Traveling wave solutions for the dispersive models describing population dynamics of Aedes aegypti

In recent decades the global incidence of dengue has grown dramatically by increased human mobility and urbanization. The study of the mosquitoes population is of great importance for public health in countries where climatic and environmental conditions are favorable for the propagation of this disease. Therefore, this work is based on the study of mathematical models dealing with the life cycle of the mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through direct numerical simulations using finite difference schemes. We also present initial study concerning structural stability of traveling wave solution.