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
收藏
页码：188 / 199
页数：12
相关论文
共 61 条
[21]   Optimal control and stability analysis of an epidemic model with population dispersal [J].
Jana, Soovoojeet ;
Haldar, Palash ;
Kar, T. K. .
CHAOS SOLITONS & FRACTALS, 2016, 83 :67-81
[22]   Optimal control of an HIV immunology model [J].
Joshi, HR .
OPTIMAL CONTROL APPLICATIONS & METHODS, 2002, 23 (04) :199-213
[23]   A theoretical study on mathematical modelling of an infectious disease with application of optimal control [J].
Kar, T. K. ;
Jana, Soovoojeet .
BIOSYSTEMS, 2013, 111 (01) :37-50
[24]   Contribution to the mathematical theory of epidemics [J].
Kermack, WO ;
McKendrick, AG .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER, 1927, 115 (772) :700-721
[25]   Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation [J].
Khajanchi, Subhas ;
Das, Dhiraj Kumar ;
Kar, Tapan Kumar .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 497 :52-71
[26]   Media coverage campaign in Hepatitis B transmission model [J].
Khan, Muhammad Altaf ;
Islam, Saeed ;
Zaman, Gul .
APPLIED MATHEMATICS AND COMPUTATION, 2018, 331 :378-393
[27]   Economic incentives and mathematical models of disease [J].
Klein, Eili ;
Laxminarayan, Ramanan ;
Smith, David L. ;
Gilligan, Christopher A. .
ENVIRONMENT AND DEVELOPMENT ECONOMICS, 2007, 12 :707-732
[28]   Dynamics and optimal control of a non-linear epidemic model with relapse and cure [J].
Lahrouz, A. ;
El Mahjour, H. ;
Settati, A. ;
Bernoussi, A. .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 496 :299-317
[29]  
Lenhart S., 2007, Optimal Control Applied to Biological Models
[30]   Hemorrhagic fever with renal syndrome in China: Mechanisms on two distinct annual peaks and control measures [J].
Li, Li ;
Wang, Cui-Hua ;
Wang, Shi-Fu ;
Li, Ming-Tao ;
Yakob, Laith ;
Cazelles, Bernard ;
Jin, Zhen ;
Zhang, Wen-Yi .
INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2018, 11 (02)
1234567