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

被引：68

作者：

Kar, T. K. ^{[1
]}

Nandi, Swapan Kumar ^{[1
,2
]}

Jana, Soovoojeet ^{[3
]}

Mandal, Manotosh ^{[1
,4
]}

机构：

[1] Indian Inst Engn Sci & Technol, Dept Math, Howrah 711103, W Bengal, India

[2] Nayabasat PM Sikshaniketan, Dept Math, Paschim Medinipur 721253, W Bengal, India

[3] Ramsaday Coll, cdept Math, Amta Howrah 711401, W Bengal, India

[4] Tamralipta Mahavidyalaya, Dept Math, Tamluk 721636, W Bengal, India

来源：

CHAOS SOLITONS & FRACTALS | 2019年 / 120卷 / 188-199期

关键词：

Infectious diseases; Treatment control; Basic reproduction number; Backward bifurcation; Optimal control; Cost-effectiveness; COST-EFFECTIVENESS ANALYSIS; TRANSMISSION DYNAMICS; MATHEMATICAL-ANALYSIS; AWARENESS PROGRAMS; CONTROL STRATEGIES; GLOBAL-STABILITY; SEIR MODEL; DISEASE; TUBERCULOSIS; IMPACT;

D O I：

10.1016/j.chaos.2019.01.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：188 / 199

页数：12

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