The Intergrability On A Class Of Chronic Wasting Desease Models

Chronic wasting disease is a prion disease that occurs in the deer family.Miller et al.established an ordinary differential equation model to study the spread of chronic wasting disease.In this paper we study the invariant algebraic surfaces and Darboux integrability of the chronic wasting disease model from the perspective of the integra-bility of dynamical systems.We use the characteristic curve method of solving partial differential equations to find all invariant algebraic surfaces of two chronic wasting dis-ease models and the parameter conditions for first integrals of the system,etc.Here main results are as follows.In Chapter 1 we mainly introduce the backgroud and current situation of chronic wasting disease model and Darboux integrability theory.In Chapter 2 we present the prerequisite knowledge.In Chapter 3 we canculate Darboux polynomials and first integrals of the chronic wasting disease model with logistic term(?)and then analyze its dynamics by restricting the system on its invariant algebraic surface.Since Darboux polynomials and first integral are closely related,the calculation of first integrals is often more complicated,but the existence conditions of the Darboux polynomial is much weaker than the existence condition of the first integrals.So in order to find first integrals,we calculate Darboux polynomials of the system firstly.Through Darboux polynomial of the system,we seek first integral,and then give the integrability of the system and some dynamics.In Chapter 4 we analyze another chronic wasting disease model(?)including additive effects of direct transmission between individuals.All irreducible Darboux polynomials of this model,and the existence of first integrals of the model are studied.In the end,we study the dynamics of the model by restricting the system on its invariant algebraic surface.