A robust modeling framework to investigate transmissible diseases: COVID-19 in Chile as a case study

Oscar Rojas^1,2*Patricio Cumsille^2,3*Carlos Conca^2,4

• ¹Universidad de Santiago de Chile Departamento de Matematica y Ciencia de la Computacion, Santiago, Chile
• ²Centre for Biotechnology and Bioengineering, Santiago, Chile
• ³Department of Basic Sciences, Universidad del Bio-Bio - Sede Chillan, Chillán, Chile
• ⁴Center for Mathematical Modeling, Universidad de Chile Departamento de Ingenieria Matematica, Santiago, Chile

Introduction: In the face of the challenges posed by pandemics like COVID-19, the need for accurate mathematical models and methods to predict the impact of outbreaks on public health in real-time is paramount. This research aims to develop a robust, adaptable, and general framework for investigating the dynamics of any transmissible disease. The primary objective of this work is to achieve robust parameter optimization for a general modeling framework, a capability crucial for effectively applying it to reconstruct and predict epidemiological curves for any transmissible disease. Methods: The main novelty of this work is that our general modeling framework automatically selects a suitable initial parameter vector under general conditions that standard initialization heuristics do not necessarily satisfy, thereby endowing the parameter estimation method with stability and the ability to calibrate any COVID-19 dataset. In addition, we have designed our framework to be adaptable, allowing it to incorporate additional modeling variables, such as ICU admissions beyond infection incidence, and a greater number of time-varying parameters, including the transmission rate, to enhance calibration accuracy. This adaptability ensures that the framework can be tailored to the specific characteristics of different diseases and datasets, enhancing its calibration capabilities. Results: The main strength of this work lies in the robustness of our general modeling framework. It has demonstrated its ability to optimize modeling parameters that accurately calibrate trends observed in epidemiological curves across all regions of Chile, with varying population sizes and distinct periods/waves of the COVID-19 pandemic, including the effective reproductive number at the national level. In addition, the quantitative measures we calculated further validate the performance of the general modeling framework. Conclusion: This research represents a significant first step in establishing a robust modeling framework to investigate the dynamics of any transmissible disease. Our findings not only provide a solid foundation for future studies but also have the potential to inform the development of effective disease control strategies, thereby advancing public health.