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Mathematical analysis demonstrates that nonzero periodic trajectories are bounded by two in periodic mosquito populations, suggesting strict limits on recurrent Wolbachia infection cycles.
We consider the periodic model introduced by B. Zheng and J. Yu, 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 nonzero periodic trajectories is bounded by two.
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José S. Cánovas (2026) studied this question.
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