Qualitative Behavioral Analysis in Mosquito Dynamics Model with Wolbachia

The Aedes Aegypti mosquito is the primary vector that can transmit diseases to humans such as zika, dengue fever, chikungunya, and yellow fever. This mosquito species is controlled to reduce the frequency of its bites on humans. Several methods have been developed to control mosquito populations, ranging from natural insecticides to artificial ones. However, the impact of these insecticides leads to resistance. Wolbachia bacteria as a promising alternative in reducing the spread of viruses on humans due to free resistance. This work constructs a genetic population model in the form of differential equation system that describes mosquito population dynamics by involving random mating between mosquito populations with and without Wolbachia bacteria. The stability of the equilibrium was analyzed locally here. Numerical simulations and sensitivity analyzes are presented to confirm the analytical results and investigate the effect of the parameters involved on the model. The results show that the success of the expansion of Wolbachia-infected mosquitoes depends on the fitness level of the mosquito species. The more Wolbachia mosquitoes are released into nature, the more possibility this mosquito expansion will be successful