A stochastic dengue transmission model: Noise-induced extinction and optimal control

Dengue fever is a mosquito-borne viral disease that continues to pose a substantial public health burden in tropical and subtropical regions. Although most existing studies are based on deterministic formulations, environmental variability and behavioral responses can significantly influence transmission dynamics. In this work, we formulate and analyze a stochastic dengue transmission model that incorporates media-driven awareness, nonlinear treatment responses, and environmental noise. The stochastic system is shown to be well posed by establishing the existence, uniqueness, and positivity of global solutions. The model parameters are estimated by calibrating the deterministic counterpart of the stochastic system against the reported data on dengue incidence, demonstrating good agreement between simulations and observations. The basic reproduction number is derived and sensitivity of the parameters is assessed using partial rank correlation coefficients under uncertainty to identify key drivers of transmission. Analytical conditions for noise-induced disease extinction are obtained, revealing that sufficiently strong environmental fluctuations can suppress endemic persistence. The impact of varying noise intensities on long-term dynamics is further characterized. Finally, we develop a stochastic optimal control framework that integrates awareness-based prevention and treatment interventions, providing a theoretical basis for evaluating control strategies under environmental uncertainty.