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Bulletin of Mathematical Biology

, Volume 80, Issue 10, pp 2633–2651 | Cite as

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
Original Article

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

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

Notes

Acknowledgements

The authors would like to thank the two anonymous reviewers for their helpful comments and suggestions.

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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduChina
  2. 2.Halmos College of Natural Sciences and OceanographyNova Southeastern UniversityFort LauderdaleUSA
  3. 3.Department of MathematicsYuncheng UniversityYunchengChina
  4. 4.Department of MathematicsUniversity of MiamiCoral GablesUSA

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