Stability Analysis Of Several Types Of Media Infectious Diseases

Infectious diseases has been a serious threat to human’s health. It has become animportant issue which needed to be solved urgently in the world today to prevent andcontrol of infectious diseases efectively. It is particularly important to establish and researcha disease model which can refect the real situation of infectious. In this article, several typesof host-vector epidemic model are formulated and studied. We predict the popular trend ofinfectious diseases and provide theoretical basis for prevent the spread of infectious diseasesefectively through researching the stability of models.Firstly, a host-vector epidemic model with standard incidence rate is formulated andstudied. The threshold which determines the outcome of disease is identifed and the exis-tence of the equilibrium is discussed. The model is shown that the disease free equilibriumis globally stability when R0<1. For the basic reproductive number R0>1, a uniqueendemic equilibrium exists and is globally asymptotically stable. The numerical simulationsare carried out to fnd the disease free equilibrium and endemic equilibrium are globallyasymptotically stable.Secondly,we study a host-vector epidemic model with vertical transmission. Throughdynamical analysis, the basic reproduction number R0is obtained and globally stability ofdisease-free equilibrium is proved if R0<1. If R0>1, the disease-free equilibrium is un-stable and the endemic equilibrium exists and is unique, which is globally stable. Numericalsimulations are performed to illustrate and verify the conclusions.Finally, a mathematical model is formulated and analyzed to describe the dynamicalfeatures of a dengue fever with latent period. The basic reproduction number is derived,thresholds conditions for the elimination of the disease are identifed. The disease free equi-librium solution of the system has been obtained and is found to be globally asymptoticallystable when R0<1using Lyapunov function theory and the disease will be cleared out of thehost. For the basic reproductive number R0>1, a unique endemic equilibrium exists andis locally asymptotically stable. Finally, numerical simulations are carried out to support the analytical conclusion of the model.