In this work, we develop a physics-informed neural network for solving coupled systems of partial differential equations governing epidemic systems. The proposed framework addresses this challenge by enabling fast modeling of epidemic systems for time-structured epidemic models with serotype change, time-varying parameters, and increasing susceptible population. This thesis presents a bibliographic review of dynamic epidemiological models, emphasizing models specifically designed for dengue modeling, exploring the theoretical foundations, common modeling frameworks, and applications of dynamic models in understanding and predicting dengue outbreaks. Our results show that our deep neural network framework is robust in solving the problem of finding the parameters of the equations that govern the behavior of dengue infection.