Pemodelan Matematika SIRI pada Penyebaran Penyakit Tifus di Sulawesi Selatan

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.

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

<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>

Pemodelan Penggunaan E-Money Pada E-Parking Kota Makassar

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

Effects of information-dependent vaccination behavior on coronavirus outbreak: insights from a SIRI model

A mathematical model is proposed to assess the effects of a vaccine on thetime evolution of a coronavirus outbreak. The model has the basic structure of SIRIcompartments (susceptible-infectious-recovered-infectious) and is implemented by tak-ing into account of the behavioral changes of individuals in response to the availableinformation on the status of the disease in the community. We found that the cumu-lative incidence may be significantly reduced when the information coverage is highenough and/or the information delay is short, especially when the reinfection rate ishigh enough to sustain the presence of the disease in the community. This analysis is in-spired by the ongoing outbreak of a respiratory illness caused by the novel coronavirusCOVID–19.