Birth-pulse models of Wolbachia-induced cytoplasmic incompatibility in mosquitoes for dengue virus control

Dengue fever, which affects more than 50 million people a year, is the most important arboviral disease in tropical countries. Mosquitoes are the principal vectors of the dengue virus but some endosymbiotic Wolbachia bacteria can stop the mosquitoes from reproducing and so interrupt virus transmission. A birth-pulse model of the spread of Wolbachia through a population of mosquitoes, incorporating the effects of cytoplasmic incompatibility (CI) and different density dependent death rate functions, is proposed. Strategies for either eradicating mosquitoes or using population replacement by substituting uninfected mosquitoes with infected ones for dengue virus prevention were modeled. A model with a strong density dependent death function shows that population replacement can be realized if the initial ratio of number of infected to the total number of mosquitoes exceeds a critical value, especially when transmission from mother to offspring is perfect. However, with a weak density dependent death function, population eradication becomes difficult as the system’s solutions are sensitive to initial values. Using numerical methods, it was shown that population eradication may be achieved regardless of the infection ratio only when parameters lie in particular regions and the initial density of uninfected is low enough