What Influence Could the Acceptance of Visitors Cause on the Epidemic Dynamics of a Reinfectious Disease?: A Mathematical Model

Abstract

The globalization in business and tourism becomes crucial more and more for the economical sustainability of local communities. In the presence of an epidemic outbreak, there must be such a decision on the policy by the host community as whether to accept visitors or not, the number of acceptable visitors, or the condition for acceptable visitors. Making use of an SIRI type of mathematical model, we consider the influence of visitors on the spread of a reinfectious disease in a community, especially assuming that a certain proportion of accepted visitors are immune. The reinfectivity of disease here means that the immunity gained by either vaccination or recovery is imperfect. With the mathematical results obtained by our analysis on the model for such an epidemic dynamics of resident and visitor populations, we find that the acceptance of visitors could have a significant influence on the disease’s endemicity in the community, either suppressive or supportive.