# Mathematical modeling of public health policy for international travelers (PHPIT): a case study of the COVID-19 pandemic in Thailand

## TL;DR

This study evaluates Thailand's public health policies for international travelers during the pandemic to reduce missed COVID-19 cases.

## Contribution

A cross-border control model integrating cluster analysis and mathematical modeling is introduced to assess the effectiveness of various public health interventions.

## Key findings

- A 14-day quarantine reduced missed cases by 94%, the highest among single interventions.
- Combining quarantine with pre-departure testing could reduce missed cases by up to 98%.
- Testing and country risk classification had limited effectiveness and potential drawbacks.

## Abstract

Following border closures implemented during the COVID-19 pandemic, Thailand subsequently reopened its international borders, employing public health policy for international travelers (PHPIT) to mitigate the importation of COVID-19 cases and minimize potential missed cases. These measures included departure country risk classification, vaccination certificate requirement, pre-departure and entry testing, and quarantine.

To assess the effectiveness of these interventions, we developed a cross-border control model, which integrates cluster analysis and mathematical modeling to estimate reductions in missed cases in Thailand under various scenarios.

Our findings indicated that, as a single measure, when compared with implementing no interventions, quarantine for 1, 3, 5, 7, 10, and 14 days reduced missed cases by 45%, 58%, 72%, 80%, 88%, and 94%, respectively. Departure country risk classification reduced missed cases by up to 72% and vaccination certificate requirement by up to 24%. Testing once at 72, 48, 24, or 0 h pre-departure reduced missed cases by 5%, 7%, 10%, and 14% respectively. Entry testing (the “test-and-go” policy) reduced missed cases by 29%. Strategically combining quarantine with other PHPIT measures could achieve a 46–98% reduction in missed cases, with the maximum reduction in missed cases when implementing 14-day quarantine together with pre-departure testing.

Quarantine could serve as a standard measure to minimize missed cases and be optimized by a vaccination certificate requirement. Meanwhile, testing and departure country risk classification could be withdrawn due to their minimal effectiveness and potential for discrimination, respectively. The combinations and their optimization should be guided by domestic transmission dynamics, healthcare system capacities, societal perspectives, and economic adaptability. Future PHPIT implementation should incorporate pre-evaluation to balance intervention effectiveness, equity for international travelers, and public health and economic security.

The online version contains supplementary material available at 10.1186/s12889-025-25811-5.