Multistate models (MSM) are well developed for continuous and discrete times under a first order Markov assumption. Motivated by a cohort of COVID-19 patients, an MSM was designed based on 14 transitions among 7 states of a patient. Since a preliminary analysis showed that the first order Markov condition was not met for some transitions, we have developed a second order Markov model where the future evolution not only depends on the current but also on the preceding state. Under a discrete time analysis, assuming homogeneity and that past information is restricted to 2 consecutive times, we expanded the transition probability matrix and proposed an extension of the Chapman- Kolmogorov equations.

翻译：多状态模型（MSM）在一阶马尔可夫假设下，已在连续时间和离散时间框架中得到充分发展。受一组COVID-19患者队列的启发，我们基于患者7个状态间的14种转移设计了一个多状态模型。由于初步分析显示部分转移不满足一阶马尔可夫条件，我们开发了二阶马尔可夫模型——该模型中未来状态演化不仅取决于当前状态，还取决于前一个状态。在离散时间分析框架下，假设齐次性且历史信息仅局限于两个连续时间点，我们扩展了转移概率矩阵，并提出了查普曼-科尔莫戈罗夫方程的推广形式。