Modelling disease outbreak models remains challenging due to incomplete surveillance data, noise, and limited access to standardized datasets. We have created BIGBOY1.2, an open synthetic dataset generator that creates configurable epidemic time series and population-level trajectories suitable for benchmarking modelling, forecasting, and visualisation. The framework supports SEIR and SIR-like compartmental logic, custom seasonality, and noise injection to mimic real reporting artifacts. BIGBOY1.2 can produce datasets with diverse characteristics, making it suitable for comparing traditional epidemiological models (e.g., SIR, SEIR) with modern machine learning approaches (e.g., SVM, neural networks).

The standard way to estimate the parameters $\Theta_\text{SEIR}$ (e.g., the transmission rate $\beta$) of an SEIR model is to use grid search, where simulations are performed on each set of parameters, and the parameter set leading to the least $L_2$ distance between predicted number of infections and observed infections is selected. This brute-force strategy is not only time consuming, as simulations are slow when the population is large, but also inaccurate, since it is impossible to enumerate all parameter combinations. To address these issues, in this paper, we propose to transform the non-differentiable problem of finding optimal $\Theta_\text{SEIR}$ to a differentiable one, where we first train a recurrent net to fit a small number of simulation data. Next, based on this recurrent net that is able to generalize SEIR simulations, we are able to transform the objective to a differentiable one with respect to $\Theta_\text{SEIR}$, and straightforwardly obtain its optimal value. The proposed strategy is both time efficient as it only relies on a small number of SEIR simulations, and accurate as we are able to find the optimal $\Theta_\text{SEIR}$ based on the differentiable objective. On two COVID-19 datasets, we observe that the proposed strategy leads to significantly better parameter estimations with a smaller number of simulations.