Modeling Dengue Virus Spread Using Differential Equations with Noise Terms to Simulate Transmission Variability

German Correa Vélez, Fernando Mesa, Rogelio Ospina

Abstract

In this paper, we propose a modeling framework to analyze the spread of the dengue virus in human populations by explicitly incorporating noise terms to simulate variability in transmission. A system of differential equations is employed to represent the transmission dynamics of the virus, and the effects of stochastic perturbations on these dynamics are systematically investigated. The effectiveness and robustness of the proposed model are demonstrated through numerical simulations that examine how the inclusion of noise influences the reliability and accuracy of transmission predictions.
The results highlight the importance of accounting for variability in transmission rates and provide valuable insights into the behavior of dengue virus spread under realistic conditions. In particular, this study addresses a key limitation of traditional deterministic dengue models by introducing noise terms to represent realistic fluctuations in transmission dynamics. The central research question focuses on how stochastic variability affects infection trajectories and the stability of dengue outbreaks.
The novelty of this work lies in the integration of noise-modulated differential equations with the Adomian Decomposition Method, which enables a semi-analytical characterization of uncertainty in disease transmission. Our findings demonstrate that random perturbations can either amplify or attenuate outbreak intensity, depending on system conditions, thereby offering a more robust framework for epidemiological forecasting. Overall, this study provides an original contribution by bridging deterministic and stochastic modeling approaches to enhance the predictive capability of vector-borne disease simulations.

 

Keywords: Adomian method, noise terms, Dengue virus, Semi-numerical method, Iterative method.

 

DOI https://doi.org/10.55463/issn.1674-2974.52.11.16

 

 

 

 


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