Model Matematika Dari Penyebaran  Penyakit Pulmonary Tuberculosis Dengan  Penggunaan Masker Medis

Inayah, Nur; Manaqib, Muhammad; Fitriyati, Nina; Yupinto, Ikhwal

doi:10.30598/barekengvol14iss3pp461-472

Cited by 7 publications

(6 citation statements)

References 4 publications

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“…Selanjutnya model dikembangkan dengan penambahan kompartemen individu dikarantina diantaranya oleh Amaku et al [19], Chinazzi et al [20], Tang et al [21], dan Xiang et al [22]. Pemodelan matematika epidemi penyakit dengan menambahkan penggunaan masker kesehatan sebelumnya telah dilakukan pada penyakit pernapasan seperti MERS-Cov [3,23] dan penyakit Pulmonary Tuberculosis (TBC) [24]. Sehingga pemodelan matematika epidemi penyakit dengan menambahkan penggunaan masker kesehatan juga dapat diaplikasikan kedalam COVID-19.…”

Section: Pendahuluanunclassified

Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina

Manaqib

Fauziah

Hartati

2021

Jambura J. Biomath.

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This study developed a model for the spread of COVID-19 disease using the SIR model which was added by a health mask and quarantine for infected individuals. The population is divided into six subpopulations, namely the subpopulation susceptible without a health mask, susceptible using a health mask, infected without using a health mask, infected using a health mask, quarantine for infected individuals, and the subpopulation to recover. The results obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point, and the basic reproduction number (R0). The existence of a disease-free equilibrium point is unconditional, whereas an endemic equilibrium point exists if the basic reproduction number is more than one. Stability analysis of the local asymptotically stable disease-free equilibrium point when the basic reproduction number is less than one. Furthermore, numerical simulations are carried out to provide a geometric picture related to the results that have been analyzed. The results of numerical simulations support the results of the analysis obtained. Finally, the sensitivity analysis of the basic reproduction numbers carried out obtained four parameters that dominantly affect the basic reproduction number, namely the rate of contact of susceptible individuals with infection, the rate of health mask use, the rate of health mask release, and the rate of quarantine for infected individuals.

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Section: Pendahuluanunclassified

Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina

Manaqib

Fauziah

Hartati

2021

Jambura J. Biomath.

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“…Salah satu cara untuk menjelaskan permasalahan dalam dunia nyata adalah dengan memodelkan matematika [14], [15]. Pemodelan matematika banyak dikembangkan untuk menggambarkan dinamika populasi termasuk permasalahan epidemologi penyakit untuk memberi gambaran karakteristik persebaran suatu penyakit [16]. Pemodelan matematika COVID-19 mulai dikembangkan sejak pandemi terjadi di awal tahun 2020.…”

Section: Pendahuluanunclassified

Analisis Model Matematika Penyebaran Penyakit Covid-19 Dengan Lockdown Dan Karantina

Manaqib

Azizah

Hartati

et al. 2021

BAREKENG: J. Il. Mat. & Ter.

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Penelitian ini menggembangakan model matematika penyebaran penyakit COVID-19 SEIR dengan lockdown dan karantina. Pembentukan model diawali dengan membuat asumsi dan diagram kompartemen alur penyebaran COVID-19 dengan lockdown dan karantina. Kemudian dibentuk sistem persamaan diferensial nonlinear berdasarkan diagram kompartemen tersebut. Analisis sistem dilakukan dengan menentukan titik ekuilibrium dan bilangan reproduksi dasar (). Hasilnya diperoleh dua buah titik ekuilibrium yakni titik ekuilibrium bebas penyakit yang eksistensinya tanpa syarat dan titik ekuilibrium endemik yang eksistensinya bergantung pada bilangan reproduksi dasar (> 1). Selanjutnya, analisis kestabilan titik ekuilibrium bebas penyakit menggunakan analisis nilai eigen matriks Jacobi dan Kriteria Routh-Hurwitz diperoleh titik kestimbangan bebas penyakit bersifat stabil asimtotik lokal jika . Terakhir simulasi model dilakukan untuk memberikan gambaran geometris dari solusi dan untuk mendukung teorema yang diperoleh. Hasil simulasi numerik yang dilakukan mendukung hasil analisis dinamik yang diperoleh.

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“…This model also assumes that individuals in the system are aware of the existence of TB disease. Implementation of optimal control in TB models is important to research, such as [9], [10], [11], and [12]. This study will discuss the analysis and optimal control of the mathematical model of the spread of TB disease by providing control in the form of vaccination and case finding.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Optimal Control of Tuberculosis Disease Spread Model With Vaccination and Case Finding Control (Case Study: Surabaya City)

Maulina,

Imron

2024

BAREKENG: J. Math. & App.

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Tuberculosis is a contagious disease that infects humans. It is caused by the bacterium Mycobacterium tuberculosis (M.tb). It is the largest infectious disease in the world and has become a major global health problem. Therefore, efforts are being made to control the spread of tuberculosis disease through vaccination and case finding, with the aim of reducing the population of latently infected and actively infected individuals. This study discusses the mathematical model of tuberculosis disease spread, disease-free and endemic equilibrium points, and stability analysis around the equilibrium points. Then, using Pontryagin's minimum principle, the optimal control problem is solved numerically by the 4th-order Runge-Kutta method. Based on the analysis and simulation results, the system is asymptotically stable around the disease-free and endemic equilibrium points. Furthermore, optimal control in the form of vaccination of susceptible individuals is required to further suppress the rate of change of susceptible individuals into latent individuals, while control in the form of case finding on latently infected individuals is required until the 9th year to minimize the population size, while on actively infected individuals, it is required until the 8th year to minimize the population size. Providing optimal control resulted in a 100% increase in the susceptible population and a 100% reduction in the latent and infected populations.

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Model Matematika Dari Penyebaran Penyakit Pulmonary Tuberculosis Dengan Penggunaan Masker Medis

Cited by 7 publications

References 4 publications

Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina

Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina

Analisis Model Matematika Penyebaran Penyakit Covid-19 Dengan Lockdown Dan Karantina

Analysis and Optimal Control of Tuberculosis Disease Spread Model With Vaccination and Case Finding Control (Case Study: Surabaya City)

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