Dynamic systems give rise to challenges in analyzing time series data that are collected over time. State-space models are a common approach for modeling unobserved transmission processes such as infectious diseases, where often only incident cases are observed by a surveillance system. We assess the inferential ability of likelihood-based methods in a multi-serotype epidemiological model for a 4-serotype dengue system. We evaluate and compare the capacity of particle filtering and iterated filtering to draw inference for unknown parameters associated with serotype interactions in a complex dynamic disease system, based on observed data from public health surveillance systems. Likelihoods obtained from particle filtering methods are highly noisy and contain complex structured variance that can lead to bias in estimating the maximum likelihood when constructing likelihood profiles. We suggest a method that adjusts for large errors coming from likelihood-based inference methods where computational intensive Monte Carlo methods are employed. We apply the proposed estimator to simulated data that is similar to likelihoods obtained from particle filtering and show that it is able to adjust the errors coming from different components and construct likelihood profiles for noisy likelihoods. It is beneficial in inference and forecasting to incorporate immunity interactions between pathogens into models. While the inherent complexity of dynamic systems results in high dimensions and large number of mechanistic parameters, an ideal model should be complex enough to explain the key relationships between components and maintain simplicity to convey features that enable the prediction of the system dynamics. We compare models with different properties and test whether multi-pathogen models with explicit interactions could improve the predictive skill of models.