Covid-19 pandemic has been going on for approximately two years in Indonesia.  During the pandemic, COVID-19 virus has undergone many mutations. mutation process produces new variants, where the latest variant that has been discovered is known as the Omicron variant.  This variant has a very rapid transmission rate.  To overcome the problem of Omicron distribution, it is necessary to analyze the distribution through mathematical modeling.  This research uses literature study method related to omicron, especially modeling using vaccination control. Study will analyze SLIR model of the spread of the omicron variant of covid with vaccination control. Formed model will be analyzed by determining equilibrium, stability and continued with the addition of controls and then numerically simulated.  Model has four subpopulations, namely Susceptible, Latent, Infected, and Recovery with the addition of migration parameters in the Susceptible and Latent subpopulations to form a system of nonlinear differential equations.  The results of the analysis of this model have two equilibrium points, namely the disease-free and endemic equilibrium points.  Stability of the disease-free equilibrium point will be stable when .  And the endemic stability meets and  so that it is concluded that it is asymptotically stable.  And with the addition of control in the form of vaccination, if vaccination can be carried out massively for at least 100 days, then the number of infected individuals can be controlled properly and the reduction in migration parameters obtained can minimize the number of latent and infected populations in Omicron sufferers so that the spread of disease can be controlled and the impact of the spread disease can be minimized.

The longer the fish population will decrease or experience extinction due to continuous fishing by humans. Conservation areas are needed as an effort to maintain the marine ecosystem and avoid extinction. The dynamics stability of the model can be seen from the equilibrium point. So that the application of mathematics can be used to make prey-predator population dynamics models and determine ways to optimize fish harvesting. The mathematical model is divided into three populations and in two different areas. To get maximum harvesting (E), use the Pontryagin Maximum Principle. So that the maximum benefit obtained when harvesting is 0.77 to 0.95.

Indeks Pembangunan Manusia (IPM) merupakan indikator yang digunakan untuk mengukur kualitas manusia. Dimana angka Indeks Pembangunan Manusia  menunjukkan maju atau tidaknya suatu wilayah. Jawa Timur merupakan salah satu provinsi di Pulau Jawa yang memiliki jumlah penduduk terbanyak pada tahun 2021, namun hal ini tidak sebanding dengan angka Indeks Pembangunan Manusia  yang rendah sehingga menyebabkan ketimpangan pembangunan. Oleh karena itu, diperlukan  penelitian untuk tujuan menganalisis faktor apa saja yang mempengaruhi angka Indeks Pembangunan Manusia menggunakan regresi semiparametrik dengan pendekatan spline truncated. Pemilihan titik knot optimum dengan menggunakan kriteria Generalized Cross Validation (GCV) minimum. Adapun hasil penelitian ini adalah model regresi semiparametrik terbaik terdapat pada 3 titik knot dengan nilai GCV minimum yaitu  serta koefsien determinasi sebesar . Selain itu, ditunjukkan bahwa variabel angka harapan hidup, rata-rata lama sekolah, harapan lama sekolah, tingkat partisipasi angkatan kerja, dan tingkat pengangguran terbuka merupakan faktor-faktor yang memiliki pengaruh signifikan terhadap Indeks Pembangunan Manusia di Jawa Timur tahun 2021.

Inflation is an economic event that often occurs even though it is not wanted. Based on data from Badan Pusat Statistik in 2015-2020 inflation in East Java was 3.08%, 2.74%, 4.04%, 2.86%, 2.12%, 1.44%. From these data, it can be seen that inflation data is fluctuating. Therefore it is necessary to control inflation because high and unstable inflation can have a negative impact on the socio-economic conditions of the community. In addition, it also makes it difficult for the government to determine future policies. Seeing the importance of controlling inflation, it is necessary to study to predict the inflation rate in the future. One of the studies/methods to predict that is often used is the Autoregressive Integrated Moving Average (ARIMA) method or also known as the Box-Jenkins method. The ARIMA method is a method that is easy to use because it is flexible in following existing data patterns and has high accuracy and tends to have a small error value because of the detailed process. From the analysis results, the best ARIMA (p,d,q) model is the ARIMA model (2,1,1) with an AIC value of 76.77. The results of forecasting with the ARIMA model (2,1,1) respectively are 0.2593698, 0.1892990, 0.1340639, 0.1368309, 0.1572021, 0.1642381, 0.1598897, 0.1557251, 0.1556074, 0.1570151, 0.1576092, 0.1573511, 0.1570423, and 0.1570111.

One of the branches of mathematics that studies the properties of graphs is graph theory. The purpose of this study is to find out how to prove the Hamiltonian on a 5-connected graph. Through the stages, including modeling a complete graph, as well as modeling a 5-connected graph using vertices and cut edges, it was found that is a graph that satisfies the characteristics of a 5-connected graph. Analysis of Hamiltonian on 5-connected graph that 5-connected graph is Hamilton's invention, but it is not uniquely Hamiltonian because it has more than one Hamiltonian circuit.Keywords: k-connected graph, Hamiltonian, vertex cuts