Stabilization and Optimal Control of the SEITR Epidemic Model with Vaccination

摘要

Almost all epidemiological models start from the same basic premise: the total population can be divided into a set of distinct classes dependent upon experience. Based on the model in [13], we establish an improved SEITR epidemic model with five components, incorporating the infective population recovered without treatment. We prove that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0when R0< 1. When the basic reproduction number R0< 1, the endemic equilibrium exists and the system is locally asymptotically stable under suitable conditions. In order to control the disease and minimize the cost, a percentage of the susceptible population is vaccinated and the fraction of infective population enter in the treatment are considered. We also show the existence of optimal controls. Finally, some numerical simulations are given to support our theoretical results.