Lyapunov functions for disease models with immigration of infected hosts

Connell McCluskey

doi:10.3934/dcdsb.2020296

Article Contents

2021, Volume 26, Issue 8: 4479-4491. Doi: 10.3934/dcdsb.2020296

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Lyapunov functions for disease models with immigration of infected hosts

Connell McCluskey

Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

Received: May 31, 2020

Revised: June 30, 2020

Early access: October 2020

Published: August 2021

The author is supported by an NSERC Discovery Grant

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Abstract

Recent work has produced examples where models of the spread of infectious disease with immigration of infected hosts are shown to be globally asymptotically stable through the use of Lyapunov functions. In each case, the Lyapunov function was similar to a Lyapunov function that worked for the corresponding model without immigration of infected hosts.

We distill the calculations from the individual examples into a general result, finding algebraic conditions under which the Lyapunov function for a model without immigration of infected hosts extends to be a valid Lyapunov function for the corresponding system with immigration of infected hosts.

Finally, the method is applied to a multi-group $ SIR $ model.

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Mathematics Subject Classification: Primary: 34D23; Secondary: 92D30.

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References

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