Forward and Backward Bifurcation in a Fractional-Order SIR Epidemic Model with Vaccination

被引：0

作者：

Rostamy D. ^{[1
]}

Mottaghi E. ^{[2
]}

机构：

[1] Department of Mathematics, Imam Khomeini International University, P.O. Box 34149, Qazvin

[2] Department of Mathematics, Imam Khomeini International University, P.O. Box 34149, Qazvin

来源：

Iranian Journal of Science and Technology, Transactions A: Science | 2018年 / 42卷 / 2期

关键词：

Epidemic model equilibrium point; Forward and backward bifurcation; Fractional derivative; Numerical solutions; Stability;

D O I：

10.1007/s40995-018-0519-7

中图分类号：

学科分类号：

摘要：

In this paper, we introduce a new fractional-order epidemic model with vaccination, using fractional derivative in the sense of the Caputo derivative of order α∈ 0 , 1. We analyze the forward and backward bifurcation by determining the basic reproduction number R0α and also a certain threshold-value of R0α. Furthermore, we present some theorems about the stability of the endemic equilibrium points and show that the stability region of the model is also related to value of the fractional-order α. Finally, we present some numerical simulations for real data of pertussis disease to show the benefits of our results. © 2018, Shiraz University.

引用

页码：663 / 671

页数：8

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