Patterns of dengue and SARS-CoV-2 coinfection in the light of deterministic and stochastic models

• Differential equations to capture the dynamics of dengue and COVID-19 infections. • Well-posedness, reproduction number, and sensitivity analysis. • Itô stochastic model and numerical simulations. • Fit to real data from Colombia, globally and over subsequent stages. • Discussion of problems, such as unidentifiable parameters and limited data availability. We propose a new mathematical model to capture the overlapping dynamics of dengue and COVID-19 infections in a susceptible population, based on a nonlinear system of ordinary differential equations. First, we calculate the basic reproduction number and present its use in the analysis of outbreaks, long-term dynamics, and parameter sensitivity. Then, we introduce an Itô stochastic version of the system and conduct numerical simulations to explore its behavior, which generalizes the deterministic counterpart. The model is validated with real-world data from Colombia, employing different approaches: global and sub-stages fitting. We describe the emerging challenges, namely, unidentifiable parameters and limited data availability. To simplify the least-squares optimization process, certain parameters were previously fixed. Consequently, the model’s results should be interpreted with caution. Overcoming these limitations will be critical to advance epidemic modeling.