The global emergence of infectious diseases, such as the coronavirus, has presented a formidable and widespread challenge, causing significant human casualties, property damage, and economic disruptions. Investigating infectious disease models becomes imperative for a comprehensive understanding of the dissemination patterns of highly contagious illnesses. Hence, research into infectious disease models is of utmost importance.
This paper introduces the application of physics-constrained machine learning (PCML) to develop a spatial domain model for infectious disease control, specifically focusing on vaccine distribution. Traditionally, dynamical systems are employed in epidemiological models to forecast the temporal evolution and growth trajectories of highly infectious diseases. In this study, we reframe the SIR models, incorporating corresponding policies through dynamical systems.
Utilizing the PCML algorithm, we derive approximate numerical solutions for the systems of dynamical partial differential equations (PDEs) with an acceptable margin of approximation error. Additionally, we present various numerical solutions to the PDEs under diverse scenarios.