scholarly journals Pemodelan Penggunaan E-Money Pada E-Parking Kota Makassar

2020 ◽  
Vol 3 (2) ◽  
pp. 88
Author(s):  
Hisyam Ihsan ◽  
Syafruddin Side ◽  
Emi Wulandari
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Primary Data ◽  
Type Model ◽  
Reproduction Numbers ◽  
Simulation Results ◽  
Siri Model

Penelitian ini bertujuan untuk membangun model penggunaan E-Money pada E-Parking tipe SIRI (Susceptible – Infected – Recovered – Infected) di Kota Makassar. Asumsi yang ditambahkan adalah manusia yang telah menggunakan E-Money dapat kembali menggunakan uang tunai pada pembayaran parkir. Model ini dibagi menjadi tiga kelas yaitu rentan/berpotensi menggunakan parkir, pengguna uang tunai, dan pengguna E-Money. Data yang digunakan adalah data primer yang diperoleh dengan survey langsung dilapangan. Survey dilakukan dengan membagikan angket kepada 100 responden secara acak. Model matematika tipe SIRI digunakan untuk menentukan titik equilibrium. Hasil simulasi model tipe SIRI menghasilkan bilangan reproduksi dasar (R0) sebesar 0.021021 yang berarti bahwa penggunaan uang tunai dapat mengalami penurunan yang menyebabkan penggunaan E-Money akan meningkat dalam kurun waktu tertentu.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Uang Elektronik, Parkiran Elektronik, Model SIRI This study aims to build a model of the use of E-Money in E-Parking type SIRI (Susceptible - Infected - Recovered - Infected) in Makassar City. The added assumption is that people who have used E-Money can may return to cash payments on parking. This model is divided into three classes, namely vulnerable / potentially using parking, cash users, and E-Money users. The data used are primary data obtained by direct survey in the field. The survey was conducted by distributing questionnaires to 100 respondents randomly. The SIRI type mathematical model is used to determine the equilibrium point. The simulation results of the SIRI type model produce a base reproduction number (R0) of 0.021021 which means that the use of cash can decrease which causes the use of E-Money will increase in a certain period of time. Keywords: Equilibrium Point, Basic Reproduction Numbers, E-Money, E-Parking, SIRI Model

scholarly journals Model Matematika SIR Sebagai Solusi Kecanduan Penggunaan Media Sosial

2020 ◽  
Vol 3 (2) ◽  
pp. 126
Author(s):  
Syafruddin Side ◽  
Wahidah Sanusi ◽  
Nur Khaerati Rustan
Keyword(s):  
Social Media ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sir Model ◽  
Primary Data ◽  
Type Model ◽  
Social Media Addiction ◽  
Reproduction Numbers ◽  
Simulation Results ◽  
Use Of Social Media

Penelitian ini bertujuan untuk membangun model SIR (Susceptible – Infected – Recovered) sebagai solusi kecanduan penggunaan media sosial dengan asumsi bahwa mahasiswa yang sembuh dari kecanduan media sosial karena memiliki kontrol diri tinggi. Model ini dibagi menjadi tiga kelas yaitu kelas mahasiswa yang berpotensi menggunakan media sosial, kelas mahasiswa yang kecanduan media sosial, dan kelas mahasiswa yang memiliki kontrol diri tinggi. Data yang digunakan adalah data primer yang diperoleh dengan membagikan kuesioner kepada 145 mahasiswa Jurusan Matematika FMIPA UNM angkatan 2017, 2018, dan 2019. Hasil data riil model tipe SIR menghasilkan bilangan reproduksi dasar (R0) sebesar  yang berarti bahwa jumlah mahasiswa yang kecanduan penggunaan media sosial akan meningkat dalam kurun waktu tertentu.Kata Kunci: Titik Ekuilibrium, Bilangan Reproduksi Dasar, Media Sosial, Kontrol Diri, Model SIRThis study aims to build the SIR (Susceptible - Infected - Recovered) model as a solution of social media addiction with the assumption that students who recover from addiction of social media because they have high selfcontrol. This model is divided into three classes: namely class of students who have potential to use social media, class of students who are addicted to social media, and class of students who have high selfcontrol. The data used are primary data that was obtained by distributing questionnaires to 145 students of mathematics departement FMIPA UNM class of 2017, 2018, and 2019. The simulation results of the SIR type model produce a basic reproduction number (R0) of 1.451136 which means that the number of students who are addicted to the use of social media will increase in a certain period of time.Keywords: Equilibrium Points, Basic Reproduction Numbers, Social Media, Selfcontrol, SIR Model

scholarly journals Model SEIRS Penyebaran Penyakit Tuberkulosis di Kota Makassar

2021 ◽  
Vol 3 (1) ◽  
pp. 11
Author(s):  
Rahmat Syam ◽  
Syafruddin Side ◽  
Citra Suci Said
Keyword(s):  
Equilibrium Point ◽  
Reproduction Number ◽  
Health Department ◽  
Reproduction Numbers ◽  
Simulation Results

