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R是一套由数据操作、计算和图形展示功能整合而成的套件。包括： ² 有效的数据存储和处理功能， ² 一套完整的数组（特别是矩阵）计算操作符， ² 拥有完整体系的数据分析工具， ² 为数据分析和显示提供的强大图形功能， ² 一套（源自S语言）完善、简单、有效的编程语言（包括条件、循环、自 定义函数、输入输出功能）。

This paper proposes and analyzes a mathematical model on an infectious disease system with a piecewise smooth incidence rate concerning media/psychological eect. The proposed models extend the classic models with media coverage by including a piecewise smooth incidence rate to repre- sent that the reduction factor because of media coverage depends on both the number of cases and the rate of changes in case number. On the basis of prop- erties of Lambert W function the implicitly dened model has been converted into a piecewise smooth system with explicit denition, and the global dynamic behavior is theoretically examined. The disease-free is globally asymptotically stable when a certain threshold is less than unity, while the endemic equilib- rium is globally asymptotically stable for otherwise. The media/psychological impact although does not aect the epidemic threshold, delays the epidemic peak and results in a lower size of outbreak (or equilibrium level of infected individuals).

This paper proposes a Filippov epidemic model with piecewise continuous function to represent the enhanced vaccination strategy being triggered once the proportion of the susceptible individuals exceeds a threshold level. The sliding bifurcation and global dynamics for the proposed system are investigated. It is shown that as the threshold value varies, the proposed system can exhibit variable sliding mode domains and local sliding bifurcations including boundary node (focus) bifurcation, double tangency bifurcation and other sliding mode bifurcations. Model solutions ultimately approach either one of two endemic states for two structures or the pseudoequilibrium on the switching surface, depending on the threshold level. The findings indicate that proper combinations of threshold level and enhanced vaccination rate based on threshold policy can lead disease prevalence to a previously chosen level if eradication of disease is impossible.