Stability and backward bifurcation in a malaria transmission model with applications to the control of malaria in China

Xiaomei Feng, Shigui Ruan, Zhidong Teng, Kai Wang

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

In this paper, we consider a deterministic malaria transmission model with standard incidence rate and treatment. Human population is divided into susceptible, infectious and recovered subclasses, and mosquito population is split into susceptible and infectious classes. It is assumed that, among individuals with malaria who are treated or recovered spontaneously, a proportion moves to the recovered class with temporary immunity and the other proportion returns to the susceptible class. Firstly, it is shown that two endemic equilibria may exist when the basic reproduction number R01. The presence of a backward bifurcation implies that it is possible for malaria to persist even if R01. To deal with this problem, the estimate of the Lozinski. ĭ measure of a 6 × 6 matrix is discussed. Finally, numerical simulations are provided to support our theoretical results. The model is also used to simulate the human malaria data reported by the Chinese Ministry of Health from 2002 to 2013. It is estimated that the basic reproduction number R0≈0.0161 for the malaria transmission in China and it is found that the plan of eliminating malaria in China is practical under the current control strategies.

Original languageEnglish (US)
Pages (from-to)52-64
Number of pages13
JournalMathematical Biosciences
Volume266
DOIs
StatePublished - 2015

Fingerprint

Backward Bifurcation
Malaria
malaria
China
Electric current control
Basic Reproduction Number
Basic Reproduction number
Health
Computer simulation
Proportion
Model
Endemic Equilibrium
Immunity
Culicidae
human population
Population
Control Strategy
Incidence
immunity
Imply

Keywords

  • Backward bifurcation
  • Geometric approach
  • Global stability
  • Lozinskiĭ measure
  • Malaria

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Medicine(all)

Cite this

Stability and backward bifurcation in a malaria transmission model with applications to the control of malaria in China. / Feng, Xiaomei; Ruan, Shigui; Teng, Zhidong; Wang, Kai.

In: Mathematical Biosciences, Vol. 266, 2015, p. 52-64.

Research output: Contribution to journalArticle

@article{5e3733fb61ac43fbbb7bf35b71492b64,
title = "Stability and backward bifurcation in a malaria transmission model with applications to the control of malaria in China",
abstract = "In this paper, we consider a deterministic malaria transmission model with standard incidence rate and treatment. Human population is divided into susceptible, infectious and recovered subclasses, and mosquito population is split into susceptible and infectious classes. It is assumed that, among individuals with malaria who are treated or recovered spontaneously, a proportion moves to the recovered class with temporary immunity and the other proportion returns to the susceptible class. Firstly, it is shown that two endemic equilibria may exist when the basic reproduction number R01. The presence of a backward bifurcation implies that it is possible for malaria to persist even if R01. To deal with this problem, the estimate of the Lozinski. ĭ measure of a 6 × 6 matrix is discussed. Finally, numerical simulations are provided to support our theoretical results. The model is also used to simulate the human malaria data reported by the Chinese Ministry of Health from 2002 to 2013. It is estimated that the basic reproduction number R0≈0.0161 for the malaria transmission in China and it is found that the plan of eliminating malaria in China is practical under the current control strategies.",
keywords = "Backward bifurcation, Geometric approach, Global stability, Lozinskiĭ measure, Malaria",
author = "Xiaomei Feng and Shigui Ruan and Zhidong Teng and Kai Wang",
year = "2015",
doi = "10.1016/j.mbs.2015.05.005",
language = "English (US)",
volume = "266",
pages = "52--64",
journal = "Mathematical Biosciences",
issn = "0025-5564",
publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Stability and backward bifurcation in a malaria transmission model with applications to the control of malaria in China

AU - Feng, Xiaomei

AU - Ruan, Shigui

AU - Teng, Zhidong

AU - Wang, Kai

PY - 2015

Y1 - 2015

N2 - In this paper, we consider a deterministic malaria transmission model with standard incidence rate and treatment. Human population is divided into susceptible, infectious and recovered subclasses, and mosquito population is split into susceptible and infectious classes. It is assumed that, among individuals with malaria who are treated or recovered spontaneously, a proportion moves to the recovered class with temporary immunity and the other proportion returns to the susceptible class. Firstly, it is shown that two endemic equilibria may exist when the basic reproduction number R01. The presence of a backward bifurcation implies that it is possible for malaria to persist even if R01. To deal with this problem, the estimate of the Lozinski. ĭ measure of a 6 × 6 matrix is discussed. Finally, numerical simulations are provided to support our theoretical results. The model is also used to simulate the human malaria data reported by the Chinese Ministry of Health from 2002 to 2013. It is estimated that the basic reproduction number R0≈0.0161 for the malaria transmission in China and it is found that the plan of eliminating malaria in China is practical under the current control strategies.

AB - In this paper, we consider a deterministic malaria transmission model with standard incidence rate and treatment. Human population is divided into susceptible, infectious and recovered subclasses, and mosquito population is split into susceptible and infectious classes. It is assumed that, among individuals with malaria who are treated or recovered spontaneously, a proportion moves to the recovered class with temporary immunity and the other proportion returns to the susceptible class. Firstly, it is shown that two endemic equilibria may exist when the basic reproduction number R01. The presence of a backward bifurcation implies that it is possible for malaria to persist even if R01. To deal with this problem, the estimate of the Lozinski. ĭ measure of a 6 × 6 matrix is discussed. Finally, numerical simulations are provided to support our theoretical results. The model is also used to simulate the human malaria data reported by the Chinese Ministry of Health from 2002 to 2013. It is estimated that the basic reproduction number R0≈0.0161 for the malaria transmission in China and it is found that the plan of eliminating malaria in China is practical under the current control strategies.

KW - Backward bifurcation

KW - Geometric approach

KW - Global stability

KW - Lozinskiĭ measure

KW - Malaria

UR - http://www.scopus.com/inward/record.url?scp=84951920702&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951920702&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2015.05.005

DO - 10.1016/j.mbs.2015.05.005

M3 - Article

C2 - 26013290

AN - SCOPUS:84951920702

VL - 266

SP - 52

EP - 64

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

ER -