Table 2 The numerical simulation values for theoretical analysis of system 1.
From: Dynamic analysis and optimal control of competitive information dissemination model
Equilibrium point | Verified theorem | Parameter values | Basic regeneration number |
|---|---|---|---|
\({E^0}\) | Theorem 1 | \(B = 1,{\alpha _1} = \beta = {\theta _1} = {\theta _2} = 0.1,{\alpha _2} = 0.01,\) | \(R_0^P = 0.33 < 1\) |
Theorem 2 | \({\lambda _1} = {\lambda _2} = {\gamma _1} = {\gamma _2} = {\varepsilon _1} = {\varepsilon _2} = \mu = 0.1\) | \(R_0^A = 0.33 < 1\) | |
\({E^{1,*}}\) | Theorem 3 | \(B = 1,{\alpha _1} = {\alpha _2} = \beta = {\theta _1} = {\theta _2} = 0.3,\) | \(R_0^P = 3 > 1\) |
Theorem 4 | \({\lambda _1} = {\lambda _2} = {\gamma _1} = {\gamma _2} = {\varepsilon _1} = {\varepsilon _2} = \mu = 0.1\) | \(R_0^A = 10 > 1\) | |
\({E^{2,*}}\) | Theorem 5 | \(B = 1,{\alpha _1} = 0.01,{\alpha _2} = \beta = {\theta _1} = {\theta _2} = 0.3,\) | \(R_0^P = 3 > 1\) |
Theorem 6 | \({\lambda _1} = {\lambda _2} = {\gamma _1} = {\gamma _2} = {\varepsilon _1} = {\varepsilon _2} = \mu = 0.1\) | \(R_0^A = 0.33 < 1\) | |
\({E^{3,*}}\) | Theorem 7 | \(B = 1,{\alpha _1} = \beta = {\theta _1} = {\theta _2} = 0.3,{\alpha _2} = 0.01,\) | \(R_0^P = 0.033 < 1\) |
Theorem 8 | \({\lambda _1} = {\lambda _2} = {\gamma _1} = {\gamma _2} = {\varepsilon _1} = {\varepsilon _2} = \mu = 0.1\) | \(R_0^A = 10 > 1\) |
