Parameter Estimation in a New Markov Jump Process Compartmental Model with Missing Data

In this paper, a novel compartmental model for a disease epidemic dynamics with both symptomatic and asymptomatic disease transmissions; exposure, vaccinated and hospitalized states; and recovery and death states is derived and studied. The dynamic model is a discrete-time approximation of a Markov jump processes with inter-jump times between states that are exponentially distributed. This study addresses the statistical inference challenges in compartmental models for disease dynamics exhibiting numerous states with missing data, such as, asymptomatic infectiousness, exposure to disease, and recovery from an asymptomatic infectious state. The rigorous method of EM-algorithm is employed to find Maximum-Likelihood estimators for the disease parameters in the model. This research is motivated by infectious diseases such as COVID-19, with non-observable compartments requiring data imputation statistical methods for parameter estimation. Numerical simulation results are presented.