Penelitian ini membahas tentang model mangsa-pemangsa dengan fungsi respon Holling Tipe II. Infeksi penyakit hanya terjadi pada populasi pemangsa dan menyebabkan kematian. Selain itu dilakukan pemanenan pada mangsa dengan asumsi mangsa memiliki nilai ekonomis. Penelitian ini bertujuan untuk memformulasikan model mangsa-pemangsa dengan fungsi respon Holling Tipe II, infeksi pada pemangsa dan pemanenan pada mangsa, menganalis kestabilan titik kesetimbangan model dan interpretasi model. Analisis kestabilan dilakukan dengan metode linearisasi. Jenis kestabilan ditentukan berdasarkan karakteristik nilai eigen yang diperoleh dengan menggunakan kriteria Routh-Hurwitz. Dari penelitian ini diperoleh bahwa kepunahan populasi tidak mungkin terjadi sedangkan mangsa eksis, kepunahan pemangsa sehat, kepunahan pemangsa sakit dan populasi eksis masih memungkinkan terjadi jika memenuhi kondisi yang disyaratkan. Simulasi numerik menunjukkan bahwa laju pemanenan yang diperbesar mengakibatkan jumlah populasi mangsa terus mengalami penurunan secara signifikan dan hampir mengalami kepunahan seiring berjalannya waktu. Semakin berkurangnya populasi mangsa ini mengakibatkan populasi pemangsa juga semakin berkurang secara signifikan dan hampir mengalami kepunahan.

Extreme weather modeling is a challenge for modeling experts in Indonesia and the world. Extreme weather prediction is a complex problem because the chances of it happening are very small, so the developed models often have a low level of accuracy. The purpose of this research is to combine the classic model, Autoregressive Integrated Moving Average (ARIMA), recurrent neural network (RNN) model using Adam and SGD estimation (RNN-Adam and RNN-SGD) with the reLU, tanh, sigmoid and gaussian activation functions. In addition, the ARIMA-RNN mix model was also demonstrated in this study. These models are applied to monthly period extreme weather data obtained from the Meteorology, Climatology and Geophysics Agency (BMKG) of West Sulawesi Province which are converted into training data and test data. The RMSE value is used to see the level of prediction accuracy in both training data and test data. Based on the research results, the best model obtained for modeling Indonesia’s extreme weather is the ARIMA-RNN-Adam mix model with the reLU activation function based on the RMSE value on the training and test data. At n = 50, the smallest RMSE and MSE values of the third model are the ARIMA-RNN-Adam model which is 0.23212 using the reLU activation function, then the ARIMA-RNN-SGD model which is 0.25432 with the same activation function, while the ARIMA value is 0.3270. At n=100 it can be seen that the smallest RMSE and MSE values of the three models are the ARIMA-RNN-Adam model which is equal to 0.25149 using the reLU activation function, then the ARIMA-RNN-SGD model which is equal to 0.25256 with the same activation function, while the ARIMA value is 0.2644.