Dynamic Analysis Of Sheep Brucellosis Model

"Brucellosis"is a zoonotic infectious disease also called wavy heat,spreading in many countries and regions.The disease caused by Brucella,classified as zoonotic disease B.Clinical features is heat,sweating,joint pain.Sheep brucellosis is more common than bovine brucellosis in China.The epidemic areas are concentrated on Inner Mongolia,Xinjiang,Tibet and Qinghai.Human infected by contact with infected animals.Brucella also enter the body from the digestive tract by eating infected food.Animals infected mainly through respiratory,mucosal,and sexual organ.Brucella can also transmitted by contaminated air.it's seriously harmful to reproductive organs,causing miscarriage,infertility,etc..Brucellosis is one of the major public health problems.With increasing of the spread of the disease,relevant departments pay more attention on it.Considering the trend of brucellosis,it is im-portant to study the rule of infection,pathogenesis,and control strategies.Different diseases have different transmission characteristics.The dynamics of infectious dis-eases is a discipline for theoretical research.It reveals transmission rules from the perspective of disease transmission principle.Using qualitative and relevant theory,the related strategies to prevention diseases were put forward,which provided us a better way to understand.In this paper,several different types of brucellosis model are established.This paper is organized as follows;Firstly,according to the growth of sheep have age-structure,a six-dimensional of a sheep brucellosis model with different infection rates is studied.After calculating the basic reproduction number R0,we have proved the existence and global asymp-totic stability of the equilibrium.Numerical simulation verified the conclusions.We concluded that increasing the times of disinfection and the rate of immunity have a good effect on disease control.Secondly,by the rising of living standards of the people,the needs for dairy and meat products is increased,causing the raise of sheep trade frequently.Brucellosis have latent,period,the symptoms of the latent individuals are not obvious,so a model of sheep brucellosis with external and exposed stage is established,a more general exponentiation term is used for birth rate.The basic reproduction number of the model is obtained.We analyzed the local and the global stability of disease free equilibrium,which exists if the immigration occurs only in the susceptible class.When all the classes have external input,the model admits a endemic equilibrium,and we proved it s global stability under some conditions.Finally,based on the incident of Jilin Changchun Changsheng Biopharmaceuti-cal Company in July 2018,a model with imperfect vaccination(which represents the false vaccine incident)and indirect transmission is considered.In the second part of this Section,an optimal control model of brucellosis is considered which takes the increase of vaccined individuals,government policy regulation on the quality of vaccines and disinfection frequency into account.Using optimal control theory we proved the existence of optimal control solution and got the expression of the solution.We concluded that the government s strict regulations on the vaccine pro-duction,increasing the environmental disinfection rate and vaccination rate will be very efficient in controlling the disease.