Analysis Of Pair Approximation Model Based On Sexually Transmitted Diseases

In the process of human evolution,venereal diseases have been harming human health in many aspects.If we can't find and treat the STD in time,it can not only damage the reproductive organs of human,but also cause infertility.Some STDs can also damage the heart,brain and other important organs of human body,even lead to death.Once some venereal diseases are infected,they are difficult to cure,such as condyloma acuminatum,genital herpes,etc.Curable or curable STDs include gonorrhea,syphilis?early syphilis?,etc.In a word,venereal diseases have existed since ancient times,but due to the expansion of human activities,increased communication,more casual sexual behavior,the scope of venereal diseases is expanding.Therefore,it is very important to use mathematical model to study sexually transmitted diseases.Considering the heterogeneity of human contact,the research based on the dynamics of network infectious diseases will be more practical and the established model will be more accurate.It is a very effective mathematical method to approximate or to approximate the model.It can not only simulate the same disease caused by different viruses in the population,but also capture the changes of the network topology in the spread of the disease.It is an effective method to study the spread law of the disease by using the single node and the side variables between nodes in the network to make a prediction.However,there are few applications of approximation model in the process of sexual transmission.Therefore,this paper mainly does two aspects.First,the SIS pair approximation epidemic model with heterosexual contact is established on the static rule network,and its equilibrium point and dynamic behavior are analyzed;second,the idea of disconnection and reconnection is added to the dynamic network considering the birth and death of the population,and the idea of difference is established The SIS pairs of sexual and homosexual contact approach the infectious disease model,and analyze its equilibrium point and dynamic behavior.The main contents are as follows:The first chapter introduces the research significance of complex network modeling,the methods of pair-approximation and dynamic network disconnection and reconnection and some related network knowledge,and the research progress of complex network in sexual disease transmission at home and abroad.Finally,the main contents and methods of this paper are introduced.Sexual contact is the main transmission route of sexually transmitted diseases,which is a social relationship by sexual relations forms sexual contact network,It is more practical and accurate to estabilish a modeal to study sexually transmitted diseases on the network of sexual contact.Therefore,this article on the sexual contact network considering the contain heterosexual sexually transmitted diseases established the susceptible person-infected person-susceptible person?SIS?propagation model.Using the Internet for approximation method became a 8 d closed differential system and calculated the model of the basic reproduction number R₀.Furthermore,the existence and stability of all kinds of equilibrium points of the model are illustrated by numerical simulation.In the third chapter,based on the impact of birth and death on the spread of disease and network structure,a model of heterosexual and homosexual contact SIS with birth and death is established.When the number of neighbors of the infected individuals obeys the binomial distribution,a high dimension closed differential system is obtained by using the pair-approximation method on the interest network.In this chapter,it is considered that disconnection and reconnection are more suitable for life,the model is more accurate,and the scope of application is also expanded.Through theoretical analysis,the existence of disease-free equilibrium point is obtained and the basic regeneration number R₀ is given.Furthermore,the existence and stability of all kinds of equilibrium points of the model are illustrated by numerical simulation.