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The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage. (English) Zbl 1221.34034
Summary: A SIS epidemic model incorporating media coverage is presented in this paper. The dynamics of this disease model under constant and pulse vaccination are analyzed. First, stability analysis of the model with constant vaccination shows that the disease free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the endemic equilibrium is globally asymptotically stable if it exists. Second, we consider the impulsive vaccination. Using the discrete dynamical system determined by the stroboscopic map, the exact periodic infection-free solution is globally asymptotically stable under some conditions. We also show that the system is permanent. Furthermore, by bifurcation theory we obtain the existence of a positive periodic solution. In order to apply vaccination pulses frequently enough so as to eradicate the disease, the threshold for the period of pulsing, i.e., $$\tau_{max}$$ is shown. Our theoretical results are confirmed by numerical simulations. The effectiveness of constant and pulse vaccination policies are compared.

##### MSC:
 34A37 Ordinary differential equations with impulses 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 92D30 Epidemiology
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##### References:
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