On a reaction-diffusion system modeling the dengue transmission with nonlocal infections and crowding effects

Huei Li Lin; Feng Bin Wang

doi:10.1016/j.amc.2014.09.101

On a reaction-diffusion system modeling the dengue transmission with nonlocal infections and crowding effects

Huei Li Lin, Feng Bin Wang^*

^*Corresponding author for this work

Center for General Education

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

17 Scopus citations

Abstract

In this paper, we intend to understand the influences of the spatial heterogeneity, crowding effect and non-local infection caused by the movements of the latent mosquitoes on the dynamics of dengue transmission. For this purpose, we modify the homogeneous system provided in Esteva and Vargas (1998) to obtain a nonlocal and time-delayed reaction-diffusion system with the Neumann condition on the boundary. Then the basic reproduction number R₀ is defined for the model system, and it can be obtained explicitly when all model parameters are constants. Finally, we show that the global threshold dynamics of the model system can be determined by R₀.

Original language	English
Pages (from-to)	184-194
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	248
DOIs	https://doi.org/10.1016/j.amc.2014.09.101
State	Published - 01 12 2014

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc. All rights reserved.

Keywords

Basic reproduction number
Crowding effect
Dengue transmission
Persistence
Threshold dynamics
Time delays

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.amc.2014.09.101

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abstract = "In this paper, we intend to understand the influences of the spatial heterogeneity, crowding effect and non-local infection caused by the movements of the latent mosquitoes on the dynamics of dengue transmission. For this purpose, we modify the homogeneous system provided in Esteva and Vargas (1998) to obtain a nonlocal and time-delayed reaction-diffusion system with the Neumann condition on the boundary. Then the basic reproduction number R0 is defined for the model system, and it can be obtained explicitly when all model parameters are constants. Finally, we show that the global threshold dynamics of the model system can be determined by R0.",

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AU - Lin, Huei Li

AU - Wang, Feng Bin

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N2 - In this paper, we intend to understand the influences of the spatial heterogeneity, crowding effect and non-local infection caused by the movements of the latent mosquitoes on the dynamics of dengue transmission. For this purpose, we modify the homogeneous system provided in Esteva and Vargas (1998) to obtain a nonlocal and time-delayed reaction-diffusion system with the Neumann condition on the boundary. Then the basic reproduction number R0 is defined for the model system, and it can be obtained explicitly when all model parameters are constants. Finally, we show that the global threshold dynamics of the model system can be determined by R0.

AB - In this paper, we intend to understand the influences of the spatial heterogeneity, crowding effect and non-local infection caused by the movements of the latent mosquitoes on the dynamics of dengue transmission. For this purpose, we modify the homogeneous system provided in Esteva and Vargas (1998) to obtain a nonlocal and time-delayed reaction-diffusion system with the Neumann condition on the boundary. Then the basic reproduction number R0 is defined for the model system, and it can be obtained explicitly when all model parameters are constants. Finally, we show that the global threshold dynamics of the model system can be determined by R0.

KW - Basic reproduction number

KW - Crowding effect

KW - Dengue transmission

KW - Persistence

KW - Threshold dynamics

KW - Time delays

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SP - 184

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JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

On a reaction-diffusion system modeling the dengue transmission with nonlocal infections and crowding effects

Abstract

Bibliographical note

Keywords

UN SDGs

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