scholarly journals PENGEMBANGAN MODEL EPIDEMIK SIRA UNTUK PENYEBARAN VIRUS PADA JARINGAN KOMPUTER

2019 ◽  
Vol 2 (1) ◽  
pp. 13
Author(s):  
Panca Putra Pemungkas ◽  
Sutrisno Sutrisno ◽  
Sunarsih Sunarsih
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Computer Network ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Virus Spread ◽  
Computer Based ◽  
Stability Issues ◽  
Spread Analysis

This paper is addressed to discuss the development of epidemic model of SIRA (Susceptible-Infected-Removed-Antidotal) for virus spread analysis purposes on a computer network. We have developed the existing model by adding a possibility of antidotal computer returned to susceptible computer. Based on the results, there are two virus-free equilibrium points and one endemic equilibrium point. These equilibrium points were analyzed for stability issues using basic reproduction number and Routh-Hurwitz Method.

scholarly journals On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

2020 ◽  
Vol 10 (22) ◽  
pp. 8296 ◽  
Author(s):  
Malen Etxeberria-Etxaniz ◽  
Santiago Alonso-Quesada ◽  
Manuel De la Sen
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Impulsive Vaccination ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.

scholarly journals Analisis dinamik model SVEIR pada penyebaran penyakit campak

2020 ◽  
Vol 1 (2) ◽  
pp. 57-64
Author(s):  
Sitty Oriza Sativa Putri Ahaya ◽  
Emli Rahmi ◽  
Nurwan Nurwan
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Total Population ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Model ◽  
Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this article, we analyze the dynamics of measles transmission model with vaccination via an SVEIR epidemic model. The total population is divided into five compartments, namely the Susceptible, Vaccinated, Exposed, Infected, and Recovered populations. Firstly, we determine the equilibrium points and their local asymptotically stability properties presented by the basic reproduction number R0. It is found that the disease free equilibrium point is locally asymptotically stable if satisfies R01 and the endemic equilibrium point is locally asymptotically stable when R01. We also show the existence of forward bifurcation driven by some parameters that influence the basic reproduction number R0 i.e., the infection rate α or proportion of vaccinated individuals θ. Lastly, some numerical simulations are performed to support our analytical results.

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

2021 ◽  
Vol 2 (2) ◽  
pp. 68-79
Author(s):  
Muhammad Manaqib ◽  
Irma Fauziah ◽  
Eti Hartati
Keyword(s):  
Numerical Simulations ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Reproduction Numbers ◽  
Geometric Picture ◽  
Disease Free ◽  
The Basic Reproduction Number

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.

scholarly journals Stability Analysis of SEIL Tuberculosis Epidemic Model with Logistic Growth in Susceptible Compartment

2021 ◽  
Vol 16 ◽  
pp. 1-9
Author(s):  
Joko Harianto
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Tuberculosis Disease ◽  
Disease Free ◽  
The Basic Reproduction Number

This article discusses modifications to the SEIL model that involve logistical growth. This model is used to describe the dynamics of the spread of tuberculosis disease in the population. The existence of the model's equilibrium points and its local stability depends on the basic reproduction number. If the basic reproduction number is less than unity, then there is one equilibrium point that is locally asymptotically stable. The equilibrium point is a disease-free equilibrium point. If the basic reproduction number ranges from one to three, then there are two equilibrium points. The two equilibrium points are disease-free equilibrium and endemic equilibrium points. Furthermore, for this case, the endemic equilibrium point is locally asymptotically stable.

scholarly journals Kestabilan Model Epidemi Seir dengan Matriks Hurwitz

2016 ◽  
Vol 11 (2) ◽  
pp. 74
Author(s):  
Roni Tri Putra ◽  
Sukatik - ◽  
Sri Nita
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Local Stability ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Stability Of Equilibrium ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, it will be studied local stability of equilibrium points of  a SEIR epidemic model with infectious force in latent, infected and immune period. From the model it will be found investigated the existence and its stability of points its equilibrium by Hurwitz matrices. The local stability of equilibrium points is depending on the value of the basic reproduction number  If   the disease free equilibrium is local asymptotically stable.

scholarly journals Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination

2021 ◽  
Vol 4 (2) ◽  
pp. 106-124
Author(s):  
Raqqasyi Rahmatullah Musafir ◽  
Agus Suryanto ◽  
Isnani Darti
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Asymptomatic Infection ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Proposed Model ◽  
Disease Free ◽  
The Basic Reproduction Number

We discuss the dynamics of new COVID-19 epidemic model by considering asymptomatic infections and the policies such as quarantine, protection (adherence to health protocols), and vaccination. The proposed model contains nine subpopulations: susceptible (S), exposed (E), symptomatic infected (I), asymptomatic infected (A), recovered (R), death (D), protected (P), quarantined (Q), and vaccinated (V ). We first show the non-negativity and boundedness of solutions. The equilibrium points, basic reproduction number, and stability of equilibrium points, both locally and globally, are also investigated analytically. The proposed model has disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable if basic reproduction number is less than one. The endemic equilibrium point exists uniquely and is globally asymptotically stable if the basic reproduction number is greater than one. These properties have been confirmed by numerical simulations using the fourth order Runge-Kutta method. Numerical simulations show that the disease transmission rate of asymptomatic infection, quarantine rates, protection rate, and vaccination rates affect the basic reproduction number and hence also influence the stability of equilibrium points.

