• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권2호
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• pp.203-220
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• 2023

A new modification of the SIS epidemic model incorporating the adaptive host behavior is proposed. Unlike the common situation in most epidemic models, this system has two disease-free equilibrium points, and we were able to prove that as the basic reproduction number approaches the threshold of 1, these two points merge and a Bogdanov-Takens bifurcation of codimension three occurs. The occurrence of this bifurcation is a sign of the complexity of the dynamics of the system near the value 1 of basic reproduction number. Both local and global stability of disease-free and endemic equilibrium point are studied.

• ETRI Journal
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• 제28권5호
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• pp.692-695
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• 2006

Recently, there has been a constant barrage of worms over the Internet. Besides threatening network security, these worms create an enormous economic burden in terms of loss of productivity not only for the victim hosts, but also for other hosts, as these worms create unnecessary network traffic. Further, measures taken to filter these worms at the router level incur additional network delays because of the extra burden placed on the routers. To develop appropriate tools for thwarting the quick spread of worms, researchers are trying to understand the behavior of worm propagation with the aid of epidemiological models. In this study, we present an optimization model that takes into account infection and treatment costs. Using this model we can determine the level of treatment to be applied for a given rate of infection spread.