• DOI:10.1103/PHYSREVE.87.012709
• Corpus ID: 16596586

Stochastic dynamics of dengue epidemics.

@article{deSouza2013StochasticDO,
  title={Stochastic dynamics of dengue epidemics.},
  author={David R de Souza and T{\^a}nia Tom{\'e} and Suani T. R. Pinho and Florisneide Rodrigues Barreto and M{\'a}rio J. de Oliveira},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={87 1},
  pages={
          012709
        }
}

• David R de Souza, T. Tomé, +2 authors M. J. de Oliveira
• Published 5 August 2012
• Mathematics
• Physical review. E, Statistical, nonlinear, and soft matter physics

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice versa, so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible, for any death rate of infected mosquitoes.