Nonhomogeneous Continuous-Time Markov Chain (NH-CTMC) is a stochastic process that can be used to model problems where the future state depends only on the current state and is independent of the past. The transition intensity in NH-CTMC is not constant but is a function of time. In this paper, NH-CTMC is employed to model information dissemination on Twitter, where transitions occur only from followee groups to follower groups. Information is considered spread on Twitter when followers retweet posts from their followees. The tweet-retweet process on Twitter satisfies the Markov property, as a retweet from a follower depends only on the tweet posted just before by the corresponding followee. The probability of a tweet spreading is determined by the transition intensity, assumed to be a Sigmoid function whose parameters are estimated using Maximum Likelihood Estimation (MLE). This method is applied to Twitter data from Indonesia related to discussions on Covid-19 vaccination. The results indicate that information about Covid-19 vaccination on Twitter spreads rapidly from followees to followers in the first 20 hours, and then slows down after 40 hours. The NH-CTMC model outperforms the Homogeneous Continuous-Time Markov Chain (H-CTMC) approach, where the transition intensity (tweet spreading intensity) is assumed to be constant.

Cocoa is a plantation commodity whose role is essential for the economy, so it is necessary to be aware of its health to maximize production. Cocoa plant disease data is a time series data because it is observed continuously. One of the time series forecasting models is the Fuzzy Time Series Markov Chain (FTS-MC), a combination of the Fuzzy Time Series (FTS) and Markov Chain models. The model uses the principle of fuzzy logic by transferring FTS data to fuzzy logic and using the obtained fuzzy logic groups to derive the Markov chain transition matrix. In this research, a Python script of the FTS-MC model was built in the Google Colaboratory to forecast the number of cocoa plant diseases in Bendungan District to simplify and speed up the data processing. Python was used in this research because of its easy-to-use, flexible, and open-source syntax. In building Python scripts, libraries and functions are needed by utilizing loop processes and if-else statements. Based on the processing results, forecasting with the FTS-MC model using Python only takes less than 1 minute.

In this paper, a homogeneous continuous time Markov chain (CTMC) is used to model information diffusion or dissemination, also to determine influencers on Twitter dynamically. The tweeting process can be modeled with a homogeneous CTMC since the properties of Markov chains are fulfilled. In this case, the tweets that are received by followers only depend on the tweets from the previous followers. Knowledge Discovery in Database (KDD) in Data Mining is used to be research methodology including pre-processing, data mining process using homogeneous CTMC, and post-processing to get the influencers using visualization that predicts the number of affected users. We assume the number of affected users follows a logarithmic function. Our study examines the Indonesian Twitter data users with tweets about covid19 vaccination resulted in dynamic influencer rankings over time. From these results, it can also be seen that the users with the highest number of followers are not necessarily the top influencer.