The Dynamics Models Analysis Of Pertussis

Pertussis is a respiratory infection which can be controlled by vaccine,and its vaccine is one of the first vaccines that was included in the planned immunization.However,pertussis disease is still very threatening to human health.Many scholars want to control and eliminate the spread of pertussis disease.For that a lot of efforts have been made to control the disease.This thesis is mainly to construct a theoretical analysis of the two pertussis kinetic models,and then to obtain the methods of con-trol the infection of pertussis.The main purpose of the first chapter of this thesis is to point out the importance of research on pertussis by introducing the epidemiology of pertussis and establish the model according to it.One model is established under the premise that the incubation period is contagious and the vaccine is not invalid.Another model is established considering the contagious patient’s infectivity and the vaccine will fail.In both models,the basic reproduction number RO is calculated by using reproduction matrix method.It is found that when RO<1,there exists only a disease-free equilibrium point.The disease-free balance point which is locally asymp-totically stable on the positive invariant set;When R0>1,the group of equations has only an endemic balance point which is also globally asymptotically stable on the pos-itive invariant set.Then the effective way to control the transmission of pertussis is obtained by analyzing the parameters of the expression of basic reproduction number.