Impulsive Release Strategies for Wolbachia-Infected Mosquitoes under Temperature-Induced Infection Loss

The release of Wolbachia-infected mosquitoes is a promising strategy for controlling Aedes aegypti populations, but exposure to high temperatures can induce temporary infection loss and compromise long-term persistence. In this work, we propose a population-dynamics model based on impulsive differential equations to describe the interaction between wild and infected mosquitoes, incorporating cytoplasmic incompatibility, periodic release interventions, and temperature-driven infection loss. Analytical threshold conditions are derived to characterize the existence and stability of periodic solutions associated with successful Wolbachia establishment. Numerical simulations illustrate the theoretical results and enable a comparative analysis of the wMelPop, wMel, and wAlbB strains, highlighting how differences in thermal tolerance and fitness costs influence persistence after the release phase. The results emphasize the importance of accounting for environmental stress and impulsive interventions when designing effective and robust Wolbachia release strategies.

💡 Research Summary

This paper develops a rigorous impulsive differential equation framework to study the release of Wolbachia‑infected Aedes aegypti mosquitoes under the realistic threat of temperature‑induced infection loss. The authors first formulate a continuous‐time two‑population model (wild mosquitoes S₁ and Wolbachia‑infected mosquitoes S₂) that incorporates logistic growth limited by a shared carrying capacity K, birth and death rates (ψᵢ, δᵢ), and cytoplasmic incompatibility (CI) through a parameter γ. Under biologically plausible assumptions (wild mosquitoes have higher fitness than infected ones, ψ₁>δ₁, ψ₂>δ₂, ψ₂<ψ₁, δ₂>δ₁), they prove existence, uniqueness, positivity, and global boundedness of solutions (Theorem 1) and identify up to three equilibria: a Wolbachia‑free equilibrium E₁, an infected‑only equilibrium E₂, and a coexistence equilibrium E₃ (Theorem 2). E₁ is stable when the wild basic reproduction number R₁=ψ₁/δ₁ exceeds both 1 and R₂; E₂ is stable when R₂>1 and R₂>(1−γ)R₁; the coexistence point, existing only when 1−γ<R₁R₂<1, is always a saddle and thus biologically irrelevant for long‑term control.

The novel contribution lies in embedding two impulsive events: (i) periodic releases of Q infected mosquitoes at times τᵣ, and (ii) episodic temperature spikes that instantaneously reduce the infected fraction by a proportion α (0<α<1) at times τₗ, converting the lost infected individuals into wild mosquitoes. The resulting hybrid system is analyzed via a Poincaré map, leading to an explicit threshold condition for the release magnitude:

 Q > Q₍crit₎ =