# Mathematical modeling of dengue epidemic: control methods and vaccination strategies

• Sylvestre Aureliano Carvalho
• Stella Olivia da Silva
• Iraziet da Cunha Charret
Original Article

## Abstract

Dengue is, in terms of death and economic cost, one of the most important infectious diseases in the world. So, its mathematical modeling can be a valuable tool to help us to understand the dynamics of the disease and to infer about its spreading by the proposition of control methods. In this paper, control strategies, which aim to eliminate the Aedes aegypti mosquito, as well as proposals for the vaccination campaign are evaluated. In our mathematical model, the mechanical control is accomplished through the environmental support capacity affected by a discrete function that represents the removal of breedings. Chemical control is carried out using insecticide and larvicide. The efficiency of vaccination is studied through the transfer of a fraction of individuals, proportional to the vaccination rate, from the susceptible to the recovered compartments. Our major find is that the dengue fever epidemic is only eradicated with the use of an immunizing vaccine because control measures, directed against its vector, are not enough to halt the disease spreading. Even when the infected mosquitoes are eliminated from the system, the susceptible ones are still present, and infected humans cause dengue fever to reappear in the human population.

## Keywords

Dengue Aedes aegypti Controls Vaccine

## Notes

### Acknowledgements

This work was partially supported by the Brazilian agencies CAPES, CNPq and FAPEMIG. We thank Dr. Marcelo Lobato Martins of the Physics Department—Federal University of Viçosa—for the kindness of your priceless suggestions. We also thank the comments and suggestions provided by anonymous referees, which contributed to improving this paper.

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