Study On Some Epidemic Model With The Effect Of Media Coverage Andtime Delay

When infectious diseases outbreaks, media coverage can timely report related knowledge of infectious diseases. It makes people to enhance the protection awareness of infectious diseases, and educates people the correct protective measures. On the other hand, with the development of theory about delay differential equations, the effect of time delay on infectious diseases has been concerned by experts and scholars with the theory of delay differential equations. This paper will study three models with time delay and media coverage, and discuss the stability of equilibria and the existence of Hopf bifurcation by the theory of ordinary differential equation and the theory of delay differential equations.In chapter 2, a class of SIRS model with media coverage and immune period will be discussed. To describe the effect of the contact rate with media coverage, we give a functional response function f （I）=β₁-β₂I/ （m +I）. The conditions of the stability of equilibria have been obtained by the theory of the characteristic equation, we also get the conclusion of Hopf bifurcation. The conditions of numerical simulation shows that the large the value of time delay is, the smaller the number of infected population is. So if immune period will be delayed, epidemic desease can be well controlled.In chapter 3, a kind of SISmRM model with media coverage and immune period will be studied. The variation of media coverage is added to this model, time delay still represent immune period. The conditions of the stability of equilibria have been given by the theory of the characteristic equation, and the conclusion for Hopf bifurcation to occur is also yielded. The large the value of time delay and the value of media coverage is, the small the number of infected population is. As the same time, the number of infected population decreases with the natural decay rate of media coverage decrease.In chapter 4, a class of SISmM model, with media coverage effected by time delay, will be constructed. Some recovery people who keep awareness of disease will transfer to susceptible responsive, the others will be susceptible non-responsive. The basic reproduction number 0R is given. The conditions of the stability of equilibria and the existence of Hopf bifurcation have been obtained by the theory of the characteristic equation and the threshold. The conclusions show if the smaller the rate of transmision from susceptible non-responsive to susceptible responsive is, the smaller the number of infected population is.