Optimal control strategies for dengue transmission under varying adult prevalence of <i>Wolbachia</i> -carrying mosquitoes: a deterministic mathematical modeling study

Objectives: This study aimed to develop prevalence-informed post-release dengue control strategies for settings in which Wolbachia-carrying Aedes aegypti mosquitoes have become established through population replacement and to quantify how optimal supplementary intervention intensity and duration vary with adult Wolbachia prevalence, pW. Methods: A deterministic human-mosquito model was formulated that included Wolbachia-free and Wolbachia-carrying mosquitoes and incorporated cytoplasmic incompatibility, maternal transmission, and reduced vector competence. Two bounded supplementary controls were optimized over a 3-year horizon: reduction of effective human-mosquito contact and conventional adult mosquito suppression, represented by increased adult mortality. A quadratic-cost optimal-control problem was solved numerically using the Pontryagin maximum principle and a forward/backward sweep algorithm. Outcomes were compared across representative pW scenarios and prevalence scans. Results: The optimal policies applied high-intensity supplementary control early in the planning horizon and then relaxed control as infection pressure declined. Higher pW reduced the uncontrolled infection burden, decreased the incremental benefit of additional intervention, and shortened the duration of maximum control. In coarse scans with umax=0.30, the terminal dengue infection near-elimination indicator, defined as IH (T)≤10-4 at T=3 years, changed between pW=0.45 and pW=0.50 for all tested cost-weight combinations. A separate refined continuation example demonstrated non-monotonic mean control use and a sharp decrease in cumulative incidence. Conclusion: Adult Wolbachia prevalence measured through entomological surveillance may represent an actionable index for post-release dengue management. The identified transition band is a model-based planning indicator, not a universal field threshold or evidence of mosquito population elimination.