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Qualitative analysis of the SICR epidemic model with impulsive vaccinations. (English) Zbl 06159268
Summary: Control of epidemic infections is avery urgent issue today. To develop an appropriate strategy for vaccinations and effectively prevent the disease from arising and spreading, we proposed amodified Susceptible-Infected-Removed model with impulsive vaccinations. For the model without vaccinations, we proved global stability of one of the steady states depending on the basic reproduction number R 0 . As typically in the epidemic models, the threshold value of R 0 is 1. If R 0 is greater than 1, then the positive steady state called endemic equilibrium exists and is globally stable, whereas for smaller values of R 0 , it does not exist, and the semi-trivial steady state called disease-free equilibrium is globally stable. Using impulsive differential equation comparison theorem, we derived sufficient conditions under which the infectious disease described by the considered model disappears ultimately. The analytical results are illustrated by numerical simulations for Hepatitis B virus infection that confirm the theoretical possibility of the infection elimination because of the proper vaccinations policy. Copyright ©2012 John Wiley & Sons, Ltd.
MSC:
92D30Epidemiology
34B60Applications of theory of BVP for ODE
34D05Asymptotic stability of ODE
34D23Global stability of ODE
34K45Functional-differential equations with impulses