With Time Delay The Spread Of The Existence Of Solutions In The Musca Domestica Flies Model Wave

This paper deals with the existence of travelling wave fronts for the diffusive Musca domestica houseflies model with delay.The whole paper consists of three chapters. In Chapter 1, we introduce some elementary concepts and results. In Chapter 2, we consider the existence of travelling wave fronts for the diffusive Musca domestica houseflies model with spatio-temporal delay. By applying the geometric singular perturbation theory, specifically Fenichel invariant manifold theory, we prove that steady travelling wavefronts persist when the delay is sufficently small. In Chapter 3, we consider the existence of travelling wave fronts for the diffusive Musca domestica houseflies model with a discrete delay. By using the upper-lower solution technique and the monotone iteration method developed by Wu and Zou [27], the existence theorem of travelling wavefronts of this model is established.