A Class Of Hosts With Vertically Transmitted Chagas Disease Dynamics Analysis

Chagas disease is extremetly harmful to human body,and seriously endangers human life.Effective prevention and control of Chagas disease has become a major problem to-day.Therefore,it's extremely important to study Chagas disease by mathematical model.Through the analizing the different influence in the built model of Chagas disease,we pro-vided a reliable basis to effectively control the spreading of Chagas disease.The main research contents are as follows:Firstly,in this paper based on previous research on Chagas disease,the humans and media are infected by this disease?mainly spread by Triatoma?,through Triatoma bites the human skin and sucks the blood of the human body,which contains the pathogen?Trypanosoma cruzi?in human blood and insect?triatomine?in vivo spread each other.In this way the disease is spread between people and animal and combined with the actual fact that infected pregnant women can make the baby infected through maternal transmission?vertical transmission?.We have established a host with Chagas disease dynamics model of vertical transmission.We discuss in two cases when the vertical transmission rate of p=0and 0<p<1,and get this conclusion:?1?When p=0 there is always a disease-free system in the system and it is locally asymptotically stable when R₀<1,it has a positive equilibrium point and locally asymptotically stable when R₀>1;?2?When 0<p<1 the system always has a positive equilibrium point and locally asymptotically stable.In the end,according to the Lyapunov function we prove the global stability of the equilibrium point.In the real life Chagas disease can be controlled by the related factors to reduce the spreading of the disease.For example,pregnant women's should also do regular grams Trypanosoma sera tests during pregnancy.Secondly,we considered the incubation period of chagas disease and the vertical trans-mission of the disease,based on the transmission mechanism of the disease and various ways of transmission.Different incidence rates are used in this paper,which is closer to reality.Through the analysis of the model of the existence and stability of the model are discussed at the vertical transmission rate of p=0 and 0<p<1.When the vertical transmission rate of p=0,the basic reproduction is calculated.The regeneration number is R₀.The system always has a disease-free equilibrium in this case and there is a local asymptotic stability of the disease-free equilibrium point when R₀<1.The system could have two,one or zero positive balance point;When the vertical transmission rate is 0<p<1,There is no disease-free equilibrium in the system,and there may be a positive balance in different conditions.