Stochastic invasion thresholds for transmission-blocking symbionts and malaria control under environmental noise

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Introduction Transmission-blocking symbionts may complement existing malaria vector-control tools, but their public-health value depends on two linked conditions: ecological establishment in mosquito populations and long-run prevalence high enough to suppress malaria transmission. Methods Motivated by Microsporidia MB in Anopheles mosquitoes, we developed a scale-free stochastic differential-equation model for uninfected and symbiont-infected adult female mosquitoes with density-dependent recruitment, vertical transmission, mating-mediated horizontal conversion, and multiplicative environmental noise. We derived a rare-symbiont stochastic invasion index, analyzed extinction and invasion thresholds, used Malliavin-Hörmander analysis to characterize inter-class noise transfer, and linked stationary symbiont prevalence to an effective Ross-Macdonald malaria reproduction number. Results The invasion index separates vertical and horizontal transmission contributions while quantifying the opposing effects of infected-mosquito mortality and environmental variance. The analysis identifies a win zone in which the symbiont both establishes and reduces malaria transmission below threshold. Climate-driven Monte Carlo maps and dual-population simulations show that ecological invasion and epidemiological control are related but not equivalent. Discussion The framework provides an interpretable basis for spatial threshold screening, trait prioritization, experimental design, and dissemination planning for symbiont-based malaria control under environmental uncertainty.

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