Modeling The Transmission Dynamics Of Clonorchiasis And The Analysis Of Competition System

In this thesis,we set up a corresponding dynamic model to discuss the transmission rule of clonorchiasis disease.By using a series of related mathematical theories and methods,we had obtained valuable results when we analysed some dynamic behaviors of the models carefully.It is of great theoretical and practical significance for the purpose of guiding prevention and control efforts.The dynamic interaction between competitive Lotka-Volterra systems has long been a research focus in mathematical biology,and will continuous being one of the dominant topics in both ecology and mathematical ecology for its universality and important prac-tical significant.The competitive Lotka-Volterra systems have been widely studied,such as investigating the stability,permanence,existence of positive equilibrium and proving the global state,and other tremendous results were obtained.In reality,the interference of various external environmental factors is ubiquitous in the actual survival of the species,which will affect all aspects of species growth to varying degrees.Therefore,it is an practical significance and interesting work to study the dynamic behavior of the perturba-tion system of a deterministic dynamic system affected by the external environment.The content of this paper is as follows:The first chapter is the introduction of the thesis,which mainly introduces the re-search background,research status and difficulties encountered in the research process of clonorchiasis and the competition system,and the main work of this paper is briefly described.In the second chapter,we set up a mathematical model on the basic life cycle of clonorchiasis to fit the data of human clonorchiasis infection ratios of Guangzhou City of Guangdong Province in China from 2006-2012.By this model,we have proved that the condition of the basic reproductive numberR0>1 or R0<1 corresponds the globally asymptotically stable of the endemic equilibrium or the disease-free equilibrium,respec-tively.The basic reproductive number is estimated as 1.41 with those optimal parameters.Some efficient strategies to control clonorchiasis are provided by numerical analysis of the mathematical model.In the third chapter,we propose a deterministic model to describe the spread of clonorchiasis among human-snail-fish populations and use the model to simulate the data on the numbers of inspected and infected individuals of Foshan City,located in Guang-dong Province in the southeast of P.R China,from 1980-2010.Mathematical and nu-merical analyses of the model are carried out to understand the transmission dynamics of clonorchiasis and explore effective control measures for the local outbreaks of the dis-ease.We find that(i)the transmission of clonorchiasis between cercariae to fish plays a more important role than that from eggs to snails and from fish to humans;(ii)As the cycle of infection-treatment-reinfection continues,it is unlikely that treatment with drugs alone can control and eventually eradicate clonorchiasis.These strongly suggest that a more comprehensive approach needs to include environmental modification in order to break the cercariae-fish transmission cycle,to enhance awareness about the disease,and to improve prevention measures.The fourth chapter,considering the survival status of the two competing species and the influence of the surrounding environment on the competitive state,we analyze and study the dynamic behavior of the perturbation system,which is corresponding to a class of simple competitive systems and based on the idea and method of ordinary differential equations.Under the condition of the existence of the positive equilibrium point of the original competitive system,the full space analysis is carried out on the parameters of the perturbation term,including the existence of the non-negative equilibrium point of the perturbation system,the behavior of the nonnegative equilibrium point,the existence of the infinite singularities and their behavior,the existence of limit cycles and the global analysis of the perturbation system under different conditions are carried out,too.In the fifth chapter,the original competition system is improved closer to the actual biological background,and we consider its disturbance system,too.Although the im-provement of the competing system is less,but the analysis of the dynamic behavior of the perturbation system is become more complex.For the perturbation system of the im-proved competitive system,we analyze the perturbation system in the full parameter space through parameter variation,including the existence of the corresponding non-negative e-quilibrium point in the range of different parameters,the existence of the non-negative equilibrium point,the existence of the infinite singularity and its behavior and the exis-tence of limit cycles Similarly,the drawing software is used to draw the corresponding global phase portraits in all cases.Finally,we summarize the current works and make a prospect for the future works.