Analyzing The Transmission Dynamics Of Brucella

Biochemical weapons include biological and chemical weapons. Biological weaponsare composed of biological agents and their release devices. For biological weapons, a fewagents can cause massive infection of the human or animals. Biological warfare agents referto pathogenic microorganism and toxins which are usually used to kill human, livestock anddestroy crops. Brucella is a parasitic bacteria in animal and human cells which easilyinvades organism and causes the body to be infected. It has strong infectivity, larger damageto the human body and long duration, and even affects the growth of the next generation ofhuman.Dynamics method is one of the most powerful mathematical tools to accurately depictthe internal mechanism, to reveal the evolution rules with time, to forecast the future trend,and to evaluate the effects of various factors on the development of things. This thesismainly applies dynamics method to study transmission mechanism of brucella, and to assessthe effect of control measures on the prevention and control of brucella. The study not onlyhas strategic importance, but also has certain practical significance. On one hand, bacteriacan be used as a kind of chemical and biological weapons. Once it is used in the war byterrorists or hostile countries, humans and environment can be damaged on a large scale.Although the international organization has banned research and development about thebacteriological weapons, it cannot be neglected that some terrorists try to develop bacteriaweapons in secret. Therefore, from the point of national security, this study can be used as atheoretical foundation for emergency processing of brucella in case of terrorist attacks or inthe war. Brucellosis, on the other hand, is a recognized, global and most serious zoonoticinfectious diseases. Among more than200countries around the world, nearly170countrieshave reported brucella epidemics. Since the1990s, the disease has been rising in the globalscope. The purpose of the study is to understand the propagation law and developing trendof brucella, and to provide theoretical support for the prevention and control of brucella. In this thesis, various dynamical models are established to solve several practicalproblems involved in brucella spreading. To test and verify the rationality of the models, toincrease persuasion of the results of the study and to improve the practical significance ofthe research contents, this thesis combines real cases in some regions and dynamical modelsto carry out numerical simulations. The main research content of this thesis is divided intofour parts.1. Suppose that terrorists randomly put infected individuals to a certain region to carryout terrorist attack. Based on this background, both stochastic dynamic models and thecorresponding deterministic models are established to discuss the effect of randomimmigration of the infected individuals on the spread of diseases in the area, and to preventbrucella CBW attacks of terrorists. Theoretically, the dynamics of the deterministic model isanalysed. In addition, combined with the actual data, the least square parameter estimationmethod is used to simulate the stochastic model, to predict the trend of brucellosis, and toevaluate the effect of prevention and control measures. Through the research for dairybrucella in Zhejiang, it is obtained that the following measures can be taken to prevent andcontrol the terrorist attack:(1) Increasing the force of monitoring for the input of theindividuals.(2) Disinfect the environment regularly. The frequency of disinfection need bepaid attention.(3) Controlling the number of individuals in the area.2. The case data over the years in some traditional brucellosis areas has obviousseasonality. To excavate inducing factors of the periodic phenomenon of brucellosis, anonautonomous dynamical model is established to describe the spread of brucella betweensheep and human. The influence law of inducing factors on the peak value and the numberof peaks of human cases can be mastered to provide theoretical basis and guidance forestablishment of brucella prevention and control measures. First of all, dynamical behaviorof the model is analyzed. Epidemics transmission threshold is obtained. Global stability ofthe disease-free periodic solution and the existence of positive periodic solutions are proved.Moreover, the data fitting about human cases confirms the rationality of the model, at the same time also shows that the current periodicities of birth, sale and discharging brucellacan indeed lead to the observed cyclical phenomenon about the number of human cases. Bysensitivity analysis, it is found that with the change of the peak time of birth, sale of sheepand bacterium discharge, the peak value about the number of human cases and the numberof peak will change.3. Suppose that a target area has been attacked by a terrorist using chemical andbiological weapons, individuals and the environment in the area are infected with brucella.With the individual migration and the diffusion of bacteria between regions, brucellosis willquickly spread to other areas. Based on this background, a patch dynamics model withindividual migration is established to study the transmission mechanism of brucella amongsome regions to prevent the use of chemical and biological weapons. First, the dynamicalbehavior of patch model is analyzed. Moreover, by numerical simulations of propagation ofbrucella between two patches, the following conclusion is drawn. The relationship betweenthe migration of susceptible individuals and the basic reproduction number is nonlinear. Theinfluence of the spreading of the infectious individuals on the basic reproduction numberdepends on the diffusion rate of susceptible individuals. In general, in order to reduce thebasic reproductive number, the size of the two patches should be made to be equal.4. Based on that the total population in an area has a strong correlation with thespreading trend of brucellosis, a dynamic model about population size is established topredict the trend of human population, and to provide theoretical foundation for the researchon the spread of brucellosis in China. China’s family planning policy and the age structureof the population are considered in model. The human population data from1986to2012are used to verify the rationality of the model. By numerical simulations of the model, it isfound that the fertility rate before2006is continued to be adopted, the total number ofhuman population in China would continue to rise. If fertility rate after2006is continued tobe adopted, the total number of human population in China will increase firstly, thendecrease. Finally, the sensitivity analysis of parameters implies that, mathematically, late marriage and late child birth and increasing the time interval of birth between the first childand the second child birth are helpful to slow down the speed of population growth.