On global stability analysis for SEIRS models in epidemiology with nonlinear incidence rate function

Abstract

We study an SEIRS epidemic model with an isolation and nonlinear incidence rate function. We have obtained a threshold value [Formula: see text] and shown that there is only a disease-free equilibrium point, when [Formula: see text] and an endemic equilibrium point if [Formula: see text]. We have shown that both disease-free and endemic equilibrium point are globally stable.

The global dynamics for a stochastic SIS epidemic model with isolation

“…The various types of classical epidemic models with quarantine/isolation have been investigated in many articles. See, for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references cited therein.…”

Modeling Control, Lockdown & Exit Strategies for COVID-19 Pandemic

“…To establish this, they have used Poincaré Bendixson criterion in three dimensions. Following this, the global stability properties of SEIRS type has been improved by Fan, Li, Driessche, Wan 7,18 . Thereafter, Korobeinikov and Maini 35,36 studied the global stability of SEIR and SEIS type models using Lyapunov functions.…”

“…By Routh-Hurwitz Criterion ( see, 34 :1.6-6), the roots of the equation ( 6) have negative real parts if and only if 1 > 0, 3 > 0, and 1 2 > 3 . From relation (7) it is obvious that 1 > 0. Relation (9) may be rewritten as…”

“…The last condition 1 2 > 3 may be easily verified in some simple steps. Multiplying (7) and (8), we obtain…”