An evolutionary game modeling to assess the effect of border enforcement measures and socio-economic cost: Export-importation epidemic dynamics.

In the wake of the novel coronavirus, SARS-CoV-19, the world has undergone a critical situation in which grave threats to global public health emerged. Among human populations across the planet, travel restraints, border enforcement measures, quarantine, and isolation provisions were implemented to control and limit the spread of the contagion. Decisions on implementing and enforcing various control policies should be determined based on available real-world evidence and theoretical prediction. Further, countries around the globe-imposed force-quarantine and strict lockdown against the spreading could be unsustainable in the long run because of economic burden and people's frustration. This study proposes a novel exportation- importation epidemic model associated with behavioral dynamics under the evolutionary game theory by considering the two-body system: a source country of a contagious disease and a neighboring disease-free state. The model is first applied to the original COVID-19 data in China, Italy, and the Republic of Korea (ROK) and observed through consistent fitting results with equivalent goodness-of-fit. Then, the data are estimated per the appropriate parameters. Driven by these parametric settings and considering the normalized population, the numerical analysis, and epidemiological exploration, this work further elucidates the substantial impact of quarantine policies, healthcare facilities, socio-economic cost, and the public counter-compliance effect. Extensive numerical analysis shows that funds spent on the individual level as "emergency relief-package" can reduce the infection and improve quarantine policy success. Our results also explore that controlling border measurement can work well in the final epidemic stage of disease only if the cost is low.