title: Complex Dynamics of an SIR Epidemic Model with Saturated Incidence Rate and Treatment.
abstract: This paper describes a traditional SIR type epidemic model with saturated infection rate and treatment function. The dynamics of the model is studied from the point of view of stability and bifurcation. Basic reproduction number is obtained and it is shown that the model system may possess a backward bifurcation. The global asymptotic stability of the endemic equilibrium is studied with the help of a geometric approach. Optimal control problem is formulated and solved. Some numerical simulation works are carried out to validate our analytical results.
authors.affiliation: Department of Mathematics, Abhedananda Mahavidyalaya, Sainthia, Birbhum, West Bengal, 731234, India. soovoojeet@gmail.com.
authors.forename: Soovoojeet
authors.initials: S
authors.lastname: Jana
authors.affiliation: Department of Mathematics, Nayabasat P. M. Sikshaniketan, Paschim Medinipur, West Bengal, 721253, India. nandi.swapan89@gmail.com.
authors.forename: Swapan Kumar
authors.initials: SK
authors.lastname: Nandi
authors.affiliation: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India. tkar1117@gmail.com.
authors.forename: T K
authors.initials: TK
authors.lastname: Kar
mesh_terms: D000465:Algorithms; D003141:Communicable Diseases / Q000453:epidemiology* / Q000628:therapy*; D003198:Computer Simulation; D006801:Humans; D015994:Incidence; D008962:Models, Theoretical
keywords: Backward bifurcation; Basic reproduction number; Epidemiology; Global stability; Optimal treatment control