Understanding pandemics through molecular gas dynamics

While the COVID-19 pandemic is over, the road ahead is still clouded by concern about new variants and other similar infectious diseases. Human society, as an inherently complex system, is inextricably linked to the dynamics of respiratory infectious diseases from the interplay of individual behaviors, social interactions, and public policies. However, comprehending and predicting large-scale pandemic evolution based on fundamental individual behavior models remains a big challenge. In this study, we analogize the spread of respiratory infectious diseases to the nonequilibrium chemical reaction in a molecular gas, another complex system. Concepts and methodologies from molecular gas dynamics are extended to elucidate the pandemic. Individuals at distinct infection stages are treated as moving molecules of different species that undergo collisions and reactions. The velocity and collision cross-section are set according to real-world scenarios. Additionally, the viral load in human body is analogized to molecular vibrational energy level which affects the chemical reaction rate. Consequently, we introduce a specific nonequilibrium compartmental model incorporating a time-varying transmission rate, drawing upon the nonequilibrium gas dynamics. By employing the Direct Simulation Monte Carlo method, we directly derive key epidemiological metrics, including the secondary infection number, generation interval, and reproduction number. Furthermore, an initial exploration of the interplay between infection and individual behavior displays how the disease spread mitigates when the mobility of patients is reduced. This novel analogy highlights the generalized similarity between distinct complex systems and opens a new avenue for applying advanced concepts and methods from molecular gas dynamics to the pandemic study.