Stability and bifurcation analysis of an epidemic model with the effect of media

T.K. Kar, Swapan Kumar Nandi, Soovoojeet Jana and Manotosh Mandal

Chaos, Solitons & Fractals, 2019, vol. 120, issue C, 188-199

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.

Keywords: Infectious diseases; Treatment control; Basic reproduction number; Backward bifurcation; Optimal control; Cost-effectiveness (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:120:y:2019:i:c:p:188-199

DOI: 10.1016/j.chaos.2019.01.025

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