Research Article Open Access

SIR Transmission Model of Dengue Virus Taking Into Account Two Species of Mosquitoes and an Age Structure in the Human Population

R. Sungchasit1, P. Pongsumpun1 and I. M. Tang2
  • 1 Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Chalongkrung Road, Ladkrabang, Bangkok, 10520, Thailand
  • 2 Department of Materials Science, Faculty of Science, Kasetsart University, 50 Ngam Wong Wan Road, Lat Yao Chatuchak, Bangkok 10900, Thailand

Abstract

Dengue is a vector-borne disease. It is transmitted to humans by the bites of the Aedes aegypti and Aedes albopictus mosquitoes. The human population is separated into two classes, a child class and an adult class, each class being described by a SIR model. The transmission rates of the two mosquito species are different and depend on what class the humans belong to. We develop a single model taking into account the presence of two type of mosquitoes and two age classes and apply it to dengue fever. The model shows how it is possible for the maximum level of infected human to be reached in a short time. The nature of stability of the equilibrium state and the trajectories of the individual classes in the model are determined by the values of the basic reproduction number by setting the values of the parameters in the model to different values which reflect the environment in which the epidemic is occurring in the model.

American Journal of Applied Sciences
Volume 12 No. 6, 2015, 426-444

DOI: https://doi.org/10.3844/ajassp.2015.426.444

Submitted On: 30 July 2014 Published On: 28 July 2015

How to Cite: Sungchasit, R., Pongsumpun, P. & Tang, I. M. (2015). SIR Transmission Model of Dengue Virus Taking Into Account Two Species of Mosquitoes and an Age Structure in the Human Population. American Journal of Applied Sciences, 12(6), 426-444. https://doi.org/10.3844/ajassp.2015.426.444

  • 1,538 Views
  • 1,502 Downloads
  • 3 Citations

Download

Keywords

  • Aedes Aegypti
  • Aedes Albopictus
  • Dengue Disease
  • Endemic Disease State
  • Equilibrium State
  • SIR Model