Stability Analysis Of Two Types Of Brucellosis Infection Models

Brucellosis is an infectious disease caused by brucella,one of the main chron-ic diseases of zoonotic diseases.It is prevalent in more than 160 countries around the world.It can cause infection between humans and livestock and wild mammal-s.The main infections in humans are B.melitensis and B.abortus.Brucellosis can cause intermittent fever,sweating,headaches,joint and bone pain,mental disorders and other symptoms in humans.The disease mainly affects cattle and sheep,and sometimes horses,dogs,pigs,etc.For animals it mainly affects the reproductive sys-tem,causing abortion or infertility in females,and orchitis or epididymitis in males.About human brucellosis infections are mainly caused by contact with infected live-stock,ingestion of unsterilized dairy products and contaminated meat.In animals,brucellosis infection has two ways:one is through direct exposure to infected ani-mals,and indirect transmission through the infected environment.Although animal infectious diseases have been controlled in some developed countries,they are still a common clinical disease in developing countries.The huge economic loss caused by brucellosis has attracted worldwide attention.Due to the early stages of brucellosis,there are no obvious clinical features and it is difficult to diagnose.Strict animal quarantine,combined with slaughter policies and alternative vaccine strategies,are necessary measures to effectively prevent and control the spread of brucellosis.In this paper,two dynamic models of different types of brucellosis transmission were established,mainly from the following two aspects:Firstly,the documents on the dog brucellosis infection show that the overall prevalence rate of canine Brucellosis in Urumqi is about 25 percent,besides,the brucella of canine and ovine species coexists poses a severe threat to public health.Dogs with brucellosis can not only infect other dogs,but also easily infect people,and also release pathogenic bacteria into the environment.Thus we proposed a dynamic model of sheep-dog-human brucellosis transmission.At the same time,we also considered the environmental bacterial infections of sheep,dogs and humans in our model.Ten we have Calculated the basic reproduction number R0.Proved stability of the system using proper Lyapunov functions.If R0<1,the disease-free equilibrium is globally asymptotically stable.If R0>1,the system is uniformly persistent and the only endemic equilibrium is globally asymptotically stable.Secondly,Considered that brucellosis is transmission from mother to child.The disease is mainly transmitted by infected animals,and the fastest period of transmis-sion is the childbearing period and the herd abortion.During pregnancy,Brucella can infect the fetus through the placenta.During delivery,the fetus passes through the maternal birth canal when in contact with the mother's secretions and blood,they can infect brucella,which is called vertical transmission.Therefore we stud-ied the nonlinear dynamic model of brucella transmission in bison populations by horizontal and vertical infection.In the SIR model,we considered the factors of brucellosis in the environment and proposed a new SIRB model.Using the regener-ation matrix to get the threshold R0 of the model.We also proved that the stability of the model equilibrium points.