Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE)

Mathematical Biosciences
Jean Claude Kamgang, Gauthier Sallet

Abstract

One goal of this paper is to give an algorithm for computing a threshold condition for epidemiological systems arising from compartmental deterministic modeling. We calculate a threshold condition T(0) of the parameters of the system such that if T(0)<1 the disease-free equilibrium (DFE) is locally asymptotically stable (LAS), and if T(0)>1, the DFE is unstable. The second objective, by adding some reasonable assumptions, is to give, depending on the model, necessary and sufficient conditions for global asymptotic stability (GAS) of the DFE. In many cases, we can prove that a necessary and sufficient condition for the global asymptotic stability of the DFE is R(0)< or =1, where R(0) is the basic reproduction number [O. Diekmann, J.A. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, 2000]. To illustrate our results, we apply our techniques to examples taken from the literature. In these examples we improve the results already obtained for the GAS of the DFE. We show that our algorithm is relevant for high dimensional epidemiological models.

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Citations

Nov 1, 2011·Journal of Mathematical Biology·Y Dumont, J M Tchuenche
Jan 15, 2013·Mathematical Biosciences and Engineering : MBE·Sukhitha W Vidurupola, Linda J S Allen
Oct 24, 2012·Computational and Mathematical Methods in Medicine·Mohammad A Safi, Salisu M Garba
May 31, 2011·Mathematical Biosciences·Daozhou Gao, Shigui Ruan
Jun 18, 2010·Journal of Theoretical Biology·Jianhua PangXueyong Zhou
Aug 24, 2011·Computational and Mathematical Methods in Medicine·Jing LiRobert J Smith
Apr 16, 2015·PloS One·Dany Pascal Moualeu-NganguePeter Deuflhard
Jun 21, 2016·Mathematical Biosciences·Hamadjam AbboubakarDaniel Tieudjo
Mar 31, 2017·Bulletin of Mathematical Biology·Indrajit GhoshJoydev Chattopadhyay
Mar 18, 2017·BMC Public Health·Peter M MwamtobeJean M Tchuenche
Jun 27, 2017·Journal of Biological Dynamics·Muhammad ZamirAli Saleh Alshomrani
Jul 10, 2019·Bulletin of Mathematical Biology·Jean Claude Kamgang, Christopher Penniman Thron
Apr 9, 2020·Journal of Biological Dynamics·Asha Hassan, Nyimvua Shaban
Sep 30, 2020·Journal of Biological Dynamics·Abdul-Rahman J Mumbu, Alfred K Hugo
Jan 18, 2017·BioMed Research International·Muhammad Altaf KhanZahoor Ul Haq
Aug 9, 2018·Bulletin of Mathematical Biology·Longxing QiTianping Wang
Nov 17, 2020·Journal of Theoretical Biology·Hyacinthe M Ndongmo TeytsaJean Lubuma
Feb 16, 2021·Nonlinear Dynamics·Indrajit GhoshJoydev Chattopadhyay
Jul 1, 2021·Acta Biotheoretica·Solomon KadalekaJean M Tchuenche
Jul 1, 2017·Applied Mathematical Modelling·Chang-Yuan Cheng

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