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

Publication Type

Journal Article

Journal Name

Frontiers in Applied Mathematics and Statistics

Name of Author

• Steeven Belvinos Affognon, University of Nairobi
• Philip Ngare, University of Nairobi
• Henri E.Z. Tonnang, International Institute of Tropical Agriculture (IITA)
• Benard Kipchumba Kiplangat, University of Nairobi
• Shirley Abelman, University of the Witwatersrand, Johannesburg
• Jeremy K. Herren, International Centre of Insect Physiology and Ecology Nairobi

Publication Date

9-7-2026

Abstract

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.

Keywords

Hörmander condition, malaria vector control, Malliavin calculus, Microsporidia MB, Ross–Macdonald model, stochastic invasion, transmission-blocking symbiont

Recommended Citation

Affognon, S., Ngare, P., Tonnang, H., Kiplangat, B., Abelman, S., & Herren, J. (2026). Stochastic invasion thresholds for transmission-blocking symbionts and malaria control under environmental noise. Frontiers in Applied Mathematics and Statistics, 12 https://doi.org/10.3389/fams.2026.1924647

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.