scholarly journals Pemodelan Matematika SIRI pada Penyebaran Penyakit Tifus di Sulawesi Selatan

2021 ◽  
Vol 4 (2) ◽  
pp. 55
Author(s):  
Syafruddin Side ◽  
Ahmad Zaki ◽  
S. Sartika
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
South Sulawesi ◽  
Research Procedure ◽  
The Stability ◽  
Siri Model ◽  
The Basic Reproduction Number

Penelitian ini bertujuan untuk membangun model penyebaran penyakit Tifus tipe SIRI (Susceptible-Infected-Recovered-Infected), dengan menambahkan asumsi bahwa manusia yang sembuh dapat kembali terinfeksi penyakit Tifus. Model ini di bagi menjadi 3 kelas yaitu rentan, terinfeksi dan sembuh. Adapun prosedur penelitian dilakukan melalui tahapan-tahapan: membangun model penyebaran penyakit Tifus tipe SIRI, Menguji Kestabilan titik kesetimbangan dan menentukan bilangan reproduksi dasar , kemudian menerapkannya pada kasus Penyakit Tifus di Provinsi Sulawesi Selatan. Data yang digunakan dalam membangun model adalah jumlah penderita penyakit Tifus tahun 2018 dari Dinas Kesehatan Provinsi Sulawesi Selatan. Model matematika tipe SIRI digunakan untuk menentukan titik equilibrium. Berdasarkan hasil simulasi model SIRI diperoleh bilangan reproduksi dasar (  sebesar 0,000903 yang menandakan bahwa penyebaran penyakit Tifus di Provinsi Sulawesi Selatan pada tahun 2018 bukan kejadian luar biasa atau dapat dikatakan bahwa seseorang yang terinfeksi penyakit Tifus ini tidak menyebabkan orang lain terkenapenyakit yang sama, dengan kata lain tidak terjadi wabah pada populasi tersebut.Kata kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Tifus, Model SIRI. The research aims to build a SIRI model of the Typhoid spread (Susceptible-Infected-Recovered-Infected) by adding assumption that people who are recovered might be infected again. This model is divided into three classes, namely, susceptible, infected and recovered. the research procedure is carried out through several stages: Building SIRI model for the spread of Typhoid, examining the stability of the equilibrium point and determining the basic reproduction number, and applying the model to Typhoid cases in South Sulawesi. The data is the number of Typhus patients in 2018 that was obtained from Health office of South Sulawesi Province. SIRI type mathematical models are used to determine the equilibrium point. Based on the simulation results of the SIRI model, the basic reproduction number is 0,000903 indicate that, indicating that the spread of Typhus in the Province of South Sulawesi in 2018 was not an extraordinary event or it can be said that someone who is infected with this Typhoid does not cause another person to contract the same disease, in other words there was no outbreak in that population.Keywords: equilibrium Point, Basic Reproductive Number, Typhoid, SIRI Model.

scholarly journals APLIKASI MODEL EPIDEMIK SEIAR-SEI PADA PENYEBARAN PENYAKIT MALARIA DENGAN INFEKSI ASIMTOMATIK DAN SUPER INFEKSI

2018 ◽  
Vol 15 (2) ◽  
pp. 67
Author(s):  
Stella Maryana Belwawin
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Asymptomatic Infection ◽  
Endemic Equilibrium ◽  
Asymptomatic Infections ◽  
The Stability ◽  
Super Infection ◽  
The Basic Reproduction Number

AbstractThis aim of this study is to determine the point of equilibrium and analyze the stability of SEIAR-SEI model on malaria disease with asymptomatic infection, super infection and the effect of the mosquito's life cycle. This study also aim is to measure the sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes through the magnitude of . The method in this research is deductively, through several stage, such as  determination of disease-free equilibrium point and endemic equilibrium point, determination of basic reproduction number (), analyze of the basic reproduction number sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes. The endemic equilibrium point was obtained using rule of Descartes. The result show that the change in the value of parameter , , and  has effect on the basic reproduction number (). Treatment factors in the human population influence the elimination of malaria in a population. Whereas asymptomatic infection factors and the birth rate of adult mosquitoes influence the increase in malaria infection. Keywords:  Malaria, asymptomatic infection, super infection, basic reproduction number, rule of descrates. AbstrakPenelitian ini bertujuan menentukan titik keseimbangan dan menganalisis kestabilan dari model SEIAR_SEI pada penyakit malaria dengan pengaruh infeksi asimtomatik, super infeksi, dan siklus hidup nyamuk. Penelitian ini juga bertujuan mengukur tingkat sensitivitas penyebaran penyakit malaria terhadap parameter infeksi asimtomatik, laju pengobatan, serta laju kelahiran nyamuk.melalu besaran .  Metode yang digunakan dalam penelitian ini adalah metode deduktif dengan langkah-langkah : menentukan titik keseimbangan bebas penyakit dan endemik dan menentukan bilangan reproduksi dasar ). Analisis sensitivitas bilangan reproduksi dasar dilakukan terhadap parameter infeksi asimtomatik, pengobatan, dan laju kelahiran nyamuk. Tititk keseimbangan endemik diperoleh dengan aturan descrates. Hasil yang diperoleh menunjukkan parameter , , dan  berpengaruh terhadap bilangan reproduksi dasar (). Faktor pengobatan berpengaruh terhadap eliminasi penyakit malaria. Sedangkan faktor infeksi asimtomatik dan laju kelahiran nyamuk dewasa berpengaruh terhadap peningkatan infeksi penyakit malaria. Kata kunci: Malaria, Infeksi Asimtomatik, Super Infeksi, Bilangan Reproduksi Dasar, Aturan Descrates . 

