Abstract
Understanding effectiveness of control policies can be helpful to prevent and control diseases. In this paper, we evaluate effects of control strategies containing two vaccinations, which are given to the newly born and the susceptible individuals. An SIVS epidemic model with two degree-dependent vaccination rates on scale-free networks is developed. We argue the effects of the vaccinations on the basic reproduction number R0. And spatial immunity and time-varying optimal vaccination schemes are performed. Particularly, we discuss effects of different weights in the objective function on disease control. We find that, two vaccinations can give rise to decreasing of R0; especially for R0>1, the effect of the booster vaccination is larger than that of the primary. Thus, strengthening the booster vaccination, or enlarging costs for the infected individuals and the booster vaccination, or reducing costs for the primary vaccination can be beneficial to stop and control diseases more effectively. These results can provide a new insight into controlling infectious disease on networks.
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