The Study On The Control Of Singular Epidemic Models

It is well-known that epidemic is the enemy of human health and has effect on human life, such as the SARS in 2003, HPAI in 2004 and H1N1 in 2009. Elimination of the disease is good wishes to people. For a long time, in the process of struggle with epidemic diseases, some achievements are gained. people more and more clearly realize: the measures are effectively taken to control diseases, only when the law of epidemic disease is mastered, the weak links in the spread of epidemic disease are seized.Based on these, according to the principles of epidemic dynamics and bio-economics, the two singular systems are proposed respectively in this paper. Using the theory of singular system, the stability of the systems are disscussed, the conditions of bifurcation are given. By the control theory, the controllers are designed to make the systems are given for feedback control, making the two systems stable at the disease-free equilibrium.As follows:First, according to the principles of epidemic dynamics, a singular epidemic model with stage-structure is proposed. By Liapunov functions and the theory of singular epidemic, the sufficient conditions of the global stability for the system are given. Using linearization theory and pole placement, the control which makes the model stable at the free equilibrium is obtained. Numerical simulations is given to prove the results.Secend, using the principles of ecological dynamics and bio-economics, a singular prey-predator econmic system with infected prey is proposed. By bifurcation theory, the controllers which make the system stable at the free equilibrium. some numerical simulations is given to prove the results.