Susceptible-Exposed-Infectious Model Using Markov Chains

In the present work we introduced and analyzed the most basic transmission SEI (susceptible-exposed-infective) model for a directly transmitted infectious disease caused by Coronavirus disease 2019 (COVID-19). The SEI model is modeling as a Markov chain and we computed a closed form formula of the mean first passage times (MFPT’s) vector arising from non-homogeneous Markov chain random walk (NHMC-RW) on the non-negative integers. Some particular cases, which lead to a relationship between the elements of the MFPT’s vectors. An efficient algorithm applied on mathematica program for computing MFPT’s vector of the NHMC-RW is given.