scholarly journals Stability Analysis of Model tuberculosis Spread in Diabetes Mellitus Patients with Treatment Factors

2020 ◽  
Vol 17 (1) ◽  
pp. 50-60
Author(s):  
Nursamsi Nursamsi
Keyword(s):  
Diabetes Mellitus ◽  
Numerical Simulation ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Immune Function ◽  
Blood Sugar ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Sugar Levels ◽  
The Stability

Diabetes mellitus (Dm) is a disease associated with impaired immune function so it is more susceptible to get infections including Tuberculosis (Tb). Tb disease can also worsen blood sugar levels which can cause Dm disease. This study aims to analyze and determine the stability of the equilibrium point of the spread of Tb disease in patients with Dm with consideration nine compartments, which are susceptible Tb without Dm, susceptible Tb without Dm complication, susceptible Tb with Dm complication, expose Tb without Dm, expose Tb with Dm, infected Tb without Dm, infected Tb with Dm, recovered Tb without Dm, and recovered Tb with Dm with treatment factors. The result obtained from the analysis of the model is two equilibrium points, which are the non endemic and endemic equilibrium points. The endemic equilibrium point does not exist if , endemic will appear if . Analytical and numerical simulation show that the spread of disease can be reduced and stopped if treatment is given to the infected compartment.

scholarly journals ANALISIS KESTABILAN MODEL INTERAKSI PREDATOR-PREY DENGAN FUNGSI RESPON MONOD-HALDANE DAN PERILAKU ANTI PEMANGSA

2020 ◽  
Vol 8 (2) ◽  
pp. 51-59
Author(s):  
Muhammad Bachtiar Gaib ◽  
Wahdania At. Ja'a
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Predator Prey ◽  
First Case ◽  
Point Determination ◽  
Predator Model ◽  
The Stability ◽  
Predator Behavior

This article examines a competing prey-predator model using the Monod-Haldane response function and anti-predator behavior. This article discusses equilibrium point determination, equilibrium point stability analysis, and numerical simulation. Obtained three equilibrium points, namely T1, T2, and T3, where the equilibrium-point is always saddle, the stability of the equilibrium points T2 and T3 will be stable if it meets the predetermined parameter requirements. There are two cases in the equilibrium point where the first case is vertically stable and the second case is spiral stable.

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

scholarly journals Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Huda Abdul Satar ◽  
Raid Kamel Naji
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Food Web ◽  
Equilibrium Points ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Stability And Bifurcation ◽  
Periodic Dynamics ◽  
The Stability ◽  
Food Web Model

In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.

The Relationship of Compliance to Follow Prolanis with the Stability of Blood Sugar Levels of Patients with Type 2 Diabetes Mellitus at the Lumpue Health Center in Pare-Pare City

2020 ◽  
Vol 1 (1) ◽  
pp. 21-26
Author(s):  
Sri Syatriani ◽  
Yenni Purnamawati
Keyword(s):  
Diabetes Mellitus ◽  
Type 2 Diabetes ◽  
Type 2 Diabetes Mellitus ◽  
Health Center ◽  
Blood Sugar ◽  
Sugar Levels ◽  
The Stability ◽  
Relationship Of ◽  
The Relationship

Diabetes Mellitus is a disease that can cause complications to prevent complications can be done by maintaining the stability of blood sugar in people with diabetes. One of the efforts of patientss of Diabetes mellitus (DM) in maintaining the stability of blood sugar levels is to adhere to one of the Corneal Disease Management Programs (PROLANIS). The prevalence of diabetes mellitus in Indonesia in 2018 will reach 10.9%. The purpose of this study was to determine the relationship of compliance to follow prolanis with the stability of blood sugar levels of patientss with type 2 diabetes mellitus. This type of research is analytic research with cross sectional study design. The sample in this study were all patientss of diabetes mellitus who participated in the prolanis activities of 40 respondents at the Lumpue Health Center in Parepare City in September 2018 - January 2019 which were selected by total sampling technique. Data were analyzed by Chi-Square test. The results showed that most of the respondents included in the category of obediently followed prolanis, as many as 31 (77.5%) people and the majority with stable blood sugar, as many as 31 (77.5%) people. Relationship test results obtained p value (0,000) <α (0.05), which means there is an relationship compliance to follow Prolanis  with the stability of blood sugar in patientss with diabetes mellitus in the Lumpue Health Center in Parepare City. The conclusion of this research is that there is an relationship compliance to follow Prolanis with the stability of blood sugar. Patientss with diabetes mellitus are expected to routinely participate in prolanis activities held at each puskesmas to stabilize blood sugar levels.

