Stochastic Modeling with Poisson Hidden Markov in Hepatitis B Cases

Hepatitis B is transmitted through blood or body fluids contaminated with the virus from Hepatitis B sufferers (carriers). The factors that cause a person to contract Hepatitis B are sexual intercourse, blood contact, placental contact from the mother to the baby, and saliva. The incubation period for Hepatitis B Virus (HBV) ranges from 30 - 180 days with an average of 60 - 90 days. HBV can be detected 30 - 60 days after infection and persists for a certain period. Thus, the behaviour of infectious diseases can be observed and described using mathematical modelling. Mathematical modelling is a field of mathematics that represents and explains physical systems or problems that occur in the real world and are solved in mathematical statements. The mathematical model used to overcome uncertainty in variable values ​​is a stochastic model. These causal factors are not directly observed and form a Markov chain. The model that can be used for the uncertainty of an event is the Hidden Markov Model. The Hidden Markov Model (MHM) is a type of stochastic modelling that does not recognize the factors that trigger the problem being modelled. The Poisson Hidden Markov model is used to model Hepatitis B disease. Hepatitis B disease data is a series of observations that experience overdispersion and depend on the trigger of Hepatitis B disease, which is assumed not to be observed directly and forms a Markov chain. The aim to be achieved in this research is to model Hepatitis B disease at the Medan Haji Hospital using the Poisson Hidden Markov model and to find parameter estimates using the Expectation Maximization Algorithm. This type of research uses quantitative research methods. The conclusions that can be drawn based on the results and previous discussions are as follows: the method for determining the average number of patients in patient B can use the PHMM (Poisson Hidden Markov Model) method with the EiM (Expectation-Maximization Algorithm) algorithm, the best model for the number of Hepatitis B patients in Haji Hospital at this hospital is the model with three hidden cases with the parameter estimation value. The average number of Hepatitis B patients is 0.0324 in 1 month, and the average predicted results obtained by the hidden condition model 3 align with the original conditions in the previous months.