Dynamical Behaviors of Rumor Spreading Model with Control Measures

Table 2

Equilibria and stability of system (1).

Cases		Conditions	Positive equilibria
	𝜉2<2𝜉1	𝑥1<0,𝑥2<0,𝑥3<0	No positive equilibrium
𝑅0<1	𝜉2=2𝜉1	𝑥1=0,𝑥2<0,𝑥3<0	No positive equilibrium
	𝜉2>2𝜉1	𝑥1>0,𝑥3<0	Unique positive equilibrium 𝐸^∗
𝑅0>1	𝜉2<2𝜉1	𝑥1<0,𝑥3>0	Unique positive equilibrium 𝐸^∗
	𝜉2=2𝜉1	𝑥1=0,𝑥2<0,𝑥3>0	Unique positive equilibrium
	𝜉2>2𝜉1	𝑥2≥0,𝑥1>0,𝑥3>0	No positive equilibrium
		𝑥2<0,𝑥1>0,𝑥3>0,Δ<0	No positive equilibrium
		𝑥2<0,𝑥1>0,𝑥3>0,Δ=0	Unique positive equilibrium
		𝑥2<0,𝑥1>0,𝑥3>0,Δ>0	Two positive equilibria