Stability and bifurcation analysis of an epidemic model with the effect of media. (March 2019)

• Record Type: Journal Article
• Authors: Kar, T.K.; Nandi, Swapan Kumar; Jana, Soovoojeet; Mandal, Manotosh
• Is Part Of: Chaos, solitons and fractals. Volume 120(2019)
• Page Start: 188
• Page End: 199
• Publication Date: 2019-03
• Subjects: Infectious diseases -- Treatment control -- Basic reproduction number -- Backward bifurcation -- Optimal control -- Cost-effectiveness; 92D30 -- 34A07; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.01.025
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: An SEIR type epidemic model with both saturated incidence rate and treatment function is proposed and analyzed. We consider here two control parameters namely treatment and media effect. The system may undergoes a backward bifurcation at basic reproduction number R 0 = 1 . A geometric approach is used to examine the global stability criteria of the endemic equilibrium point. We use optimal control theory and cost effectiveness analysis to sort out best strategy to control the disease. Abstract: In the present study, we develop and analyze an SEIR epidemic model to assess the consequences of media awareness program and treatment control. The disease transmission rate as well as the treatment function are taken in the saturated form. Different equilibrium points and their stability are discussed. The threshold parameter, basic reproduction number is obtained and it is seen that the system may posses a backward bifurcation. An optimal control problem is formulated with treatment and media awareness parameters as control parameters and solved it analytically. The cost-effectiveness analysis is performed to find out the best strategy to be applied to control the transmission of diseases. In addition to our analytical results, several numerical simulations are also illustrated. Finally, a brief discussion is given regarding the role of treatment and media awareness program.