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 $R_0$ 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.

KEYWORDS:

• Epidemic model
• vaccination and treatment controls
• basic reproduction number
• isolation
• global stability

2000 AMS SUBJECT CLASSIFICATIONS:

• 37N25
• 92D30
• 34K20

Acknowledgement

We would like to thank the anonymous reviewers and Editor-in-chief of the journal Prof. Choi-Hong Lai for their constructive comments and useful suggestions to improve both the quality and presentation of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research of T. K. Kar is financially supported by the Council of Scientific and Industrial Research (CSIR), Government of India, [File No. 25(0224)/14/EMR-II, Dated: 2/12/2014].