Analisis Stabilitas Model SIR (Susceptibles, Infected, Recovered) Pada Penyebaran Penyakit Demam Berdarah Dengue di Provinsi Maluku

Leleury, Zeth Arthur; Lesnussa, Yopi Andry; Bension, Johan B.; Kakisina, Yulia S.

doi:10.24843/jmat.2017.v07.i02.p91

Cited by 6 publications

(5 citation statements)

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“…Lebih lanjut, [12] menggunakan pemodelan matematika sebagai strategi pencegahan endemik HIV/AIDS. Adapula [13] yang telah melakukan pemodelan matematika pada penyebaran HIV/AIDS tipe SIA (Susceptible, Infected, Abstained) dengan menganalisis stabilitas dan simulasi model. [14] juga telah membuat dinamika model penyebaran HIV/AIDS berdasarkan jumlah CD4.…”

Section: Pendahuluanunclassified

“…[14] juga telah membuat dinamika model penyebaran HIV/AIDS berdasarkan jumlah CD4. Pemodelan matematika yang dilakukan pada penelitian ini merupakan modifikasi dari model yang telah dilakukan oleh [9] dan [13] dengan menambahkan kompartemen Treatment sehingga model penyebarannya menggunakan 4 kompartemen yakni Susceptible, Infected, Treatment, AIDS atau SITA pada populasi tertutup. Adapun tujuan dari penelitian ini adalah: 1) untuk mengonstruksi model matematika pada penyebaran HIV/AIDS tipe SITA, 2) menentukan titik kesetimbangan dan kestabilan titik kesetimbangan dari model, 3) menentukan bilangan reproduksi dasar (𝑅 0 ), dan 4) melakukan simulasi dinamik model.…”

Section: Pendahuluanunclassified

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Pemodelan Matematika dan Analisis Kestabilan Model Pada Penyebaran HIV/AIDS Tipe SITA (Susceptible, Infected, Treatment, AIDS)

Mahuda,

Rofiroh

2024

JOSTECH

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HIV/AIDS still become a major public health problem that occurs in almost all countries in the world. Until now, no medicine has been found that can treat HIV/AIDS. However, there is therapy or treatment that can be done to slow the spread of the virus, namely antiretroviral (ARV) or called Antiretroviral Therapy (ART). The mathematical modeling carried out in this study uses the SITA type where there are 4 compartments, namely Susceptible (S), Infected (I) Treatment (T), and AIDS (A) in a closed population. The objectives of this research are: 1) to construct a mathematical model for the spread of SITA type HIV/AIDS, 2) determine the equilibrium point and stability of the equilibrium point of the model, 3) determine the basic reproduction number (R_0), and 4) carry out a dynamic simulation of the model. Mathematical modeling of the spread of SITA type HIV/AIDS produces two equilibrium points, namely the disease-free equilibrium point (E_1) and the endemik equilibrium point (E_2). From the results of the analysis, the basic reproduction ratio (R_0) was also obtained by building a matrix called the Next Generation Matrix (NGM). The basic reproduction ratio number (R_0) also determines the existence and stability of the equilibrium point and can control the rate of spread of HIV/AIDS. Based on the simulation results, the parameter value that greatly influences population dynamics is the rate of treatment given to the Infected (I) sub population.

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Section: Pendahuluanunclassified

Pemodelan Matematika dan Analisis Kestabilan Model Pada Penyebaran HIV/AIDS Tipe SITA (Susceptible, Infected, Treatment, AIDS)

Mahuda,

Rofiroh

2024

JOSTECH

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“…Human Immunodeficiency Virus (HIV) is the primary cause of acquired immunodeficiency syndrome (AIDS) [1]. HIV is a contagious virus with various transmission sources, including blood, cervical secretions, and breast milk from individuals with HIV [2].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Analysis of Hiv/Aids Disease Spread Model in Indonesia

Utami,

Dzaky,

Fanani

2024

BAREKENG: J. Math. & App.

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The Human Immunodeficiency Virus (HIV) is a contagious virus that weakens the immune system of infected individuals, making them more susceptible to various diseases. These individuals are referred to as those exposed to the AIDS disease, which unfortunately, cannot be cured. To effectively manage AIDS, prevention is crucial in slowing down the spread and growth of the HIV virus. Mathematical modeling can play a significant role in the optimal control of AIDS. In this study, the , , , , model with three different optimal controls were employed. Optimal control involves public health education campaigns, screening, and treatment. The goal is to minimize the number of individuals infected with HIV/AIDS using Pontryagin's Maximum Principle. This principle considers various factors, such as population class coefficients, cost weights, and control variables to determine the most effective approach. The simulation results indicate that counseling control in the exposed population class ( ) yields better outcomes compared to counseling control in the susceptible class and treatment control in the HIV-infected population class. This implies that focusing on educating and counseling individuals who are exposed to HIV can be more efficient in AIDS control than targeting those already infected or at risk. By applying these optimal control strategies, it may be possible to mitigate the impact of HIV/AIDS and improve public health outcomes.

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“…A new model introduced in this study refers to the modified model [24] by adding a vaccine subpopulation class that represents individuals who have been vaccinated. This vaccine protects the body from getting sick from Covid-19 by generating or stimulating specific immunity.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Sirv Model for the Spread of Covid-19 in Maluku Province

Sapulette,

Lesnussa,

Rijoly

2023

BAREKENG: J. Math. & App.

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COVID-19 (Coronavirus Disease 2019) is caused by the SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2) coronavirus spreading around the world. In this study, the SIRV model was used, which is an epidemic model carried out by grouping the population into four subpopulations, namely the subpopulation of susceptible individuals who can be infected (Susceptible), the subpopulation of infected individuals (Infected), the subpopulation of individuals who recover from illness (Recovered), and the subpopulation of individuals who have been vaccinated (Vaccination). Based on the dynamic system analysis conducted, two equilibrium points were obtained, namely the disease-free equilibrium point and the endemic equilibrium point. In addition, based on data processing and model simulation results obtained, was obtained so that it can be concluded that the higher the number of vaccinated populations, the lower the level of Covid-19 spread, which means that vaccines can suppress cases of Covid-19 spread in Maluku Province

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Analisis Stabilitas Model SIR (Susceptibles, Infected, Recovered) Pada Penyebaran Penyakit Demam Berdarah Dengue di Provinsi Maluku

Cited by 6 publications

References 0 publications

Pemodelan Matematika dan Analisis Kestabilan Model Pada Penyebaran HIV/AIDS Tipe SITA (Susceptible, Infected, Treatment, AIDS)

Pemodelan Matematika dan Analisis Kestabilan Model Pada Penyebaran HIV/AIDS Tipe SITA (Susceptible, Infected, Treatment, AIDS)

Optimal Control Analysis of Hiv/Aids Disease Spread Model in Indonesia

Dynamics of a Sirv Model for the Spread of Covid-19 in Maluku Province

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