Almost periodic stable Wolbachia-infected mosquito population replacement

In the control of wild mosquito populations, releasing Wolbachia-infected males has shown to be a useful technique. We propose to adopt an oscillatory release rate in a simple mathematical model for this procedure in the form of a quasi-periodic and almost periodic release rate. This choice has conceptual advantages since we do not restrict time to be strictly periodic. There is also a practical advantage, since we may consider several non-synchronized fluctuating environmental factors such as annual proliferation, seasonal and daily temperature changes. We give criteria for global stability. In our examination two main phenomena occur: either the wild population is replaced by the infected population or the wild population persists in oscillating. We provide analytical proofs as well as numerical simulations.