Markovian Epidemic Queueing Model with Exposed, Infection and Vaccination based on Treatment

In this investigation, an epidemic Markov queueing model with alert, infection, vaccination and death has been considered. The main focus of this work is on the vaccination to provide the infection in a population. Healthy person may be affected from some disease that may cause death. The vaccination is the power tool for the prevention of the diseases spreading over the population size. Healthy person become alert when symptoms of the disease can be seen on them and the alert may be injected due to more infection. The provision of vaccination is provided in both alert and infected stages. The transition rates as followed by exponential distribution. A Markov model is developed by using inflow and outflow transition rates of the model. The transient state probabilities are evaluated by solving the transient state equations by using runge kutta method which are further used for calculating the model performances. A numerical illustration is also provided to validate the model.