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Analysis of a simple vector-host epidemic model with direct transmission. (English) Zbl 1190.92029
Summary: Vector-host epidemic models with direct transmission are proposed and analyzed. It is shown that the stability of the equilibria in the proposed models can be controlled by the basic reproduction number of the disease transmission. One model considers that the dynamics of human hosts and vectors are described by SIS and SI models, respectively, where the global asymptotical stability for the equilibria of the models is analyzed by constructing Lyapunov functions, respectively. The other model considers that the dynamics of the human hosts and vectors are described by SIRS and SI models, respectively, where the global stability of the disease-free equilibrium and the persistence of the disease in the model are also analyzed, respectively.
MSC:
92D30Epidemiology
34D20Stability of ODE
37N25Dynamical systems in biology