Global stability of a heroin epidemic model with psychological effect. (Chinese. English summary) Zbl 1424.34165
Summary: A heroin epidemic model is constructed and analyzed. Considering the psychological effect, the basic reproduction number \({R_0}\) of the model is given. When \({R_0} \le 1\), the drugfree equilibrium is globally asymptotical stable. When \({R_0} > 1\), the drug use-free equilibrium is unstable, and there exists unique drug spread equilibrium. By using the Routh-Hurwitz criterion, a Lyapunov function and the LaSalle invariance principle, the global asymptotical stability of the drug-free equilibrium and the drug spread equilibrium is obtained.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34D23 | Global stability of solutions to ordinary differential equations |
| 92D30 | Epidemiology |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
