Essa Novalia, Hamidah Nasution

Menguji Kestabilan dan Kekonsistenan Metode Heun Pada Model Epidemi Susceptible, Exposed, Infected and Recovered Untuk Penyakit Demam Berdarah Dengue

Introduction

Menguji kestabilan dan kekonsistenan metode heun pada model epidemi susceptible, exposed, infected and recovered untuk penyakit demam berdarah dengue. Uji stabilitas & konsistensi Metode Heun pada model epidemi SEIR Demam Berdarah Dengue. Metode ini stabil & konsisten untuk solusi model, diterapkan pada kasus di Medan.

Abstract

The Heun method is an improvement from the Euler method so that it has better accuracy, because in the Heun method, the solution of the Euler method is used as a predictor solution and then the initial estimation solution is corrected by the Heun method (corrector). In this study the method of Heun was used to complete the epidemic model of Susceptible, Exposed, Infected and Recovered (SEIR) of dengue fever while at the same time observing the stability and consistency of the Heun method. The observations of the Heun method are seen geometrically. From the results of the study it was found that the heun method was a stable and consistent method for finding solutions for almost the SEIR epidemic model. While from the data and completion of the approach obtained, the area of Medan Helvetia Subdistrict and Medan Sunggal District is an area that is endemic to dengue hemorrhagic fever. [TESTING THE STABILITY AND CONSISTENCY OF THE HEUN METHOD IN THE SUSCEPTIBLE, EXPOSED, INFECTED AND RECOVERED EPIDEMIC MODEL FOR DENGUE FEVER](J. Sains Indon., 42(1): 52-58, 2018)Keywords:Heun Method, Epidemic Model, Dengue Fever

Review

This paper presents a timely investigation into the application of the Heun method for solving the Susceptible, Exposed, Infected, and Recovered (SEIR) epidemic model, specifically tailored for dengue fever. The authors aim to assess the stability and consistency of this numerical scheme, highlighting its improved accuracy over the simpler Euler method due to its predictor-corrector structure. This research is highly pertinent, addressing the crucial need for robust and accurate computational tools in epidemiological modeling, particularly for diseases like dengue that pose significant public health challenges globally. The methodology involves applying the Heun method to the SEIR model and evaluating its performance through geometric observations of stability and consistency. A key finding is that the Heun method is indeed stable and consistent for "almost" the entire SEIR epidemic model. Beyond this numerical analysis, the study also leverages the method with specific data to identify Medan Helvetia Subdistrict and Medan Sunggal District as endemic areas for dengue hemorrhagic fever. This dual approach effectively demonstrates both the theoretical properties of the Heun method and its practical utility in pinpointing geographical areas at high risk. While the study offers valuable contributions, several points could enhance its impact and rigor. The statement that the Heun method is stable and consistent for "almost the SEIR epidemic model" necessitates further clarification regarding the specific conditions or parameter ranges where this might not hold. A more formal, potentially analytical, demonstration of stability and consistency, complementing the geometric observations, would significantly strengthen the methodological claims. Additionally, while the identification of endemic areas is a compelling practical outcome, the abstract could more explicitly detail how the *proven stability and consistency* of the Heun method directly contribute to the reliability and accuracy of these epidemiological predictions. Future research could benefit from a comparative analysis with other higher-order numerical integrators, a more detailed error analysis, and a sensitivity analysis of the SEIR model parameters.

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