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Multi-state SVIRD Model with Continuous-time Markov Chain Assumption on the Spread of Infectious Diseases


  • Faihatuz Zuhairoh Universitas Gadjah Mada
  • Dedi Rosadi Universitas Gadjah Mada
  • Adhitya Ronnie Effendie Universitas Gadjah Mada


The spread of infectious diseases is generally described using mathematical models. This paper discusses the spread of infectious diseases using a multi-state SVIRD model, assuming that a continuous-time Markov chain (CTMC) occurs in a closed population and is examined regularly. This article aims to generate transition probabilities and parameter estimates using the maximum likelihood method. The multi-state SVIRD model assuming CTMC uses a transition intensity and transition probability approach consisting of five primary states: susceptible, vaccinated, infected, recovered, and deceased. The infected state is divided into two: infected before and after being vaccinated. The result is an estimator of transition intensity with sojourn time which is exponentially distributed to produce a transition probability matrix. Then the algorithm for the CTMC SVIRD model is given. The multi-state SVIRD model algorithm can be used directly if the epidemic case is still in single-wave to determine the transition probability. In contrast, for multi-wave cases, it is necessary to detect changepoints to determine wave boundaries to make predictions more accurate. The main contributions of this study are using the CTMC assumption, a stochastic model for determining the parameters of the differential equation formed by the compartment model and adding vaccinated status to the model. In addition, it also provides ways to overcome multi-wave epidemic cases so the prediction results are more accurate.


How to Cite

Zuhairoh, F., Rosadi, D., & Effendie, A. R. Multi-state SVIRD Model with Continuous-time Markov Chain Assumption on the Spread of Infectious Diseases. Austrian Journal of Statistics, 53(1), 70–94. Retrieved from