A Filippov model describing the effects of media coverage and quarantine on the spread of human influenza

被引:14
作者
Chen, Can [1 ]
Chong, Nyuk Sian [2 ]
Smith, Robert [3 ,4 ]
机构
[1] Zhengzhou Univ Aeronaut, Dept Math & Phys, Coll Sci, Zhengzhou 450015, Henan, Peoples R China
[2] Univ Malaysia Terengganu, Sch Informat & Appl Math, Kuala Terengganu 21030, Malaysia
[3] Univ Ottawa, Dept Math, 585 King Edward Ave, Ottawa, ON K1N 6N5, Canada
[4] Univ Ottawa, Fac Med, 585 King Edward Ave, Ottawa, ON K1N 6N5, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Influenza; Filippov model; Media coverage; Quarantine; Threshold policy; Sliding mode; 2-STRAIN INFLUENZA; INFECTED BIRDS; DYNAMICS; VIRUSES;
D O I
10.1016/j.mbs.2017.12.002
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
Mass-media reports on an epidemic or pandemic have the potential to modify human behaviour and affect social attitudes. Here we construct a Filippov model to evaluate the effects" of media coverage and quarantine on the transmission dynamics of influenza. We first choose a piecewise smooth incidence rate to represent media reports being triggered once the number of infected individuals exceeds a certain critical level I-C1. Further, if the number of infected cases increases and exceeds another larger threshold value I-C2 (> I-C1), we consider that the incidence rate tends to a saturation level due to the protection measures taken by individuals; meanwhile, we begin to quarantine susceptible individuals when the number of susceptible individuals is larger than a threshold value S-c. Then, for each susceptible threshold value S-c, the global properties of the Filippov model with regard to the existence and stability of all possible equilibria and sliding-mode dynamics are examined, as we vary the infected threshold values I-C1 and I-C2. We show generically that the Filippov system stabilizes at either the endemic equilibrium of the subsystem or the pseudoequilibrium on the switching surface or the endemic equilibrium E-C = (S-C, I-C2), depending on the choice of the threshold values. The findings suggest that proper combinations of infected and susceptible threshold values can maintain the number of infected individuals either below a certain threshold level or at a previously given level.
引用
收藏
页码:98 / 112
页数:15
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