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Analysis of Population and Epidemic Based on Malthus and Logistic Model

Published: 22 December 2021 Publication History

Abstract

In order to predict the population without bound or inevitable extinction, we need to use the Malthus model and the Logistic model. Considering about the growth rate and environment carrying capacity, in terms of Poincare-Bendixson theorem, it shows the the long-time behavior of solutions to ODEs. However, SIR model discovers the change of population during the time. In this essay, we use a new perspective and proof method to verify the feasibility of Malthus and Logistic model.

References

[1]
Logistic population growth. url=shorturl.at/ekru5, 2020.
[2]
Nicholas F. Britton. Essential Mathematical Biology. Springer London, 2003.
[3]
Norman Levinson Earl A. Coddington. Theory of Ordinary Differential Equations. McGraw-Hill, 1955.
[4]
Jonathan Luk. Notes on the Poincare-Bendixson Theorem. http://web.stanford.edu/ jluk/math63CMspring17/Periodic.170529.pdf, 2017.
[5]
Steven H. Strogatz. Nonlinear Dynamics and Chaos. CRC Press, 2018.

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  1. Analysis of Population and Epidemic Based on Malthus and Logistic Model

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    ISAIMS '21: Proceedings of the 2nd International Symposium on Artificial Intelligence for Medicine Sciences
    October 2021
    593 pages
    ISBN:9781450395588
    DOI:10.1145/3500931
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 22 December 2021

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    Author Tags

    1. SIR model
    2. epidemic models

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