The Dynamics And Optimal Control Of The SIQRS Epidemic Model With Pulse Vaccination And Delay

Through analyzing tuberculosis disease pathology, using the knowledge of infectious disease model, this paper establishes the corresponding pulse model of infectious disease with delay. This paper uses time delay to simulate the incubation period of the disease and adopts pulse vaccination for susceptible people. The paper is organized as follows:In the third chapter, we study the dynamics of this model. In this section, the existence of the disease-free periodic solution is firstly proved. And on this basis, this paper researches the global attractivity about it through using pulse comparison principle. The paper shows that the disease-free periodic solution (S,0,0) is global attractive. In other words, disease will be eliminated. Then, this paper researches the persistence of the disease through using the same pulse comparison principle. It shows that the disease is persistent.In the fourth chapter, we study the optimal control of this model. In this section, the control variables and objective function are firstly made sure. Among these, the objective function is created to make the number of people infected in the epidemic process and the coast least. Then, this chapter gives the corresponding continuous and discrete pulse Hamiltonian by used the Pontryagin minimum principle and gives the form of the necessary condition for the optimal control by means of the extreme conditions and the co-state equation. Finally, this chapter makes the corresponding numerical simulation using matlab. The results show that humans can control the prevalence of the infectious diseases through optimal control about inoculation time and number of individuals vaccinated.The study of this paper shows that:using the optimal inoculation strategy can effectively decrease the spread of the disease and make the number of the patients at least. This paper provides the theoretical basis for the control of infectious diseases.