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 On an SE(Is)(Ih)AR epidemic model with combined vaccination and antiviral controls for COVID-19 pandemic

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. De la Sen ◽  
A. Ibeas
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Antiviral Treatment ◽  
Stability Properties ◽  
Local Asymptotic Stability ◽  
Proposed Model ◽  
And Control ◽  
The Basic Reproduction Number

AbstractIn this paper, we study the nonnegativity and stability properties of the solutions of a newly proposed extended SEIR epidemic model, the so-called SE(Is)(Ih)AR epidemic model which might be of potential interest in the characterization and control of the COVID-19 pandemic evolution. The proposed model incorporates both asymptomatic infectious and hospitalized infectious subpopulations to the standard infectious subpopulation of the classical SEIR model. In parallel, it also incorporates feedback vaccination and antiviral treatment controls. The exposed subpopulation has three different transitions to the three kinds of infectious subpopulations under eventually different proportionality parameters. The existence of a unique disease-free equilibrium point and a unique endemic one is proved together with the calculation of their explicit components. Their local asymptotic stability properties and the attainability of the endemic equilibrium point are investigated based on the next generation matrix properties, the value of the basic reproduction number, and nonnegativity properties of the solution and its equilibrium states. The reproduction numbers in the presence of one or both controls is linked to the control-free reproduction number to emphasize that such a number decreases with the control gains. We also prove that, depending on the value of the basic reproduction number, only one of them is a global asymptotic attractor and that the solution has no limit cycles.

scholarly journals Modifikasi Model SIR pada Penyebaran Penyakit Demam Berdarah Dengue di Kabupaten Bone

2019 ◽  
Vol 1 (2) ◽  
pp. 169
Author(s):  
Syafruddin Side ◽  
A Alimuddin ◽  
Alvioni Bani
Keyword(s):  
Dengue Fever ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sir Model ◽  
District Health Office ◽  
District Health ◽  
Reproduction Numbers

Abstrak. Artikel ini membahas mengenai modifikasi model epidemik SIR pada penyebaran penyakit DBD di Kabupaten Bone dengan penembahan asumsi baru bahwa 20% penderita DBD yang sembuh akan kembali terinfeksi dan 80 % dari individu yang telah sembuh, tidak akan kembali menjadi rentan. Data yang digunakan adalah jumlah penderita DBD di Kabupaten Bone tahun 2016 dari Dinas Kesehatan Kabupaten Bone. Pembahasan dimulai dari penentuan titik equilibrium, stabilitas, bilangan reproduksi dasar  dan simulasi menggunakan Maple. Dalam penelitian ini diperoleh dua titik equilibrium dengan nilai reproduksi dasar . Hal ini menunjukkan bahwa penyakit DBD di Kabupaten Bone akan terus meningkat dan menjadi endemik.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, DBD, Modifikasi Model SIR.  Abstract. The research discusses a modification of epidemic model SIR on the spreadof dengue fever disease in Bone District. With some addition of the assumption that 20% of patients who recovered will be re-infected and 80% of individuals who have recovered will not be susceptible. The data used in the number of dengue fever patients in Bone District in 2016 from Bone District Health Office. The discussion starts by the determination of equilibrium points, stability and basic reproduction numbers . In this study, we obtained that two equilibrium points and basic reproduktion value . This indicates that dengue fever disease in Bone District will increase and become endemic.Keywords: Equilibrium Point, Basic Reproduction Number, Dengue Fever, The Modification of SIR Model. 

scholarly journals ANALISIS MODEL MATEMATIKA PENYEBARAN PENYAKIT H1N1 DENGAN TINGKAT KEJADIAN TERSATURASI

2018 ◽  
Vol 1 (April) ◽  
pp. 29-33
Author(s):  
M. Ivan Ariful Fathoni
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Infected Individual ◽  
Swine Flu ◽  
Occurrence Rate ◽  
Model Formation ◽  
The Basic Reproduction Number

Swine flu is an acute respiratory infection that attacks the body's organs especially the lungs. The disease is caused by Influenza Virus Type A, type H1N1. In this article constructed mathematical model of the spread of H1N1 disease. Mathematical model that created the model Susceptible, Exposed, Infective, and Treatment. The existence of behavior change and influence of infected individual density become the reason of model formation with saturation occurrence rate. From the dynamic analysis, the model has two equilibrium points, that is, a stable equilibrium free equilibrium point when the basic reproduction number is less or equal to one, and an endemic equilibrium point that exists and is stable when the basic reproduction number is greater than one. Finally, the results of the analysis prove the control of the spread of disease into a disease-free state.   Flu babi adalah infeksi saluran pernapasan akut yang menyerang organ tubuh terutama paru-paru. Penyakit ini disebabkan oleh Virus Influenza tipe A, jenis H1N1. Pada artikel ini dikonstruksi model matematika penyebaran penyakit H1N1. Model matematika yang dibuat yaitu model Susceptible, Exposed, Infective, dan Treatment. Adanya perubahan perilaku dan pengaruh kepadatan individu terinfeksi menjadi alasan pembentukan model dengan tingkat kejadian tersaturasi. Dari hasil analisis dinamik, model memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit yang bersifat stabil saat bilangan reproduksi dasar bernilai lebih kecil atau sama dengan satu, dan titik kesetimbangan endemi yang eksis dan bersifat stabil saat bilangan reproduksi dasar bernilai lebih besar dari satu. Pada akhirnya, hasil analisis membuktikan adanya kontrol penyebaran penyakit menjadi keadaan bebas penyakit.

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