JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
On global behavior of a some SIR epidemic model based on the Poincaré compactification
Yu Ichida
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2022 Volume 14 Pages 65-68

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Abstract

It is important to study the global behavior of solutions to systems of ordinary differential equations describing the transmission dynamics of infectious disease. In this paper, we present a different approach from the Lyapunov function used in most of the study. This approach is based on the Poincaré compactification. We then apply the method to an SIR endemic model as a test case, and discuss its effectiveness and the potential applications of this approach. In addition, we refine the discussion of dynamics near the equilibrium, derive the asymptotic behavior, and mention its relation to the basic reproduction number.

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© 2022, The Japan Society for Industrial and Applied Mathematics
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