A note on the periodic orbits of Wolbachia spread dynamics in mosquito populations in periodic environments

TL;DR

This paper analyzes a periodic model of Wolbachia spread in mosquito populations, disproves previous conjectures, and establishes that the number of non-zero periodic trajectories is at most two for any period.

Contribution

It refutes earlier conjectures about the number of periodic orbits and proves a new bound of two for all periodic sequences in the model.

Findings

Disproved previous conjectures on the number of periodic orbits.

Established that the number of non-zero periodic trajectories is at most two.

Applied the result to models of Wolbachia spread in mosquito populations.

Abstract

We consider the periodic model introduced in [20] and disprove the conjectures on the number of periodic orbits the model can have. We rebuild the conjecture to prove that for periodic sequences of maps of any period, the number of non-zero periodic trajectories is bounded by two.