Global dynamics of a nonautonomous SEIRS epidemic model with vaccination and nonlinear incidence

Abstract

In this paper, a class of nonautonomous SEIRS epidemic models with vaccination and nonlinear incidence is investigated. Under some quite weak assumptions, a couple of new threshold values in the form of integral, i.e., R1, R1∗, R2, and R2∗ on the extinction and permanence of disease for the model, are established. As special cases of our model, the autonomous, periodic, and almost periodic circumstances are discussed. The nearly necessary and sufficient criteria of threshold on the extinction and permanence of disease for above cases are obtained as well. Numerical examples and simulations are presented to illustrate the analytic results.

Analysis of a stochastic SVIR model with time‐delayed stages of vaccination and Lévy jumps

“…When it comes to scientific modeling, mathematical models have proven to be efficacious in the prediction of ways in which the disease can spread and the suggestion of possible control strategies. In this context, Kermack and McKendrick have laid foundation to compartmental modeling [1], which has been used and based upon widely in the aim of incorporating different disease characteristics (see earlier studies [2][3][4][5][6][7][8][9] and references therein).…”

Dynamical behavior of a stochastic SIQS model via isolation with regime-switching

“…Two important measures to reduce the infection rate are vaccination and isolation(or quarantine) [ 4 , 7 – 10 ]. Due to economic level, cultural concept and other reasons, the vaccination rate is sometimes not high in some regions, and isolation is one of the economic, practical and effective measures to control the spread of the disease.…”