Analysis of a Dengue Model with Vertical Transmission and Application to the 2014 Dengue Outbreak in Guangdong Province, China

Lan Zou; Jing Chen; Xiaomei Feng; Shigui Ruan

Analysis of a Dengue Model with Vertical Transmission and Application to the 2014 Dengue Outbreak in Guangdong Province, China

Lan Zou, Jing Chen, Xiaomei Feng, Shigui Ruan

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

There is evidence showing that vertical transmission of dengue virus exists in Aedes mosquitoes. In this paper, we propose a deterministic dengue model with vertical transmission in mosquitoes by including aquatic mosquitoes (eggs, larvae and pupae), adult mosquitoes (susceptible, exposed and infectious) and human hosts (susceptible, exposed, infectious and recovered). We first analyze the existence and stability of disease-free equilibria, calculate the basic reproduction number and discuss the existence of the disease-endemic equilibrium. Then, we study the impact of vertical transmission of the virus in mosquitoes on the spread dynamics of dengue. We also use the model to simulate the reported infected human data from the 2014 dengue outbreak in Guangdong Province, China, carry out sensitivity analysis of the basic reproduction number in terms of the model parameters, and seek for effective control measures for the transmission of dengue virus.

Original language	American English
Pages (from-to)	2633-2651
Number of pages	19
Journal	Bulletin of Mathematical Biology
Volume	80
Issue number	10
State	Published - Oct 1 2018

Funding

This work was partially supported by NSF grant DMS-1412454, NSFC Grants Nos. 11771168 and 11501498, and a start-up grant from Yuncheng University (YQ-2016004).

Funders	Funder number
Yuncheng University	YQ-2016004
National Science Foundation	DMS-1412454
National Science Foundation
National Natural Science Foundation of China	11771168, 11501498
National Natural Science Foundation of China

ASJC Scopus Subject Areas

General Neuroscience
Immunology
General Mathematics
General Biochemistry,Genetics and Molecular Biology
General Environmental Science
Pharmacology
General Agricultural and Biological Sciences
Computational Theory and Mathematics

Keywords

Basic reproduction number
Dengue
Disease-free and disease-endemic equilibra
Mathematical model
Vertical transmission

Disciplines

Disease Modeling
Mathematics
Physical Sciences and Mathematics

Cite this

@article{ff5a0b033c274c0dbc6a30bbc728525b,

title = "Analysis of a Dengue Model with Vertical Transmission and Application to the 2014 Dengue Outbreak in Guangdong Province, China",

abstract = " There is evidence showing that vertical transmission of dengue virus exists in Aedes mosquitoes. In this paper, we propose a deterministic dengue model with vertical transmission in mosquitoes by including aquatic mosquitoes (eggs, larvae and pupae), adult mosquitoes (susceptible, exposed and infectious) and human hosts (susceptible, exposed, infectious and recovered). We first analyze the existence and stability of disease-free equilibria, calculate the basic reproduction number and discuss the existence of the disease-endemic equilibrium. Then, we study the impact of vertical transmission of the virus in mosquitoes on the spread dynamics of dengue. We also use the model to simulate the reported infected human data from the 2014 dengue outbreak in Guangdong Province, China, carry out sensitivity analysis of the basic reproduction number in terms of the model parameters, and seek for effective control measures for the transmission of dengue virus.",

keywords = "Basic reproduction number, Dengue, Disease-free and disease-endemic equilibra, Mathematical model, Vertical transmission",

author = "Lan Zou and Jing Chen and Xiaomei Feng and Shigui Ruan",

note = "Publisher Copyright: {\textcopyright} 2018, Society for Mathematical Biology.",

year = "2018",

month = oct,

day = "1",

language = "American English",

volume = "80",

pages = "2633--2651",

journal = "Bulletin of Mathematical Biology",

issn = "0092-8240",

number = "10",

}

TY - JOUR

T1 - Analysis of a Dengue Model with Vertical Transmission and Application to the 2014 Dengue Outbreak in Guangdong Province, China

AU - Zou, Lan

AU - Chen, Jing

AU - Feng, Xiaomei

AU - Ruan, Shigui

PY - 2018/10/1

Y1 - 2018/10/1

N2 - There is evidence showing that vertical transmission of dengue virus exists in Aedes mosquitoes. In this paper, we propose a deterministic dengue model with vertical transmission in mosquitoes by including aquatic mosquitoes (eggs, larvae and pupae), adult mosquitoes (susceptible, exposed and infectious) and human hosts (susceptible, exposed, infectious and recovered). We first analyze the existence and stability of disease-free equilibria, calculate the basic reproduction number and discuss the existence of the disease-endemic equilibrium. Then, we study the impact of vertical transmission of the virus in mosquitoes on the spread dynamics of dengue. We also use the model to simulate the reported infected human data from the 2014 dengue outbreak in Guangdong Province, China, carry out sensitivity analysis of the basic reproduction number in terms of the model parameters, and seek for effective control measures for the transmission of dengue virus.

AB - There is evidence showing that vertical transmission of dengue virus exists in Aedes mosquitoes. In this paper, we propose a deterministic dengue model with vertical transmission in mosquitoes by including aquatic mosquitoes (eggs, larvae and pupae), adult mosquitoes (susceptible, exposed and infectious) and human hosts (susceptible, exposed, infectious and recovered). We first analyze the existence and stability of disease-free equilibria, calculate the basic reproduction number and discuss the existence of the disease-endemic equilibrium. Then, we study the impact of vertical transmission of the virus in mosquitoes on the spread dynamics of dengue. We also use the model to simulate the reported infected human data from the 2014 dengue outbreak in Guangdong Province, China, carry out sensitivity analysis of the basic reproduction number in terms of the model parameters, and seek for effective control measures for the transmission of dengue virus.

KW - Basic reproduction number

KW - Dengue

KW - Disease-free and disease-endemic equilibra

KW - Mathematical model

KW - Vertical transmission

UR - https://nsuworks.nova.edu/math_facarticles/251

UR - http://www.scopus.com/inward/record.url?scp=85051699867&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051699867&partnerID=8YFLogxK

M3 - Article

SN - 0092-8240

VL - 80

SP - 2633

EP - 2651

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

IS - 10

ER -

Analysis of a Dengue Model with Vertical Transmission and Application to the 2014 Dengue Outbreak in Guangdong Province, China

Abstract

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

Other files and links

Cite this