On Global Stability of Disease-Free Equilibrium in Epidemiological Models



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Submitted Feb 19, 2021
Published Jul 14, 2021
10.24018/ejmath.2021.2.3.21

Abstract viewed = 551 times

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This paper considers the problem of constructing appropriate Lyapunov function for establishing the global stability of a disease-free equilibrium in epidemiological models. A generalised algorithm is proposed and it is tested for some selected epidemiological models. Experience from the application of the algorithm on test examples shows that the algorithm is easy to use, less cumbersome, and yielded the desired result, particularly in models with homogeneous population. Thus, the proposed algorithm provides a direct approach for establishing global stability of disease-free equilibrium.

Keywords: Disease-free equilibrium, Basic reproduction number, Lyapunov function, Lasalle’s invariance principle, Global asymptotic stability

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