scholarly journals Pengembangan Model Matematika SIRD (Susceptibles-Infected-Recovery-Deaths) Pada Penyebaran Virus Ebola

2016 ◽  
Vol 5 (1) ◽  
pp. 23
Author(s):  
Endah Purwati ◽  
Sugiyanto Sugiyanto
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Direct Contact ◽  
Ebola Virus ◽  
Reproduction Number ◽  
Body Fluids ◽  
Endemic Equilibrium ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

Ebola is a deadly disease caused by a virus and is spread through direct contact with blood or body fluids such as urine, feces, breast milk, saliva and semen. In this case, direct contact means that the blood or body fluids of patients were directly touching the nose, eyes, mouth, or a wound someone open. In this paper examined two mathematical models SIRD (Susceptibles-Infected-Recovery-Deaths) the spread of the Ebola virus in the human population. Both the mathematical model SIRD on the spread of the Ebola virus is a model by Abdon A. and Emile F. D. G. and research development model. This study was conducted to determine the point of disease-free equilibrium and endemic equilibrium point and stability analysis of the dots, knowing the value of the basic reproduction number (R0) and a simulation model using Matlab software version 6.1.0.450. From the analysis of the two models, obtained the same point for disease-free equilibrium point with the stability of different points and different points for endemic equilibrium point with the stability of both the same point and the same value to the value of the basic reproduction number (R0). After simulating the model using Matlab software version 6.1.0.450, it can be seen changes in the behavior of the population at any time.

scholarly journals DINAMIKA LOKAL MODEL EPIDEMI SVIR DENGAN IMIGRASI PADA KOMPARTEMEN VAKSINASI

2020 ◽  
Vol 14 (2) ◽  
pp. 297-304
Author(s):  
Joko Harianto ◽  
Titik Suparwati ◽  
Inda Puspita Sari
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Mathematical Epidemiology ◽  
Unique Equilibrium ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstrak Artikel ini termasuk dalam ruang lingkup matematika epidemiologi. Tujuan ditulisnya artikel ini untuk mendeskripsikan dinamika lokal penyebaran suatu penyakit dengan beberapa asumsi yang diberikan. Dalam pembahasan, dianalisis titik ekuilibrium model epidemi SVIR dengan adanya imigrasi pada kompartemen vaksinasi. Dengan langkah pertama, model SVIR diformulasikan, kemudian titik ekuilibriumnya ditentukan, selanjutnya, bilangan reproduksi dasar ditentukan. Pada akhirnya, kestabilan titik ekuilibirum yang bergantung pada bilangan reproduksi dasar ditentukan secara eksplisit. Hasilnya adalah jika bilangan reproduksi dasar kurang dari satu maka terdapat satu titik ekuilbirum dan titik ekuilbrium tersebut stabil asimtotik lokal. Hal ini berarti bahwa dalam kondisi tersebut penyakit akan cenderung menghilang dalam populasi. Sebaliknya, jika bilangan reproduksi dasar lebih dari satu, maka terdapat dua titik ekuilibrium. Dalam kondisi ini, titik ekuilibrium endemik stabil asimtotik lokal dan titik ekuilibrium bebas penyakit tidak stabil. Hal ini berarti bahwa dalam kondisi tersebut penyakit akan tetap ada dalam populasi. Kata Kunci : Model SVIR, Stabil Asimtotik Lokal Abstract This article is included in the scope of mathematical epidemiology. The purpose of this article is to describe the dynamics of the spread of disease with some assumptions given. In this paper, we present an epidemic SVIR model with the presence of immigration in the vaccine compartment. First, we formulate the SVIR model, then the equilibrium point is determined, furthermore, the basic reproduction number is determined. In the end, the stability of the equilibrium point is determined depending on the number of basic reproduction. The result is that if the basic reproduction number is less than one then there is a unique equilibrium point and the equilibrium point is locally asymptotically stable. This means that in those conditions the disease will tend to disappear in the population. Conversely, if the basic reproduction number is more than one, then there are two equilibrium points. The endemic equilibrium point is locally asymptotically stable and the disease-free equilibrium point is unstable. This means that in those conditions the disease will remain in the population. Keywords: SVIR Model, Locally Asymptotically stable.

