On Epidemic Dynamical Models With Impulsive Effects And Period Environmental

The history of human is a history of struggling with a variety of diseases, with the devel-opment of interdisciplinary, mathematics workers try to reveal or predict the related problems in life science, medicine and other subjects by mathematics, statistics, etc, which enrich the theory of epidemic dynamical. In the research of infectious diseases, many natural phenomena and human interventions do exhibit impulsive effects and fit for describing by impulsive differen-tial equation; with the change of climate and environmental, many infectious diseases fluctuate over time and show seasonal patterns, epidemic models with period coefficients have received much attention by a lot of scholars. Based on previous work, we made an in-depth discussion on a general epidemic model, epidemic models with incomplete immunization of vaccine and mosquito-borne parasitic infection model in period environmental.In Chapter2, we propose two delayed SEIR epidemic models with nonlinear incidence rate, continuous treatment and impulsive vaccination for a class of epidemic disease with latent period and vertical transition, we obtain the conditions of disease-free and persistent. Numeri-cal simulations indicate that pulse vaccination strategy or a longer latent period will make the infected population size decrease.In Chapter3, we consider two epidemic models with imperfect vaccination compartment. Based on HBV infection, we introduce the incomplete immune compartment, latent period and impulsive vaccination to the dynamic model of hepatitis B. By using the comparative theorem of impulsive differential equation we get the global asymptotic stability of the disease-free periodic solution and permanence of disease.For SEIVS models which incorporate a imperfect vaccination compartment, we focus the psychology inhibition effect of the vaccinated individuals and the efficacy of vaccine on the spread of disease. For the vaccinated individuals we consider the psychology inhibition effect through the non-monotone incidence rate. We prove the conditions of disease persistent and disease-free. We also give some numerical simulations to demonstrate the effect of behavioral change of vaccinated individuals and the efficiency of vaccine on infectious number.In Chapter4, we consider that lymphatic filariasis is a parasitic disease caused by filarial nematode worms and is a mosquito-borne disease, proper temperature and humidity are more beneficial for mosquito population to give birth and propagate, a mosquito-borne parasitic in-fection model in period environmental is proposed. Threshold parameter R0is given by linear next infection operator, which determined the dynamical behaviors of the system. Numerical simulations support the results and sensitivity analysis show effect of parameters on R0, which provided references for seek optimal measures to control the transmission of lymphatic filariasis.