Open AccessGlobal asymptotic stability of a compartmental model for a pandemic
Author(s) -
Surya Lamichhane,
Yuming Chen
Publication year - 2015
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2014.04.001
Subject(s) - basic reproduction number , mathematics , invariance principle , stability (learning theory) , stability theory , mathematical economics , pandemic , epidemic model , exponential stability , equilibrium point , mathematical optimization , covid-19 , disease , mathematical analysis , computer science , infectious disease (medical specialty) , demography , population , medicine , epistemology , philosophy , physics , nonlinear system , quantum mechanics , machine learning , sociology , differential equation , pathology
With influenza as a prototype, we propose a compartmental model for a pandemic by taking into account of recruitment. The model has a threshold dynamics. Precisely, when the basic reproduction number R0⩽1, the disease free equilibrium is globally asymptotically stable; when R0>1, the disease free equilibrium is unstable and there is a unique endemic equilibrium which globally attracts all solutions except the trivial one (the disease free equilibrium). These results are established by applying the LaSalle’s invariance principle