SIR Model Analysis for Transmission of Dengue Fever Disease with Climate Factors Using Lyapunov Function

Nur, Wahyudin; Rachman, Hirman; Abdal, Nurul Mukhlisah; Abdy, Muhammad; Side, Sumiati

doi:10.1088/1742-6596/1028/1/012117

Cited by 21 publications

(17 citation statements)

References 5 publications

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“…(12) We note that the total number of the host population and the total number of the vector population are constants, which can be verified by adding Eqs. (1-3), resulting in 0 (13) and adding Eqs. (4-5) leading to 0.…”

Section: Given Thatmentioning

confidence: 99%

“…Recently, a number of researchers have studied the spread of dengue, for example, Wagner, et al [8], Windarto, et al [9], and Zhu, et al [10]. A type of mathematical model that is suitable for simulation of the spreading of dengue fever is the SIR-type model [11][12][13][14]. In SIR-type models, the total population is subdivided into three groups, namely, S (susceptible), I (infected), and R (recovered).…”

Section: Introductionmentioning

confidence: 99%

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Improved Variational Iteration Solutions to the SIR Model of Dengue Fever Disease for the Case of South Sulawesi

Mungkasi

2020

J. Math. Fund. Sci.

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The susceptible-infected-recovered (SIR) model of the spread of dengue fever for the case of South Sulawesi is considered. Rangkutiâ€™s variational iteration method (RVIM) is recalled. This paper makes four contributions. The first one is to provide a successive approximation method (SAM) for solving the considered model. The second one is to show that SAM and RVIM are identical. Thirdly, a modification of RVIM is proposed. Fourthly, it is shown that the modification leads to an improvement of the accuracy of the method. Both RVIM and the improved version are quite accurate for short time periods. However, the improved version is more accurate and is able to provide more realistic explicit solutions to the model.

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Section: Given Thatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Improved Variational Iteration Solutions to the SIR Model of Dengue Fever Disease for the Case of South Sulawesi

Mungkasi

2020

J. Math. Fund. Sci.

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“…Berbagai penelitian terkait penyakit menular terus dilakukan oleh berbagai pihak mulai dari peneliti dibidang kesehatan hingga peneliti dibidang matematika. Penelitian terkait kesehatan dan matematika biasanya mengkaji model penyebaran penyakit menular seperti penyakit DBD (Nur, Wahyudin dkk 2018), malaria (Darmawati, 2019) maupun penyakit tidak menular seperti penyakit diabetes. Model matematika yang digunakan untuk mengetahui penyebaran suatu penyakit di daerah tertentu dikenal sebagai model epidemik deterministik.…”

Section: Pendahuluanunclassified

Penaksiran Parameter Model SIS Stokastik Penyebaran Penyakit Malaria Dengan Metode Stepest Descent

Darmawati¹,

Nur

Musafira

2019

saintifik

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Simulasi numerik dilakukan untuk memperoleh solusi dan gambaran penyebaran penyakit malaria dengan model Susceptible Infected Susceptible (SIS) Stokastik. Laju infeksi penyakitnya dimodelkan mengikuti Distribusi Poisson. Simulasi dilakukan dengan menggunakan data jumlah pasien malaria di kabupaten Majene., Sulawesi Barat. Untuk simulasi numerik, peneliti menaksir parameter model yang mengikuti distribusi poisson dengan menggunakan maksimum likelihood estimator. Untuk menaksir parameter yang memaksimumkan fungsi log likelihoodnya, peneliti menggunakan metode stepest descent. Hasil yang diperoleh adalah Metode Stepest Descent merupakan metode yang sangat cocok digunakan untuk menaksir parameter model karena kecilnya kemungkinan nilai fungsi log likelihood menuju . Selain itu, metode Stepest Descent lebih memudahkan dalam penentuan parameter awal.

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“…Infectious diseases are expected to disappear as medical research for vaccines, antibiotics, and quality of life improves in the mid-20th century (Nur et al, 2018), but because it takes time to process, a model is needed to analyse the impact to find solutions of the current problems.…”

Section: A Introductionmentioning

confidence: 99%

Using SAPR Model for Solution of Social Poverty Problem Due to Covid-19 in Makassar City

Annas

Side

Pandjajangi

et al. 2021

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This study aims to build an SAPR model on the problem of poverty, analyze the model, predict the number of poverty rates in the city of Makassar, and determine the parameters that affect the decrease in the number of poverty rates due to Covid-19 in the city of Makassar. This research is quantitative. The population of this study is the number of people in Makassar City who are affected by the spread of COVID-19, while the sample of this study is 400 people. The research stages are: Building the SAPR model on the level of social poverty, determining and analyzing the stability of the equilibrium point, determining the value of the basic reproduction number (R0), conducting model simulations using Maple. The results shown that the mathematical model of SAPR which is a non-linear system of differential equations can be a reference model for the problem of poverty; The results also shown that the analysis of the social poverty level of the population finds two equilibrium points, namely the free equilibrium point for the poor and the poor; the stability of the equilibrium point is free-poor and poor; The basic reproduction number R0 = 0.426 indicates that the poverty level of the social population can be controlled even though it has increased. Based on the model simulation, it was found that the parameter in the form of business funding assistance from the government could reduce the poverty rate due to the Covid-19 pandemic in Makassar city.

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SIR Model Analysis for Transmission of Dengue Fever Disease with Climate Factors Using Lyapunov Function

Cited by 21 publications

References 5 publications

Improved Variational Iteration Solutions to the SIR Model of Dengue Fever Disease for the Case of South Sulawesi

Improved Variational Iteration Solutions to the SIR Model of Dengue Fever Disease for the Case of South Sulawesi

Penaksiran Parameter Model SIS Stokastik Penyebaran Penyakit Malaria Dengan Metode Stepest Descent

Using SAPR Model for Solution of Social Poverty Problem Due to Covid-19 in Makassar City

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