accuracy of computational methods, specifically the Euler and four-order Runge-Kutta methods, for solving the SIR-SI differential equations.
  • To analyze spatial and temporal patterns of DHF cases in Kendari, Indonesia, and identify high-risk areas for targeted interventions.

Main Methods:

  • A cross-infection SIR-SI (Susceptible-Infectious-Recovered for humans; Susceptible-Infectious for vectors) model was formulated as a system of differential equations.
  • The SIR-SI model was computationally solved using the Euler and four-order Runge-Kutta methods for discretization.
  • Parameter estimation for the Bayesian SIR-SI model was performed using Markov Chain Monte Carlo (MCMC) simulations on monthly DHF data from Kendari, Indonesia (2019-2021).

Main Results:

  • The four-order Runge-Kutta method demonstrated superior accuracy with the least deviance (106.5) compared to the Euler method after convergence at 10,000 iterations.
  • Relative risk analysis revealed consistent DHF case fluctuations from January to July, with high consistency observed between January and May.
  • Kadia and Wua-Wua districts exhibited high DHF case consistency, indicating spatial clustering and a need for focused intervention strategies.

Conclusions:

  • The four-order Runge-Kutta approach is the preferred computational method for modeling DHF transmission dynamics due to its accuracy.
  • Targeted interventions and intensive monitoring in Kadia and Wua-Wua districts, starting in early January, are recommended to curb DHF spread.
  • The findings provide a foundation for developing advanced dynamic models to improve Dengue Hemorrhagic Fever control strategies.