Mathematical analysis of an epidemic model with isolation and optimal controls

ABSTRACT In this article, we consider a susceptible–infectious–recovered (SIR) type epidemic model with some isolation to the susceptible, treatment for infectives, and vaccination to the newly recruited individuals. The basic reproduction number is obtained, and both the existence and stability of the disease-free and endemic equilibrium are discussed. We study the influence of isolation on infected individuals. We also study the existence of optimal control for both vaccination and treatment to minimize both the infected population and the costs required to control the disease. All the theoretical results are verified through numerical simulations and some of the key findings are given at the end of the article.

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