A mathematical model for assessing control strategies against West Nile virus

C. Bowman, Abba Gumel, P. Van Den Driessche, J. Wu, H. Zhu

Research output: Contribution to journalArticle

169 Citations (Scopus)

Abstract

Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and therapeutic treatment against WNV, public health officials have focussed on the use of preventive measures in an attempt to halt the spread of WNV in humans. The aim of this paper is to use mathematical modelling and analysis to assess two main anti-WNV preventive strategies, namely: mosquito reduction strategies and personal protection. We propose a single-season ordinary differential equation model for the transmission dynamics of WNV in a mosquito-bird-human community, with birds as reservoir hosts and culicine mosquitoes as vectors. The model exhibits two equilibria; namely the disease-free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity (R0), which depends solely on parameters associated with the mosquito-bird cycle, is less than unity. The public health implication of this is that WNV can be eradicated from the mosquito-bird cycle (and, consequently, from the human population) if the adopted mosquito reduction strategy (or strategies) can make R0 < 1. On the other hand, it is shown, using a novel and robust technique that is based on the theory of monotone dynamical systems coupled with a regular perturbation argument and a Liapunov function, that if R0 > 1, then the unique endemic equilibrium is globally stable for small WNV-induced avian mortality. Thus, in this case, WNV persists in the mosquito-bird population.

Original languageEnglish (US)
Pages (from-to)1107-1133
Number of pages27
JournalBulletin of Mathematical Biology
Volume67
Issue number5
DOIs
StatePublished - Sep 2005
Externally publishedYes

Fingerprint

West Nile virus
Viruses
Virus
mosquito
Control Strategy
Theoretical Models
mathematical models
Culicidae
Mathematical Model
Mathematical models
Birds
bird
birds
Endemic Equilibrium
Public Health
Public health
public health
Cycle
disease reservoirs
Diagnostic Tests

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

A mathematical model for assessing control strategies against West Nile virus. / Bowman, C.; Gumel, Abba; Van Den Driessche, P.; Wu, J.; Zhu, H.

In: Bulletin of Mathematical Biology, Vol. 67, No. 5, 09.2005, p. 1107-1133.

Research output: Contribution to journalArticle

Bowman, C. ; Gumel, Abba ; Van Den Driessche, P. ; Wu, J. ; Zhu, H. / A mathematical model for assessing control strategies against West Nile virus. In: Bulletin of Mathematical Biology. 2005 ; Vol. 67, No. 5. pp. 1107-1133.
@article{415f8bf7bd214990b731b9d49b0e3995,
title = "A mathematical model for assessing control strategies against West Nile virus",
abstract = "Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and therapeutic treatment against WNV, public health officials have focussed on the use of preventive measures in an attempt to halt the spread of WNV in humans. The aim of this paper is to use mathematical modelling and analysis to assess two main anti-WNV preventive strategies, namely: mosquito reduction strategies and personal protection. We propose a single-season ordinary differential equation model for the transmission dynamics of WNV in a mosquito-bird-human community, with birds as reservoir hosts and culicine mosquitoes as vectors. The model exhibits two equilibria; namely the disease-free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity (R0), which depends solely on parameters associated with the mosquito-bird cycle, is less than unity. The public health implication of this is that WNV can be eradicated from the mosquito-bird cycle (and, consequently, from the human population) if the adopted mosquito reduction strategy (or strategies) can make R0 < 1. On the other hand, it is shown, using a novel and robust technique that is based on the theory of monotone dynamical systems coupled with a regular perturbation argument and a Liapunov function, that if R0 > 1, then the unique endemic equilibrium is globally stable for small WNV-induced avian mortality. Thus, in this case, WNV persists in the mosquito-bird population.",
author = "C. Bowman and Abba Gumel and {Van Den Driessche}, P. and J. Wu and H. Zhu",
year = "2005",
month = "9",
doi = "10.1016/j.bulm.2005.01.002",
language = "English (US)",
volume = "67",
pages = "1107--1133",
journal = "Bulletin of Mathematical Biology",
issn = "0092-8240",
publisher = "Springer New York",
number = "5",

}

TY - JOUR

T1 - A mathematical model for assessing control strategies against West Nile virus

AU - Bowman, C.

AU - Gumel, Abba

AU - Van Den Driessche, P.

AU - Wu, J.

AU - Zhu, H.

PY - 2005/9

Y1 - 2005/9

N2 - Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and therapeutic treatment against WNV, public health officials have focussed on the use of preventive measures in an attempt to halt the spread of WNV in humans. The aim of this paper is to use mathematical modelling and analysis to assess two main anti-WNV preventive strategies, namely: mosquito reduction strategies and personal protection. We propose a single-season ordinary differential equation model for the transmission dynamics of WNV in a mosquito-bird-human community, with birds as reservoir hosts and culicine mosquitoes as vectors. The model exhibits two equilibria; namely the disease-free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity (R0), which depends solely on parameters associated with the mosquito-bird cycle, is less than unity. The public health implication of this is that WNV can be eradicated from the mosquito-bird cycle (and, consequently, from the human population) if the adopted mosquito reduction strategy (or strategies) can make R0 < 1. On the other hand, it is shown, using a novel and robust technique that is based on the theory of monotone dynamical systems coupled with a regular perturbation argument and a Liapunov function, that if R0 > 1, then the unique endemic equilibrium is globally stable for small WNV-induced avian mortality. Thus, in this case, WNV persists in the mosquito-bird population.

AB - Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and therapeutic treatment against WNV, public health officials have focussed on the use of preventive measures in an attempt to halt the spread of WNV in humans. The aim of this paper is to use mathematical modelling and analysis to assess two main anti-WNV preventive strategies, namely: mosquito reduction strategies and personal protection. We propose a single-season ordinary differential equation model for the transmission dynamics of WNV in a mosquito-bird-human community, with birds as reservoir hosts and culicine mosquitoes as vectors. The model exhibits two equilibria; namely the disease-free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity (R0), which depends solely on parameters associated with the mosquito-bird cycle, is less than unity. The public health implication of this is that WNV can be eradicated from the mosquito-bird cycle (and, consequently, from the human population) if the adopted mosquito reduction strategy (or strategies) can make R0 < 1. On the other hand, it is shown, using a novel and robust technique that is based on the theory of monotone dynamical systems coupled with a regular perturbation argument and a Liapunov function, that if R0 > 1, then the unique endemic equilibrium is globally stable for small WNV-induced avian mortality. Thus, in this case, WNV persists in the mosquito-bird population.

UR - http://www.scopus.com/inward/record.url?scp=21444451814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21444451814&partnerID=8YFLogxK

U2 - 10.1016/j.bulm.2005.01.002

DO - 10.1016/j.bulm.2005.01.002

M3 - Article

C2 - 15998497

AN - SCOPUS:21444451814

VL - 67

SP - 1107

EP - 1133

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 5

ER -