Definitions of the parameters.

Aedes mosquitoes, known as vectors of mosquito-borne diseases, pose significant risks to public health and safety. Modeling the population dynamics of Aedes mosquitoes requires comprehensive approaches due to the complex interplay between biological mechanisms and environmental factors. This study developed a model that couples differential equations with a neural network to simulate the dynamics of mosquito population, and explore the relationships between oviposition rate, temperature, and precipitation. Data from nine cities in Guangdong Province spanning four years were used for model training and parameter estimation, while data from the remaining three cities were reserved for model validation. The trained model successfully simulated the mosquito population dynamics across all twelve cities using the same set of parameters. Correlation coefficients between simulated results and observed data exceeded 0.7 across all cities, with some cities surpassing 0.85, demonstrating high model performance. The coupled neural network in the model effectively revealed the relationships among oviposition rate, temperature, and precipitation, aligning with biological patterns. Furthermore, symbolic regression was used to identify the optimal functional expression for these relationships. By integrating the traditional dynamic model with machine learning, our model can adhere to specific biological mechanisms while extracting patterns from data, thus enhancing its interpretability in biology. Our approach provides both accurate modeling and an avenue for uncovering potential unknown biological mechanisms. Our conclusions can provide valuable insights into designing strategies for controlling mosquito-borne diseases and developing related prediction and early warning systems.