scholarly journals Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina

2021 ◽  
Author(s):  
Resmawan Resmawan ◽  
Agusyarif Rezka Nuha ◽  
Lailany Yahya
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Human Class ◽  
Existence Of Equilibrium ◽  
The Stability ◽  
Disease Free

This paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R0&lt;1 and unstable at R0&gt;1. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.

scholarly journals Analisis Kestabilan Model SEIR Penyebaran Penyakit Campak dengan Pengaruh Imunisasi dan Vaksin MR

2019 ◽  
Vol 16 (1) ◽  
pp. 107
Author(s):  
Willyam Daniel Sihotang ◽  
Ceria Clara Simbolon ◽  
July Hartiny ◽  
Desrinawati Tindaon ◽  
Lasker Pangarapan Sinaga
Keyword(s):  
Infectious Disease ◽  
Equilibrium Point ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Seir Model ◽  
Rate Of Spread ◽  
The Stability ◽  
Disease Free

Measles is a contagious infectious disease caused by a virus and has the potential to cause an outbreak. Immunization and vaccination are carried out as an effort to prevent the spread of measles. This study aims to analyze and determine the stability of the SEIR model on the spread of measles with the influence of immunization and MR vaccines. The results obtained from model analysis, namely there are two disease free and endemic equilibrium points. If the conditions are met, the measles-free equilibrium point will be asymptotically stable and the measles endemic equilibrium point will be stable. Numerical solutions show a decrease in the rate of spread of measles due to the effect of immunization and the addition of MR vaccines.

scholarly journals GAMBARAN TINGKAT STRES PASIEN DIABETES MELLITUS

2018 ◽  
Vol 2 (1) ◽  
pp. 41
Author(s):  
Livana PH ◽  
Indah Permata Sari ◽  
Hermanto Hermanto
Keyword(s):  
Diabetes Mellitus ◽  
Blood Sugar ◽  
Family Doctor ◽  
Mild Stress ◽  
Depression Anxiety Stress Scale ◽  
Stress Scale ◽  
Stress Levels ◽  
Quantitative Descriptive ◽  
Sugar Levels ◽  
The Stability

Abstrak Diabetes Mellitus merupakan kelainan metabolik yang ditandai dengan kenaikan kadar gula darah, akibat adanya kelainan sekresi insulin, kerja insulin atau keduanya.  Pasien Diabetes Mellitus harus melakukan terapi pengelolaan sepanjang hidupnya baik secara farmakologis maupun non farmakologis untuk mencegah terjadinya komplikasi dan mengontrol kestabilan kadar gula darahnya. Terapi tersebut dapat menimbulkan suatu dampak tertentu, baik secara fisik maupun secara psikologis.  Salah satu dampak psikologis yang dapat dirasakan oleh pasien Diabetes Mellitus adalah stres.  Penelitian ini bertujuan untuk mengetahui gambaran tingkat stres pada pasien Diabetes Mellitus di wilayah dokter keluarga Djazariyah Kabupaten Kendal.  Metode deskriptif kuantitatif. Alat ukur yang digunakan berupa kuesioner Depression Anxiety Stres Scale yang terdiri dari 42 pertanyaan.  Sampel berjumlah 37 responden.  Sebagian besar pasien Diabetes Mellitus mengalami stres ringan.  Peneliti memberikan saran bagi peneliti selanjutnya untuk menggunakan kuesioner Depression Anxiety Stres Scale yang telah dimodifikasi disetiap pertanyaannya, agar mempermudah responden dalam menjawab. Kata kunci: Stres pada pasien Diabetes Mellitus. Abstract the description of stress levels in Diabetes Mellitus patients. Diabetes Mellitus is a metabolic abnormality characterized by elevated blood sugar levels, due to an abnormality of insulin secretion, insulin work or both. Diabetes Mellitus patients should take life-long management therapy both pharmacologically and nonpharmacologically to prevent complications and control the stability of their blood sugar levels. The therapy can have a certain impact, both physically and psychologically. One of the psychological effects that can be felt by Diabetes Mellitus patients is stress. This study aims to determine the description of stress levels in Diabetes Mellitus patients in the area of Djazariyah family doctor Kendal District. Quantitative descriptive method. The measuring tool used is a questionnaire of Depression Anxiety Stress Scale consisting of 42 questions. The sample was 37 respondents. Most Diabetes Mellitus patients experience mild stress. Researchers provide suggestions for further researchers to use the questionnaire of Depression Anxiety Stress Scale that has been modified in each question, in order to facilitate respondents in answering. Keywords: Stress in Diabetes Mellitus clients

scholarly journals Stability Analysis of Mathematical Models of the Dynamics of Spread of Meningitis with the Effects of Vaccination, Campaigns and Treatment

