Nilpotent singularities and dynamics in an SIR type of compartmental model with hospital resources

被引：69

作者：

Shan, Chunhua ^{[1
]}

Yi, Yingfei ^{[1
,4
]}

Zhu, Huaiping ^{[2
,3
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2M7, Canada

[2] York Univ, LAMPS, N York, ON M3J 1P3, Canada

[3] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada

[4] Jilin Univ, Sch Math, Jilin, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

SIR model; Hospital resources; Nonlinear recovery rate; Large-amplitude oscillations; Degenerate Bogdanov-Takens bifurcations; Nilpotent singularities; BIFURCATIONS; BEHAVIOR;

D O I：

10.1016/j.jde.2015.11.009

中图分类号：

O1 [数学];

学科分类号：

070101 [基础数学];

摘要：

An SIR type of compartmental model with a standard incidence rate and a nonlinear recovery rate was formulated to study the impact of available resources of public health system especially the number of hospital beds. Cusp, focus and elliptic type of nilpotent singularities of codimension 3 are discovered and analyzed in this three dimensional model. Complex dynamics of disease transmission including multi-steady states and multi-periodicity are revealed by bifurcation analysis. Large-amplitude oscillations found in our model provide a more reasonable explanation for disease recurrence. With clinical data, our studies have practical implications for the prevention and control of infectious diseases. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：4339 / 4365

页数：27

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