scholarly journals Rich Dynamics of an Epidemic Model with Saturation Recovery

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hui Wan ◽  
Jing-an Cui
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Medical Resource ◽  
Sir Epidemic Model ◽  
The Impact ◽  
The Basic Reproduction Number

A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction numberℝ0is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region.

scholarly journals Stability analysis of a smoking behavior model

2021 ◽  
Vol 2106 (1) ◽  
pp. 012025
Author(s):  
S M Lestari ◽  
Y Yulida ◽  
A S Lestia ◽  
M A Karim
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Smoking Behavior ◽  
Asymptotically Stable ◽  
Runge Kutta Method ◽  
The Stability ◽  
The Basic Reproduction Number

Abstract This research discussed the mathematical model of smoking behavior. The model will be analogous to an epidemic model which will be divided into several compartments/groups. This research aimed to explain the formation of a mathematical model of smoking behavior, to investigate the equilibrium point, the value of the basic reproduction number, to analyze the stability of the model, then to determine and interpret the numerical solutions using the fourth-order Runge-Kutta method. By the results of this research, a mathematical model of smoking behavior which consists of three compartments, namely the population of non-smokers, smokers and ex-smokers, was obtained. Based on the model formed the smoke-free equilibrium point and the smoker equilibrium point, then the basic reproduction number was also obtained using the next generation matrix. Furthermore, the result of the stability analysis of the smoker-free population was asymptotically stable provided that the basic reproduction number is less than one, while the population was asymptotically stable provided that the basic reproduction number is greater than one. The simulation of the model was presented to support the explanation of the stability analysis of the model using the fourth-order Runge-Kutta method based on the parameters that met the requirements of the stability analysis.

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

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 47-58
Author(s):  
Suwardi Annas ◽  
Syafruddin Side ◽  
Andi Muhammad Ridho Yusuf Sainon Andi Pandjajangi ◽  
Nurul Fadhilah Syahrul ◽  
Luthfiah Arradiah
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Poverty Level ◽  
The Poor ◽  
The Social ◽  
The Stability ◽  
Non Linear System ◽  
The City ◽  
The Basic Reproduction Number

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.

scholarly journals ANALISIS KESTABILAN ENDEMIK MODEL EPIDEMI CVPD (CITRUS VEIN PHLOEM DEGENERATION) PADA TANAMAN JERUK

2017 ◽  
Vol 9 (2) ◽  
pp. 21
Author(s):  
Tesa Nur Padilah ◽  
Najmudin Fauji
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Type Ii ◽  
Diaphorina Citri ◽  
Asymptotic Stable ◽  
The Stability ◽  
The Basic Reproduction Number ◽  
Good Agreement

Orange fruits are important commodities in Indonesia. However, the efforts to increase production of oranges still have obstacles. One of them is because ofCVPD (Citrus Vein Phloem Degeneration) disease. The spread of CVPD disease in orange plants can be modeled by mathematical model, that is epidemic model betweenorange plants as a host plant and Diaphorina Citri as a vector. In this model, predation response follows Holling Type II response function. The model is then analyzed by checking the stability of the equilibrium point and computing basic reproduction number. This model has an endemic equilibrium point. If the basic reproduction number is more than one then an endemic equilibrium point is locally asymptotic stable or epidemic which means that it occurs in the population. The simulation result of the model are in good agreement with the model behavior analysis.

scholarly journals Model Matematika SEIR Pada Kanker Kulit Akibat Paparan Sinar Ultraviolet Di Provinsi Sulawesi Selatan

2021 ◽  
Vol 4 (2) ◽  
pp. 76
Author(s):  
Syafruddin Side ◽  
Ahmad Zaki ◽  
Norliana Rahmasari
Keyword(s):  
Mathematical Model ◽  
Skin Cancer ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Light Exposure ◽  
Infected Individual ◽  
Seir Model ◽  
South Sulawesi ◽  
Research Procedure ◽  
The Stability

