Study Of Several Types Of Epidemic Models With State Dependent Impulse Control

In recent years,the researches on impulsive differential equation are transforming from the models with pulses at fixed times to it with state-dependent pulse effects.In that context,the effects of state-dependent pulse control on dynamics of epidemic model with varying total population are studied in detail,and the main research contents are as follows1.In the first part(corresponding to the section 2),we mainly discuss dynamics of two kinds of SIS epidemic model with varying total population size,continuous vaccina-tion,and state-dependent pulse vaccination.In the first control model,the proportion of infected individuals in population as monitoring threshold value.By the Poincare map,analogue of Poincare criterion and qualitative analysis method,we analytically show the existence and orbital stability of the positive order-1 periodic solution for this control model.Secondly,the other model determines the control strategy by monitoring the proportion of susceptible individuals in population,the second control model is put forward,some general criteria for the existence and globally asymptotically stability of disease-free periodic solution is established.Finally,we carry out some numerical simu-lations to illustrate the main theoretical results and the feasibility of the state-dependent pulse control strategies.2.In the second part(corresponding to the section 3),two kinds of SIRS epidemic models with state-dependent pulse control and varying total population are established to explore the transmission dynamics of brucellosis in ruminants.Discuss the influence of state-dependent pulse control strategy on the elimination and control of the disease.Firstly,the proportion of infected individuals in population as monitoring threshold value and an SIRS epidemic model with medical resources limitedness and state-dependent pulse vaccination is put forward.Through theoretic analysis and comparison principle,the sufficient conditions in terms of existence and orbitally asymptotically stability of the positive order-1 or order-2 periodic solution are obtained.Furthermore,the other model determines the control strategy by monitoring the proportion of susceptible individuals in population,another SIRS epidemic model with state-dependent pulse control strategy is established.We analytically prove the existence and orbitally asymptotical stability of positive order-1 periodic solution and disease-free periodic solution.We carry out some numerical simulations to illustrate the main theoretical results and the feasibility of the state-dependent pulse control strategies.3.In the third part(corresponding to the section 4),Given the limited medical resources,in this section,a kind of SIR epidemic model with state-dependent pulse con-trol and disease-related mortality is established.By using Poincare map,analogue of Poincare criterion and qualitative analysis method,the sufficient conditions for the exis-tence and orbitally asymptotical stability of positive order-1 or order-2 periodic solution are obtained.Finally,some numerical simulations are given to validate our theoretical results.