Wolbachia spread dynamics in mosquito populations in cyclic environments

In this paper, we establish a discrete model with periodic parameters to depict the Wolbachia spread dynamics in mosquito populations in cyclic environments. This work modifies the models established in the existing literature that did not take into account the variation of parameters with environmental periodic changes due to seasonality and other factors. When the parameters in our model are constants, it has been extensively studied and widely used. We present a conjecture about the existence of at most two periodic solutions worthy of further study, and show that the conjecture is true for the special case of 2-periodic parameters. Numerical simulations are also provided to illustrate the occurrence of periodic phenomena.