Penelitian ini bertujuan untuk membangun  model matematika SEIR pada kanker kulit akibat paparan sinar ultraviolet dengan asumsi bahwa terdapat masa inkubasi pada kanker kulit. Model ini dibagi menjadi 4 kelas yaitu susceptible, exposed, infected dan recovered. Adapun prosedur penelitian dilakukan melalui tahapan-tahapan: membuat model SEIR pada kanker kulit di provinsi Sulawesi Selatan, menentukan titik ekuilibrium model, analisis kestabilan titik ekuilibrium, menentukan bilangan reproduksi dasar ( ). Data yang digunakan dalam membangun model adalah penderita kanker kulit tahun 2018 hingga tahun 2019 dari Rumah Sakit Wahidin Sudirohusodo kota Makassar. Hasil yang diperoleh bahwa semakin besar persentase laju kesembuhan tiap individu yang terinfeksi karena adanya pengobatan mengakibatkan populasi pada kelas recovered semakin meningkat dan populasi pada kelas infected mengalami penurunan. Dengan kata lain penyakit kanker kulit tidak mewabah di Provinsi Sulawesi Selatan.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Kanker Kulit, Model SEIRThis study aims to build a mathematical model of SEIR in skin cancer due to ultraviolet light exposure assuming that there is an incubation period in skin cancer. This model is divided into 4 classes namely susceptible, exposed, infected and recovered. The research procedure is carried out through the stages: make a SEIR model on skin cancer in the province of South Sulawesi, determine the equilibrium point of the model, analyze the stability of the equilibrium point, determine the base reproduction number ( ). The data used in building the model were skin cancer sufferers from 2018 to 2019 from Sudirohusodo Wahidin Hospital in Makassar. The results obtained that the greater the percentage of recovery rate of each infected individual due to treatment causes the population of the recovered class to increase and the population of the infected class to decrease. In other words skin cancer is not endemic in South Sulawesi Province.Keywords: Equilibrium Point, Basic Reproductive Numbers, Skin Cancer, SEIR Model

scholarly journals Spatial dynamics of a diffusive SIRI model with distinct dispersal rates and heterogeneous environment

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Lian Duan ◽  
Lihong Huang ◽  
Chuangxia Huang
Keyword(s):  
Steady State ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Spatial Dynamics ◽  
Heterogeneous Environment ◽  
Threshold Parameter ◽  
Dispersal Rate ◽  
Siri Model ◽  
The Basic Reproduction Number

<p style='text-indent:20px;'>In this paper, we are concerned with the dynamics of a diffusive SIRI epidemic model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected individuals. We first establish the basic properties of solutions to the model, and then identify the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathscr{R}_{0} $\end{document}</tex-math></inline-formula> which serves as a threshold parameter that predicts whether epidemics will persist or become globally extinct. Moreover, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected individuals approaches zero. Our analytical results reveal that the epidemics can be extinct by limiting the movement of the susceptible individuals, and the infected individuals concentrate on certain points in some circumstances when limiting their mobility.</p>

scholarly journals Modeling Gender-Structured Wildlife Diseases with Harvesting: Chronic Wasting Disease as an Example

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Mo'tassem Al-Arydah ◽  
Robert J. Smith ◽  
Frithjof Lutscher
Keyword(s):  
Basic Reproduction Number ◽  
Chronic Wasting Disease ◽  
Reproduction Number ◽  
Economic Consequences ◽  
Wildlife Diseases ◽  
Wasting Disease ◽  
Effective Strategies ◽  
Optimum Interval ◽  
The Stability ◽  
The Basic Reproduction Number

Chronic wasting disease (CWD) is a prion infectious disease that affects members of the deer family in North America. Concerns about the economic consequences of the presence of CWD have led management agencies to seek effective strategies to control CWD distribution and prevalence. Current mathematical models are either based on complex simulations or overly simplified compartmental models. We develop a mathematical model that includes gender structure to describe CWD in a logistically growing population. The model includes harvesting as a management strategy for the disease. We determine the stability conditions of the disease-free equilibrium for the model and calculate the basic reproduction number. We find an optimum interval of harvesting: with too little harvesting, the disease persists, whereas too much harvesting results in extinction of the population. A sensitivity analysis shows that the disease threshold is more sensitive to female than male harvesting and that harvesting has the greatest effect on the basic reproduction number. However, while harvesting may be a way to control CWD, the range of admissible harvesting rates may be very narrow, depending on other parameters.

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