Travel frequency and infectious diseases

Empirical and statistical evidence suggests that the number of trips taken per year varies significantly among people by age, gender, income, occupation, ethnicity, region, and so on. Only a small fraction of people are frequent travelers while most travel occasionally or never. Taking the difference in travel frequency into consideration, we propose a multipatch epidemic model where humans in each patch are divided into susceptible unfrequent, infectious unfrequent, susceptible frequent, and infectious frequent classes. The basic reproduction number \scrR 0 is derived and shown to govern the global dynamics of the model system if infection does not impede travel. Lower and upper bounds on \scrR 0 are given, and the disease can become endemic or extinct even though it dies out or persists in each isolated patch. Both analytical and numerical approaches show that the model, without distinguishing the difference in travel frequency, tends to underestimate the infection risk. Several numerical examples are presented to illustrate the impact of changes in modern travel on disease spread. We find that \scrR 0 may decreasingly, or increasingly, or nonmonotonically depend on the diffusion coefficient of the infected subpopulation. Meanwhile, the basic reproduction number of the model with uniform travel frequency is shown to be monotone decreasing in the diffusion coefficient if the connectivity matrix is symmetric. The unfrequent travelers at high transmission regions are at the highest risk of infection, and allocating resources to frequent and unfrequent travelers in high transmission regions probably yields the maximal reduction in infections and the basic reproduction number, respectively.