Backward bifurcation and control in transmission dynamics of arboviral diseases

被引:27
作者
Abboubakar, Hamadjam [1 ,2 ,3 ]
Kamgang, Jean Claude [2 ,4 ]
Tieudjo, Daniel [2 ,4 ]
机构
[1] Univ Ngaoundere, UIT, Lab Anal Simulat & Essai, POB 455, Ngaoundere, Cameroon
[2] Univ Ngaoundere, ENSAI, Lab Mathemat Expt, POB 455, Ngaoundere, Cameroon
[3] UIT, Dept Comp Sci, POB 455, Ngaoundere, Cameroon
[4] ENSAI, Dept Math & Comp Sci, POB 455, Ngaoundere, Cameroon
关键词
Arboviral diseases; Vaccination; Vector control strategies; Stability; Bifurcation; Sensitivity analysis; TETRAVALENT DENGUE VACCINE; SENSITIVITY-ANALYSIS; THRESHOLD CONDITIONS; MODEL; INFECTIONS; EFFICACY; MALARIA;
D O I
10.1016/j.mbs.2016.06.002
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this paper, we derive and analyze a compartmental model for the control of arboviral diseases which takes into account an imperfect vaccine combined with individual protection and some vector control strategies already studied in the literature. After the formulation of the model, a qualitative study based on stability analysis and bifurcation theory reveals that the phenomenon of backward bifurcation may occur. The stable disease-free equilibrium of the model coexists with a stable endemic equilibrium, when the reproduction number, R-0, is less than unity. Using Lyapunov function theory, we prove that the trivial equilibrium is globally asymptotically stable. When the disease-induced death is not considered, or/and, when the standard incidence is replaced by the mass action incidence, the backward bifurcation does not occur. Under a certain condition, we establish the global asymptotic stability of the disease-free equilibrium of the principal model. Through sensitivity analysis, we determine the relative importance of model parameters for disease transmission. Numerical simulations show that the combination of several control mechanisms would significantly reduce the spread of the disease, if we maintain the level of each control high, and this, over a long period. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码:100 / 129
页数:30
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