Models to assess how best to replace dengue virus vectors with Wolbachia-infected mosquito populations

Dengue fever is increasing in importance in the tropics and subtropics. Endosymbiotic Wolbachia bacteria as novel control methods can reduce the ability of virus transmission. So, many mosquitoes infected with Wolbachia are released in some countries so that strategies for population replacement can be fulfilled. However, not all of these field trails are successful, for example, releases on Tri Nguyen Island, Vietnam in 2013 failed. Thus, we evaluated a series of relevant issues such as (a) why do some releases fail? (b) What affects the success of population replacement? And (c) Whether or not augmentation can block the dengue diseases in field trials. If not, how we can success be achieved? Models with and without augmentation, incorporating the effects of cytoplasmic incompatibility (CI) and fitness effects are proposed to describe the spread of Wolbachia in mosquito populations. Stability analysis revealed that backward bifurcations and multiple attractors may exist, which indicate that initial quantities of infected and uninfected mosquitoes, augmentation methods (timing, quantity, order and frequency) may affect the success of the strategies. The results show that successful population replacement will rely on selection of suitable strains of Wolbachia and careful design of augmentation methods.