SVIRD epidemic model with discrete-time hybrid Markov/semi-Markov assumptions

Abstract

Multi-state models with discrete-time Markov assumptions are widely used in epidemiology. However, this model has a memoryless property, making it less suitable for specific applications. One solution to this problem is to use additional assumptions by paying attention to the sojourn time in a particular state, which brings this model into a semi-Markov form. This paper aims to model the spread of infectious diseases by combining Markov and semi-Markov assumptions in one multi-state model known as a hybrid Markov/semi-Markov model. The first step is to check whether the SVIRD epidemic model satisfies the Markov assumptions. If not, then the SVIRD epidemic model uses a hybrid Markov/semi-Markov assumption. The second step is to test the semi-Markov hypothesis for each transition in the SVIRD model. Usually, the distribution is Geometric for semi-Markov sojourn times, but if the hypothesis is rejected, it uses the discrete Weibull distribution or negative Binomial. The hybrid Markov/semi-Markov model aims to reduce the complexity of the model in terms of the number of parameters to be estimated by only taking into account the sojourn time for transitions that do not meet the Markov assumptions. The final step is to make predictions by modifying the cohort state transition model by generating the number of individuals infected with an infectious disease at time t+1.