QUALITATIVE ANALYSIS FOR A MATHEMATICAL MODEL OF AIDS

In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are also considered.in particular,the conditions for the existence of Hopf bifurcation can be given in terms of the coefficients of the characteristic equation.The method extends the application of the Hopf bifurcation theorem to higher differential equations which occur in biological models,chemical models,and epidemiological models etc.

Parametric sensitivity analysis of precipitation and temperature based on multi-uncertainty quantification methods in the Weather Research and Forecasting model

Sensitivity analysis(SA) has been widely used to screen out a small number of sensitive parameters for model outputs from all adjustable parameters in weather and climate models, helping to improve model predictions by tuning the parameters. However, most parametric SA studies have focused on a single SA method and a single model output evaluation function, which makes the screened sensitive parameters less comprehensive. In addition, qualitative SA methods are often used because simulations using complex weather and climate models are time-consuming. Unlike previous SA studies, this research has systematically evaluated the sensitivity of parameters that affect precipitation and temperature simulations in the Weather Research and Forecasting(WRF) model using both qualitative and quantitative global SA methods. In the SA studies, multiple model output evaluation functions were used to conduct various SA experiments for precipitation and temperature. The results showed that five parameters(P3, P5, P7, P10, and P16) had the greatest effect on precipitation simulation results and that two parameters(P7 and P10) had the greatest effect for temperature. Using quantitative SA, the two-way interactive effect between P7 and P10 was also found to be important, especially for precipitation. The microphysics scheme had more sensitive parameters for precipitation, and P10(the multiplier for saturated soil water content) was the most sensitive parameter for both precipitation and temperature. From the ensemble simulations, preliminary results indicated that the precipitation and temperature simulation accuracies could be improved by tuning the respective sensitive parameter values, especially for simulations of moderate and heavy rain.