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The dynamics of an interactional model of rabies transmitted between humans and dogs. (English) Zbl 1178.92050
Summary: Assuming that the population of dogs is constant and the population of humans satisfies the logistic model, an interactional model of rabies transmitted between humans and dogs is formulated. Two thresholds, $$R_0$$ and $$R_1$$, which determine the outcome of the disease are identified. Utilizing the method of Lyapunov functions and the properties of cooperative systems, we get the global asymptotic stability for both the disease-free equilibrium and the endemic equilibrium. A critical vaccination rate is obtained, which determines whether the dog rabies dies out or becomes endemic. Some suggestions are provided to the prevention and control of rabies according to the results of analysis and simulations.

##### MSC:
 92D30 Epidemiology 34D05 Asymptotic properties of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations