Stochastic modeling, analysis, and simulation of Dengue in Valle del Cauca: A case study.

Dengue remains a major public health challenge in Colombia, with Valle del Cauca experiencing recurrent outbreaks characterized by seasonal fluctuations and long-term variability. Understanding the transmission dynamics of Dengue across age groups is critical for targeted interventions. In this study, we developed an age-structured stochastic host-vector model, incorporating a compartmental SIR-SI framework within a stochastic differential equation (SDE) approach. The population is stratified into youths (0-17 years) and adults (18 years and older), enabling analysis of age-specific infection and recovery patterns. Simulations and forecasts were performed using the Euler-Maruyama method, informed by fixed parameters from the literature, estimated disease-specific parameters, and epidemiological data from Colombia's Public Health Surveillance System (SIVIGILA) spanning 2013-2023. Additionally, a Seasonal Autoregressive Integrated Moving Average (SARIMA) model was employed as a complementary approach to capture and forecast monthly Dengue incidence. Our results highlighted distinct epidemic patterns across age groups, the higher infection burden among adults, and the complementary roles of mechanistic SDE modeling and SARIMA forecasting for surveillance and control planning.