Abstrak. Penelitian ini  bertujuan untuk membangun model penyebaran penyakit tuberkulosis tipe SEIRS (Susceptible- Exposed- Infected- Recovered- Susceptible) dengan menambahkan asumsi bahwa manusia yang pulih dapat rentan kembali terkena tuberkulosis. Model ini dibagi menjadi empat kelas yaitu, rentan, terinfeksi tapi belum aktif, terinfeksi, dan sembuh. Data yang digunakan adalah data jumlah penderita penyakit tuberkulosis dari Dinas Kesehatan Kota Makassar tahun 2017. Model matematika tipe SEIRS digunakan untuk menentukan titik equilibrium. Berdasarkan hasil simulasi model SEIRS diperoleh bilangan reproduksi dasar ( ) sebesar 0,312 berarti bahwa seseorang yang terinfeksi penyakit tuberkulosis tidak menyebabkan orang lain terkena penyakit tuberkulosis di wilayah Kota Makassar.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Tuberkulosis, Model SEIRS, Pemodelan.Abstract. This research aims to model of tuberculosis type SEIRS (Susceptible-Exposed-Infected-Recovery-Susceptible) by adding assumption that human that has been recovered can be suspected again by Tuberculosis. This model can be divided to  four classes, those are suspected, exposed, infected, and recovered. The data that used is data on the number of tuberculosis sufferer from Health Department in  Makassar City 2017.  Mathematicsl model of SEIRS type is used to determine the equilibrium point. According to the simulation results of SEIRS model, obtained the base reproduction number ( )  is  0.312 means that people who infected by tuberculosis does not causes other people get tuberculosis in Makassat city.Keywords: Equilibrium Point, Basic Reproduction Numbers, Tuberculosis, SEIRS Model, modeling.

scholarly journals Pemodelan Matematika SEIRS Pada Penyebaran Penyakit Malaria di Kabupaten Mimika

2021 ◽  
Vol 4 (1) ◽  
pp. 21
Author(s):  
Hisyam Ihsan ◽  
Syafruddin Side ◽  
Musdalifa Pagga
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
District Health Office ◽  
District Health ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Malaria Model ◽  
The Basic Reproduction Number

Abstrak. Penelitian ini  bertujuan untuk membangun model penyebaran pada penyakit malaria tipe SEIRS (Susceptible-Exposed- Infected- Recovered- Susceptible) dengan menambahkan parameter penanganan(pengobatan) pada kelas Exposed dan asumsi bahwa manusia yang pulih dapat rentan kembali terkena penyakit malaria. Model ini dibagi menjadi empat kelas yaitu, rentan, terinfeksi tapi belum aktif, terinfeksi, dan sembuh. Data yang digunakan adalah data jumlah penderita penyakit malaria dari Dinas Kesehatan Kabupaten Mimika tahun 2018. Model matematika tipe SEIRS digunakan untuk menentukan titik equilibrium. Berdasarkan hasil simulasi dari model SEIRS diperoleh bilangan reproduksi dasar  sebesar 0,09 yang menandakan bahwa penyebaran penyakit malaria tidak menyebabkan orang lain terkena penyakit malaria.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Malaria, Model SEIRSAbstract. This research aims to build a model of the spread of malaria diseases type SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) by adding treatment parameters (treatment) in the Exposed class and the assumption that humans who recover can be vulnerable to malaria again. This model is divided into four classes namely, vulnerable, infected but not yet active, infected, and cured. The data used are data on the number of malaria sufferers from the Mimika District Health Office in 2018. The mathematical model of the type SEIRS is used to determine the equilibrium point. Based on the simulation results of the SEIRS model, the basic reproduction number (R0) of 0.09 indicates that the spread of malaria does not cause others to contract malaria.Keywords: Equilibrium Point, Basic Reproductive Numbers, Malaria, SEIRS Model

scholarly journals Qualitative properties of mathematical model of English language education

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Atena Ghasemabadi ◽  
Nahid Soltanian
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Equilibrium Point ◽  
English Language ◽  
Language Education ◽  
Qualitative Properties ◽  
English Language Education ◽  
Compound Matrices ◽  
Reproduction Numbers ◽  
Coexistence Equilibrium

AbstractThis paper presents a mathematical model that examines the impacts of traditional and modern educational programs. We calculate two reproduction numbers. By using the Chavez and Song theorem, we show that backward bifurcation occurs. In addition, we investigate the existence and local and global stability of boundary equilibria and coexistence equilibrium point and the global stability of the coexistence equilibrium point using compound matrices.

MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
The Mathematical Model ◽  
Globally Stable ◽  
Well Posed ◽  
The Basic Reproduction Number ◽  
Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

THE EFFECTS OF VACCINATION AND TREATMENT ON THE SPREAD OF HIV/AIDS

2004 ◽  
Vol 12 (04) ◽  
pp. 399-417 ◽  
Author(s):  
M. KGOSIMORE ◽  
E. M. LUNGU
Keyword(s):  
Equilibrium Point ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Treatment Programs ◽  
Asymptotically Stable ◽  
Reproduction Numbers ◽  
Threshold Conditions ◽  
Existence And Stability ◽  
Disease Free ◽  
Hiv Aids

This study investigates the effects of vaccination and treatment on the spread of HIV/AIDS. The objectives are (i) to derive conditions for the success of vaccination and treatment programs and (ii) to derive threshold conditions for the existence and stability of equilibria in terms of the effective reproduction number R. It is found, firstly, that the success of a vaccination and treatment program is achieved when R0t<R0, R0t<R0v and γeRVT(σ)<RUT(α), where R0t and R0v are respectively the reproduction numbers for populations consisting entirely of treated and vaccinated individuals, R0 is the basic reproduction number in the absence of any intervention, RUT(α) and RVT(σ) are respectively the reproduction numbers in the presence of a treatment (α) and a combination of vaccination and treatment (σ) strategies. Secondly, that if R<1, there exists a unique disease free equilibrium point which is locally asymptotically stable, while if R>1 there exists a unique locally asymptotically stable endemic equilibrium point, and that the two equilibrium points coalesce at R=1. Lastly, it is concluded heuristically that the stable disease free equilibrium point exists when the conditions R0t<R0, R0t<R0v and γeRVT(σ)<RUT(α) are satisfied.

scholarly journals A Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment

2020 ◽  
Vol 24 (5) ◽  
pp. 917-922
Author(s):  
J. Andrawus ◽  
F.Y. Eguda ◽  
I.G. Usman ◽  
S.I. Maiwa ◽  
I.M. Dibal ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Line Treatment ◽  
Second Line ◽  
Tuberculosis Transmission ◽  
Disease Free

This paper presents a new mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment. We calculated a control reproduction number which plays a vital role in biomathematics. The model consists of two equilibrium points namely disease free equilibrium and endemic equilibrium point, it has been shown that the disease free equilibrium point was locally asymptotically stable if thecontrol reproduction number is less than one and also the endemic equilibrium point was locally asymptotically stable if the control reproduction number is greater than one. Numerical simulation was carried out which supported the analytical results. Keywords: Mathematical Model, Biomathematics, Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium Point

scholarly journals Modelling the Effectiveness of Epidemic Control Measures in Preventing the Transmission of COVID-19 in Malaysia

2020 ◽  
Vol 17 (15) ◽  
pp. 5509 ◽  
Author(s):  
Balvinder Singh Gill ◽  
Vivek Jason Jayaraj ◽  
Sarbhan Singh ◽  
Sumarni Mohd Ghazali ◽  
Yoon Ling Cheong ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Calibration ◽  
Reproduction Number ◽  
Close Contact ◽  
Movement Control ◽  
Control Measures ◽  
Seir Model ◽  
Epidemic Curve ◽  
Reproduction Numbers ◽  
Control Order

Malaysia is currently facing an outbreak of COVID-19. We aim to present the first study in Malaysia to report the reproduction numbers and develop a mathematical model forecasting COVID-19 transmission by including isolation, quarantine, and movement control measures. We utilized a susceptible, exposed, infectious, and recovered (SEIR) model by incorporating isolation, quarantine, and movement control order (MCO) taken in Malaysia. The simulations were fitted into the Malaysian COVID-19 active case numbers, allowing approximation of parameters consisting of probability of transmission per contact (β), average number of contacts per day per case (ζ), and proportion of close-contact traced per day (q). The effective reproduction number (Rt) was also determined through this model. Our model calibration estimated that (β), (ζ), and (q) were 0.052, 25 persons, and 0.23, respectively. The (Rt) was estimated to be 1.68. MCO measures reduce the peak number of active COVID-19 cases by 99.1% and reduce (ζ) from 25 (pre-MCO) to 7 (during MCO). The flattening of the epidemic curve was also observed with the implementation of these control measures. We conclude that isolation, quarantine, and MCO measures are essential to break the transmission of COVID-19 in Malaysia.

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 Accounting for symptomatic and asymptomatic in a SEIR-type model of COVID-19

2020 ◽  
Vol 15 ◽  
pp. 34 ◽  
Author(s):  
Jayrold P. Arcede ◽  
Randy L. Caga-anan ◽  
Cheryl Q. Mentuda ◽  
Youcef Mammeri
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Type Model ◽  
Treatment Results ◽  
Hospital Capacity ◽  
The Usa ◽  
Using Data ◽  
The Basic Reproduction Number

A mathematical model was developed describing the dynamic of the COVID-19 virus over a population considering that the infected can either be symptomatic or not. The model was calibrated using data on the confirmed cases and death from several countries like France, Philippines, Italy, Spain, United Kingdom, China, and the USA. First, we derived the basic reproduction number, R0, and estimated the effective reproduction Reff for each country. Second, we were interested in the merits of interventions, either by distancing or by treatment. Results revealed that total and partial containment is effective in reducing the transmission. However, its duration may be long to eradicate the disease (104 days for France). By setting the end of containment as the day when hospital capacity is reached, numerical simulations showed that the duration can be reduced (up to only 39 days for France if the capacity is 1000 patients). Further, results pointed out that the effective reproduction number remains large after containment. Therefore, testing and isolation are necessary to stop the disease.

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