When Strain Meets Stress: Threshold Dynamics and Regime Shifts in Wolbachia-Based Mosquito Population Replacement

Wolbachia-based mosquito population replacement is a promising biocontrol strategy to reduce arboviral disease transmission by introducing Wolbachia-infected mosquitoes into wild populations. The success of this approach depends on the strain-specific characteristics of the Wolbachia symbiont and the mosquito host. This study presents a mathematical modelling framework to evaluate how Wolbachia strains and mosquito hosts influence the success of population replacement. The model incorporates key biological factors, including incomplete cytoplasmic incompatibility (CI), imperfect maternal transmission (MT), fitness costs, immigration, and potential loss of Wolbachia from mosquitoes. Analytical and numerical simulations demonstrate that strain-specific differences significantly impact the establishment, spread, and long-term persistence of Wolbachia in mosquito populations. Results indicate that high CI and MT levels, combined with low fitness costs and minimal immigration, facilitate successful Wolbachia establishment. To account for environmental stress, the model is extended to a stochastic framework incorporating environmental noise. Analysis reveals that stochasticity can shift invasion thresholds, destabilize equilibria, and induce noise-driven transitions between coexistence states. Numerical simulations show that low noise levels allow deterministic thresholds to remain predictive, whereas stronger fluctuations can undermine replacement success despite favourable deterministic conditions. A stochastic optimal control formulation further indicates that higher and more prolonged releases are necessary in noisy environments to ensure replacement. Collectively, these findings highlight how both strain traits and environmental stress shape the deterministic and stochastic thresholds governing the success of Wolbachia-based mosquito population replacement.