Incorporating global dynamics to improve the accuracy of disease models: Example of a COVID-19 SIR model

Abstract: Mathematical models of infectious diseases exhibit robust dynamics such as stable endemic or a disease-free equilibrium, or convergence of the solutions to periodic epidemic waves. The present work shows that the accuracy of such dynamics can be significantly improved by incorporating both local and global dynamics of the infection in disease models. To demonstrate improved accuracies, we extended a standard Susceptible-Infected-Recovered (SIR) model by incorporating global dynamics of the COVID-19 pandemic. The extended SIR model assumes three possibilities for the susceptible individuals traveling outside of their community: They can return to the community without any exposure to the infection, they can be exposed and develop symptoms after returning to the community, or they can be tested positive during the trip and remain quarantined until fully recovered. To examine the predictive accuracies of the extended SIR model, we studied the prevalence of the COVID-19 infection in Kansas City, Missouri influenced by the COVID-19 global pandemic. Using a two-step model-fitting algorithm, the extended SIR model was parameterized using the Kansas City, Missouri COVID-19 data during March to October 2020. The extended SIR model significantly outperformed the standard SIR model and revealed oscillatory behaviors with an increasing trend of infected individuals. In conclusion, the analytics and predictive accuracies of disease models can be significantly improved by incorporating the global dynamics of the infection in the models.