Mathematical Analysis Of A Two-group Multipatch Malaria Model

Travel frequency of people varies with occupation,age,gender,race,income,climate and other factors.Meanwhile,the number of times people in different regions or different travel frequencies bitten by mosquitoes is not uniform.Based on the classical RossMacdonald model,we construct an epidemic patch model to study the impact of travel frequency on the spread of mosquito-borne diseases.According to the difference in travel frequency and disease status,the population in each patch is divided into four classes:susceptible unfrequent,infectious unfrequent,susceptible frequent,and infectious frequent.The disease-free equilibrium of the model is solved and the basic reproduction number R₀is defined.It is proved that the disease-free equilibrium is globally asymptotically stable if R₀? 1,and there is a unique endemic equilibrium that is globally stable if R₀> 1.We do a more detailed study on the single patch model.We use analytical and numerical methods to demonstrate that the traditional model without considering the difference of travel frequency mostly underestimates the risk of infection in comparison with the new model.Numerical simulations show that the greater the difference in travel frequency,may the greater the difference between the basic regeneration numbers of the new model and the traditional model.In addition,the basic reproduction number of the new model may be decreasing,or increasing,or nonmonotonic with respect to the exchange rates between unfrequent and frequent travelers.