Figure 1
![Figure 1](http://media.springernature.com/full/springer-static/image/art%3A10.1186%2Fs13662-020-02815-6/MediaObjects/13662_2020_2815_Fig1_HTML.png)
Time evolutions of deterministic system (2) with parameters \(u = 0.32\), \(\delta = 0.58\), \(\beta =0.3\), \(b=0.2\), \(q=0.26\), \(\varepsilon =0.32\), \({\alpha _{2}} = 0.12\), \({\alpha _{3}} = 0.23\), \(\gamma = 0.25\), \(m=0.01\), \(n=0.5\), \(A=0.48 \), where \({{ {R}}_{0}} = 0.9473 < 1 \)