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

TL;DR

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 is proposed.

Abstract

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.

Figures (9)

• Figure 1: Phase portraits of system \ref{['eq:equation_1']} for $\gamma=0.95$, illustrating the qualitative behavior of trajectories for the three Wolbachia strains. Different colors represent trajectories starting from distinct initial conditions. The equilibria $E_1$ (blue), $E_2$ (green), and $E_3$ (purple) are indicated. Parameter values are reported in Tables \ref{['tab:tab_3']}--\ref{['tab:tab_4']}.
• Figure 2: Seasonal function $\varphi(t)$ defined in \ref{['eq:equation_5']} plotted for three different values of $\varphi_{\max}$.
• Figure 3: Wild and infected mosquito dynamics under periodic releases ($\tau = 7$ days) for the strains wMelpop (a), wMel (b), and wAlbB (c), simulated under four distinct initial conditions. All release amplitudes satisfy $u_n > \eta(7)$, ensuring dominance of the infected population. Infection-loss intensities are $\varphi_{\max} = 0.0015$, $0.001$, and $0.0005$ for the respective strains.
• Figure 4: Dynamics of the wild and Wolbachia-infected mosquito populations for the three Wolbachia strains (wMelpop, wMel, and wAlbB), simulated under four distinct initial conditions and increased temperature-induced infection loss. The simulations consider $\tau = 7$ and higher loss rates, with $\varphi_{\max} = 0.015,; 0.01,; 0.005$ for wMelpop, wMel, and wAlbB, respectively. Larger values of $\varphi_{\max}$ make the thermal decay of infection more pronounced between releases, revealing the effect of stronger temperature stress on Wolbachia persistence.
• Figure 5: Dynamics of wild and Wolbachia-infected mosquitoes, simulated under four distinct initial conditions, with higher infection-loss intensities: $\varphi_{\max} = 0.0015$ (wMelPop), $0.001$ (wMel), and $0.0005$ (wAlbB), and release interval $\tau = 14$. Compared with Figure \ref{['fig:fig_3']}, temperature-induced infection loss becomes more apparent, although periodic releases continue to sustain the infected population.

Theorems & Definitions (19)

• Theorem 1: Existence, Uniqueness, Positivity, and Global Boundedness
• Theorem 2: Equilibrium Points and Stability
• Proposition 1
• proof
• Proposition 2
• proof
• Theorem 3
• Proposition 3
• proof
• Theorem 4