Effects of travel frequency on the persistence of mosquito-borne diseases

Travel frequency of people varies widely with occupation, age, gender, ethnicity, income, climate and other factors. Meanwhile, the distribution of the numbers of times people in different regions or with different travel behaviors bitten by mosquitoes may be nonuniform. To reflect these two heterogeneities, we develop a multipatch model to study the impact of travel frequency and human biting rate on the spatial spread of mosquito-borne diseases. The human population in each patch is divided into four classes: susceptible unfrequent, infectious unfrequent, susceptible frequent, and infectious frequent. The basic reproduction number R0 is defined. It is shown that the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1, and there is a unique endemic equilibrium that is globally asymptotically stable if R0 > 1. A more detailed study is conducted on the single patch model. We use analytical and numerical methods to demonstrate that the model without considering the difference of humans in travel frequency mostly underestimates the risk of infection. Numerical simulations suggest that the greater the difference in travel frequency, the larger the underestimate of the transmission potential. In addition, the basic reproduction number R0 may decreasingly, or increasingly, or nonmonotonically vary when more people travel frequently.