  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.
