What is the difference between a Markov and semi-Markov model? – Healthcare Economist

The free online book R for Health Technology Assessment has the answer:

Markov models are characterised by a memoryless property called the Markov assumption or Markov property. Under the Markov assumption, movement of an individual from their current health state to a future one, conditional on both past and current health states, depends only on the current health state of the individual and not the past health states (Jackson, 2011; Kalbfleisch and Prentice, 2002). A semi-Markov model relaxes this assumption so that transition rates can also depend on the sojourn time, which is the time spent in the current state. In this sense, a semi-Markov model is a clock-reset model (Green et al., 2023; Meira-Machado et al., 2009). Time in a Markov model is defined as time since initiation of the model, so is termed clock-forward. Markov and semi-Markov models are both examples of multistate models…

The R for Health Technology Assessment has lots of details on to use R to not only creates both types of Markov models, but also decision trees, discrete event simulations, network meta-analyses and more. A great resource for the field.