2020 ◽  
Vol 17 (1) ◽  
pp. 71-81
Author(s):  
Sulma Sulma ◽  
Syamsuddin Toaha ◽  
Kasbawati Kasbawati
Keyword(s):  
Infectious Disease ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Vaccination Campaign ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Infected People ◽  
The Stability ◽  
Vaccination Campaigns ◽  
The Mathematical Model

Meningitis is an infectious disease caused by bacteria, viruses, and protosoa and has the potential to cause an outbreak. Vaccination and campaign are carried out as an effort to prevent the spread of meningitis, treatment reduces the number of deaths caused by the disease and the number of infected people. This study aims to analyze and determine the stability of equilibrium point of the mathematical model of the spread of meningitis using five compartments namely susceptibles, carriers, infected without symptoms, infected with symptoms, and recovered with the effect of vaccination, campaign, and treatment. The results obtained from the analysis of the model that there are two equilibrium points, namely non endemic and endemic equilibrium points. If a certain condition is met then the non endemic equilibrium point will be asymptotically stable. Numerical simulations show that the spread of disease decreases with the influence of vaccination, campaign, and treatment.

DYNAMICAL ANALYSIS OF FRACTIONAL ORDER ZIKV MODEL

2021 ◽  
Vol 10 (5) ◽  
pp. 2469-2481
Author(s):  
N.A. Hidayati ◽  
A. Suryanto ◽  
W.M. Kusumawinahyu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Stability Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
S Model

The ZIKV model presented in this article is developed by modifying \cite{Bonyah2016}’s model. The classical order is changed into fractional order model. The equilibrium points of the model are determined and the stability conditions of each equilibrium point have been done using Routh-Hurwitz conditions. Numerical simulation is presented to verify the result of stability analysis result. Numerical simulation is also used to shows the effect of the order $\alpha$ to the stability of the model’s equilibrium point.

scholarly journals Efektifitas Terapi Murottal Al-Quran Terhadap Kadar Gula Darah Pasien Diabetes Mellitus Tipe 2 di RSUD Dr.Rasidin Padang

2020 ◽  
Vol 15 (1) ◽  
pp. 8-17
Author(s):  
Wiwi Sartika ◽  
Metri Lidya ◽  
Alsri Windra Doni
Keyword(s):  
Diabetes Mellitus ◽  
Blood Sugar ◽  
Control Group ◽  
Case Group ◽  
Heart Attacks ◽  
Before And After ◽  
Sugar Levels ◽  
The Stability ◽  
And Control

The condition of high and uncontrolled high blood sugar levels in Diabetes Mellitus patients increases the risk of other diseases, such as; heart attacks, strokes, blindness, kidney failure, gangrene, and even death. Various studies state that there is a relationship between Murottal Al-Qur'an therapy with the stability of blood sugar. The study aims to determine the effectiveness of Murottal Al-Qur'an on Blood Sugar Levels of Diabetes Mellitus Patients in Rasyidin District Hospital, Padang City in 2019. Interventions were conducted during August until September 2019. The population was inpatients diagnosed with Type 2 DM in RSUD Dr. Rasyidin Padang at the time of the study. A sample of 32 people consisted of a case group (given Murottal Al-Quran therapy) and a control group, each with 16 people. Data collection was carried out through observation and examination of blood sugar before and after the intervention. Data were tested by paired sample T-test. The results showed that there were differences in blood sugar levels at both the case and control groups before and after the intervention. The average blood sugar level of the patient in the case group was more controlled, namely 173.94 mg / dl (GDS <200) compared to the control group, namely 226.69 mg / dl (GDS> 200 mg / dl). Murottal Al-Quran therapy can be used as an alternative to maintain blood sugar stability for people with diabetes.

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