On a Novel SVEIRS Markov chain epidemic model with multiple discrete delays and infection rates: modeling and sensitivity analysis to determine vaccination effects

A novel discrete time general Markov chain SVEIRS (Susceptible-Vaccinated-Exposed-Infected-Recovered-Susceptible) epidemic model is derived and studied. The model incorporates finite delay times for disease incubation, natural immunity, artificial immunity, and the period of infectiousness of infected individuals. The novel platform for representing different states of the disease in the population utilizes two discrete time measures for the current time of a person's state and also how long a person has been in the current state. Two submodels are derived based on whether the drive to get vaccinated is inspired by close contacts with infectious individuals or otherwise. Sensitivity analysis is conducted on the two submodels to determine how vaccination affects disease eradication.