Traveling Wave Solutions For A Class Of Decoupled SI Infectious Disease System

In the dynamics of infectious diseases,traveling wave solutions represent a source of infection that travels in space with constant wave velocity.In this paper,we study the existence of traveling wave solutions for a class of decoupled SI system The main research method is the improved shooting method,we use shooting method to construct a ? set and find the globally defined solution in the ? set,it is proved that when t ?-? it converges to the disease-free equilibrium,;we use the Liapunov function method,we can deduce the system is proved to be globally defined solution when t ? ?,it converges to the local disease equilibrium,traveling wave solution is exit.Finally,the above results are verified by numerical simulation.The advantage of the improved shooting method do not require the complex structure of the Wazewski?s set,and the minimum wave velocity can be calculated.