A two-stage model with distributed delay for mosquito population dynamics
Studies on the population dynamics of mosquito species are essential for understanding and control the transmission and spread of mosquito-borne diseases. In this talk, I will first introduce a general system of distributed delay differential equations that models the age structure of mosquitoes with lifespan being divided into two aquatic and adult stages. By defining the reproduction number through the model with a general form of delay kernel, we present some analytical results for the general model, including the stability of the boundary equilibrium and the existence of the unique interior equilibrium. The delay kernel serves as a weighting factor which measures the contribution of daily accumulated temperature. For two specific types of popularly used delay kernels, we show the bifurcation and dynamics and present some simulations performed for each system to illustrate how the temperature dependent maturation time impacts the abundance of eggs and adult mosquitoes. This is a joint work with Juan Li and Guihong Fan.