Two-patch model for the spread of West Nile virus

Bulletin of Mathematical Biology
Juping ZhangHuaiping Zhu

Abstract

A two-patch model for the spread of West Nile virus between two discrete geographic regions is established to incorporate a mobility process which describes how contact transmission occurs between individuals from and between two regions. In the mobility process, we assume that the host birds can migrate between regions, but not the mosquitoes. The basic reproduction number [Formula: see text] is computed by the next generation matrix method. We prove that if [Formula: see text], then the disease-free equilibrium is globally asymptotically stable. If [Formula: see text], the endemic equilibrium is globally asymptotically stable for any nonnegative nontrivial initial data. Using the perturbation theory, we obtain the concrete expression of the endemic equilibrium of the model with a mild restriction of the birds movement rate between patches. Finally, numerical simulations demonstrate that the disease becomes endemic in both patches when birds move back and forth between the two regions. Some numerical simulations for [Formula: see text] in terms of the birds movement rate are performed which show that the impacts could be very complicated.

References

Jan 1, 1986·Transactions of the Royal Society of Tropical Medicine and Hygiene·C Dye, G Hasibeder
Jul 1, 1995·Mathematical Biosciences·K P Hadeler, C Castillo-Chavez
Nov 14, 1997·Mathematical Biosciences·K P Hadeler, P van den Driessche
Jul 25, 2000·Emerging Infectious Diseases·J H RappoleZ Hubálek
May 26, 2001·Bulletin of Mathematical Biology·D J Rodríguez, L Torres-Sorando
Apr 25, 2002·Emerging Infectious Diseases·Mertyn MalkinsonVincent Deubel
Sep 7, 2002·The Lancet Infectious Diseases·Grant L CampbellDuane J Gubler
Oct 22, 2002·Mathematical Biosciences·P van den Driessche, James Watmough
Feb 10, 2004·Journal of Medical Entomology·Laura B GoddardThomas W Scott
Jun 8, 2004·Malaria Journal·David L Smith, F Ellis McKenzie
Mar 22, 2005·Mathematical Medicine and Biology : a Journal of the IMA·Julien ArinoP van den Driessche
Aug 30, 2005·Bulletin of Mathematical Biology·Gustavo Cruz-PachecoCristobal Vargas
Dec 14, 2005·Mathematical Biosciences·Julien ArinoP van den Driessche
Jun 24, 2006·Bulletin of Mathematical Biology·Mark LewisP van den Driessche
Dec 27, 2007·The Canadian Journal of Infectious Diseases = Journal Canadien Des Maladies Infectieuses·Michael A DrebotHarvey Artsob
Sep 23, 2008·Mathematical Biosciences·Pierre AugerBerge Tsanou
Mar 7, 2009·Journal of Theoretical Biology·C CosnerS Ruan
Jan 1, 2006·Mathematical Biosciences and Engineering : MBE·Rongsong LiuHuaiping Zhu
May 9, 2013·Journal of Mathematical Biology·Ahmed AbdelrazecHuaiping Zhu
Jan 1, 2012·SIAM Journal on Applied Mathematics·Daozhou Gao, Shigui Ruan
Apr 6, 2017·Journal of Mathematical Biology·Zhigui Lin, Huaiping Zhu
Jun 10, 2017·Journal of Occupational and Environmental Medicine·Beuy Joob, Viroj Wiwanitkit

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Mathematical Medicine and Biology : a Journal of the IMA
Julien ArinoWei Yang
SIAM Journal on Applied Mathematics
Daozhou Gao, Shigui Ruan
Mathematical Biosciences
Pierre AugerBerge Tsanou
Discrete and Continuous Dynamical Systems. Series B
Daozhou GaoShigui Ruan
© 2022 Meta ULC. All rights reserved