The Impact Of Media On The Spreading And Control Of Infectious Disease And Permanence Of The Population

The paper considers two systems: one is a predator-prey system, the other is a dynamical system of infectious disease.In the first part, we consider a predator-prey system with periodic coefficients and infinite delay, in which the prey has a history that takes them through two stages, immature and mature. We provide a sufficient and necessary condition to guarantee the permanence of the system. The system has a positive ω periodic solution under this condition. Some known results are extended to the delayed case.In the second part, we develop a three dimensional compartmental model to explore the impact of media coverage to the spread and control of infectious disease (such as SARS) in a given region/area. The model exhibits three equilibria: two disease-free equilibria and a unique endemic equilibrium. Stability analysis of the model shows that the non-zero disease-free equilibrium is globally-asymptotically stable if a certain threshold quantity, reproduction number (Mo), which depends solely on parameters, is less than unity. On the other hand, if R₀ > 1 it is shown that a unique endemic equilibrium appears and a Hopf bifurcation can occur which causes oscillatory phenomena. Numerical simulations suggests that when R₀ > 1 and the media impact is stronger enough, the model exhibits multiple positive equilibria which poses challenge to control and predict of infectious disease.