Sliding mode of compulsory treatment in infectious disease controlling.

Preventing the infectious disease from breakout and maintaining public health have always been placed at the first place when making public healthy policy. When the epidemic trend of infectious disease arises, compulsory treatment is an efficient pattern to control the rapid spreading. A sliding mode is carried out to evaluate the effect of compulsory treatment in the infectious disease controlling. When the number of infected persons reach a certain level I c, the policy of compulsory treatment will be carried out at rate f . We analyze the influence of the compulsory treatment rate f and threshold value I c to commence the control. Finally we investigate the theorems and the existence of the optimality combination.