Wolbachia establishment and invasion in Aedes Aegypti population to suppress Zika transmission

Arboviral diseases such as dengue and Zika are diseases that pose a threat to health problems globally. Traditional control methods against mosquito populations that transmit arboviral diseases should be complemented by longer lasting and larger scale methods such as the use of an intracellular bacterium called Wolbachia. Wolbachia-based control strategy is an eco-friendly strategy that is carried out by infecting wild mosquitoes with a Wolbachia strain and then strategically releasing the Wolbachia infected mosquitoes in hopes of reducing disease transmission. In this study we develop and analyze an ordinary differential equation model to quantify the effectiveness of different release strategies of Wolbachia infected mosquitoes in order to create a sustained infection of Wolbachia in the mosquito population and reduce Zika transmission. The model accounts for mating between mosquitoes, assumes complete cytoplasmatic incompatibility and allows for different parameters related to vector-born transmission. We compute all the reproduction numbers and derive analytic forms of equilibria, where possible. Then local stability analysis is performed for these equilibria. Using numerical simulations we investigate different release strategies of Wolbachia infected mosquitoes and observe that there are multiple ways to reach persistence of Wolbachia mosquitoes. We also notice that for realistic parameter values the two mosquito populations are in a competitive-exclusion regime where only one species will survive. We perform sensitivity analysis on the reproduction numbers to determine their relative importance to Wolbachia transmission and Zika prevalence.