Mathematical Model as a Tool for the Control of Vector-Borne Diseases: Wolbachia Example

Dengue is a vector-borne disease that risks two-thirds of the world ’ s population particularly in tropical and subtropical regions. Strategies have been implemented, but they are only effective in the short term. A new innovative and promising strategy against dengue is by the use of Wolbachia bacterium. This requires that Wolbachia -carrying mosquitoes should persist in the population. To assess the persistence of Wolbachia -carrying mosquitoes and its effects on dengue, a number of mathematical models have been formulated and analysed. In this chapter, we review the existing mathematical models of Wolbachia carrying mosquito population dynamics and dengue with Wolbachia intervention and provide examples of the mathematical models. Simulations of the models are presented to illustrate the model ’ s solutions.