The Traveling Waves Of Two Epidemic Models

In this thesis, we mainly consider the existence of traveling waves of two kinds of epidemic model. In the second chapter, we consider a diffusive SIR model with nonlinear incidence rate and treatment. By employing the geometric singular perturbation method we derive that there exists a traveling wave connects the disease-free stead state and the endemic steady state. In the third chapter, we use the same method as the second chapter to study a diffusive SIV model with constant total population and we derive the existence of traveling waves of this system. The same result is also suitable to another SIV system with nonconstant total population.