A singular perturbation approach to epidemics of vector-transmitted diseases

被引：14
作者：
Brauer, Fred [1 ]
机构：
[1] Univ British Columbia, Vancouver, BC, Canada
来源：
INFECTIOUS DISEASE MODELLING | 2019年 / 4卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
D O I：
10.1016/j.idm.2019.04.004
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In vector-borne epidemic models there is often a substantial difference between the vector and host time scales. This makes it possible to use the quasi-steady-state to obtain final size relations. (C) 2019 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd.
引用
收藏
页码：115 / 123
页数：9
相关论文
共 14 条
[1]  
Brauer F, 2016, Dynamical systems for biological modeling: an introduction
[2]  
Brauer Fred, 2017, Infect Dis Model, V2, P12, DOI 10.1016/j.idm.2016.12.001
[3]   Estimation of the reproduction number of dengue fever from spatial epidemic data [J].
Chowell, G. ;
Diaz-Duenas, P. ;
Miller, J. C. ;
Alcazar-Velazco, A. ;
Hyman, J. M. ;
Fenimore, P. W. ;
Castillo-Chavez, C. .
MATHEMATICAL BIOSCIENCES, 2007, 208 (02) :571-589
[4]   The many guises of R0 (a didactic note) [J].
Cushing, J. M. ;
Diekmann, Odo .
JOURNAL OF THEORETICAL BIOLOGY, 2016, 404 :295-302
[5]   SINGULAR PERTURBATIONS ON INFINITE INTERVAL [J].
HOPPENSTEADT, FC .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 123 (02) :521-+
[6]  
Kucharski A. J, 2016, PLOS NEGLECT TROP D
[7]   PERTURBATIONS OF DISCONTINUOUS SOLUTIONS OF NON-LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS [J].
LEVINSON, N .
ACTA MATHEMATICA, 1950, 82 (01) :71-106
[8]   Modelling the dynamics of dengue real epidemics [J].
Pinho, S. T. R. ;
Ferreira, C. P. ;
Esteva, L. ;
Barreto, F. R. ;
Morato e Silva, V. C. ;
Teixeira, M. G. L. .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2010, 368 (1933) :5679-5693
[9]   Time-scale separation and centre manifold analysis describing vector-borne disease dynamics [J].
Rocha, Filipe ;
Aguiar, Maira ;
Souza, Max ;
Stollenwerk, Nico .
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2013, 90 (10) :2105-2125
[10]   THE QUASI-STEADY-STATE ASSUMPTION - A CASE-STUDY IN PERTURBATION [J].
SEGEL, LA ;
SLEMROD, M .
SIAM REVIEW, 1989, 31 (03) :446-477
12