The Study On A SIV Epidemic Model With Double Delay Pulse Vaccination And A Two-city SIR Epidemic Model With Transport-related Infections

In this paper, combining the infectious disease dynamics with the theories ofdifferential equation and impulsive differential equation, we establish a SIV epidemicmodel with double delay pulse vaccination and a two-city SIR epidemic model withtransport-related infections, respectively. With the help of the comparison theorems ofdifferential equation and impulsive differential equation, we have discussed theexistence and global attractivity of the disease-free equilibrium for the above SIVmodel. Applying the Hurwitz criterion and the method of Lyapunov function, a goodunderstanding of the permanence and local stability of disease-free equilibrium andendemic equilibrium for the SIR model is obtained, then we establish sufficientconditions for the global stability of the disease-free equilibrium, and thecorresponding numerical simulations are also given. The full text is divided into fourchapters.The first chapter recalls the research backgrounds and status of infectiousdisease models, and explains the meaning of the models we established, thensummarizes our main work done in this paper.The second chapter a SIV epidemic model with double delay pulse vaccinationis built up. According to the related theories on differential equation, the disease-freeequilibrium of above system is obtained. What’s more, the comparison theorems ofdifferential equation and impulsive differential equation help us contributing to globalattractivity of the disease-free equilibrium. At last, we achieve the permanence of ourresearched system.The third chapter we establish a two-city SIR epidemic model with transport-related infections, by using the related theorems of differential equation and theHurwitz criterion and the method of Lyapunov function, we have proved that thepermanence and local stability of disease-free equilibrium and endemic equilibrium,and established sufficient conditions for the global stability of the disease-freeequilibrium. Finally, we give the corresponding numerical simulations.We have summarized our work, and some research outlooks about the future work are putforword in the last chapter.