The Effect Of Transport-related Infection And Exit-entry Screening On Disease Spread

Major. Applied mathematicsSpeciality:Mathematical biologySupervisor. Liu XianningAuthor. Chen Xiaoping (112008314001347)Considering the effect of population dispersal with transport-related infection and exit-entry screening on disease spread, SIS,SIQS models are proposed and some analytical results are obtained. The parameter space which is constituted by transmission rate, the probabilities of successfully detecting an infected individual for entry screening and exit screening, is divided into several regions by the critical condition with one of the basic reproduction numbers is equal to 1. Each region represents for one case. Mathematical results suggest that exit-entry screenings are reasonable and necessary. This paper is divided into five chapters.In the first chapter, the development from population emigration model to infectious disease model with dispersal is introduced. Infectious disease model with diffusion is generalized from two patches to n patches. A general SEIRS model for multi-species on multi-patches diffusion is introduced. Some related theorems that will be used and the main purpose of this paper are introduced.In the second chapter, we formulate an SIS model with transported-related and two means of traveling, the dynamic behaviors of the model are analyzed. By comparing the size of the basic reproduction number, we show that traveling population take a smaller transmission rate of transport as much as possible, which is helpful for disease control.In the third chapter, considering the case with transported-related infection and one side screening (exit screening or entry screening), an SIQS model is established. If the basic reproduction number is not greater than the unity, there only exists the disease-free equilibrium which is proved to be globally asymptotically stable. Comprehensively using Routh-Hurwitz Criterion and Gersgorin's theorem, it is shown that endemic equilibrium is locally asymptotically stable if the basic reproduction number is greater than the one. It is also shown that the disease is endemic in the sense of permanence if and only if the endemic equilibrium exists. Mathematical results suggest that one side screening (exit screening or entry screening) is helpful for disease led by transported-related infection control, since it reduces the number of infected individuals and decreases the incidence rate during travel.In the fourth chapter, the case with both transported-related infection and exit-entry screening is discussed. Utilizing the next generation matrix method, the basic reproduc-tion number of corresponding model is computed. The dynamic behavior of the model is analyzed, if the basic reproduction number is not greater than the unity, the disease free equilibrium is globally asymptotically stable. And there exists an endemic equilibrium which is locally asymptotically stable if the reproduction number is greater than unity. The combined effects of transport-related infection enhancing and exit-entry screenings suppressing on disease spread are discussed. Since exit-entry screenings can always have the possibility to eradicate the disease endemic led by transport-related infection and fur-thermore have the possibility to eradicate disease even when the isolated cites are disease endemic. Using one kind of screening or both screenings, the disease still may be elimi-nated depending on the probabilities of successfully detecting infected individuals by the screenings. The lager the probability is, the better the suppressing effect is.In the last chapter, the mathematical difficulty in two cites with different epidemio-logical parameters is analyzed. A more tedious calculation are required for mathematical analysis of the model. Lastly, some future work are discussed.