Modeling And Analysis Of The Sexually Transmitted Disease With MSM And Vaccination

The widely spread of sexually transmitted disease(STD)has seriously threaten the health of human.Because of our country's social culture to the same-sex sexual behavior ostracism,the men who have sex with men(MSM)has become the hidden population of STD,which seriously prevents the prevention and control of sexually transmitted diseases.Therefore,it is important to analyze the impact of MSM on transmission of STD.Otherwise,vaccination are widely used as an effective prevention strategy in the prevention and control of sexually transmitted diseases,it is crucial that research voluntary vaccination of high-risk group for the propagate and control of STD.Based on these two consideration,the main contents of this paper as follows:(1)To analyze the impact of MSM on spread of disease,an epidemic dynamic model with MSM is established,the basic reproduction number is given.The dynamic behavior is analyzed,including the existence and global asymptotic stability of disease-free equilibrium,boundary equilibrium and endemic equilibrium.Finally,the theoretical results are verified by numerical simulations.Numerical results show that the control of heterosexual and MSM can effectively control the transmission of STD,but the latter effect is more pronounced.(2)Vaccination is one of the main methods for the control of infectious disease.In this chapter,we establish an infectious disease model with high-risk voluntary vaccination,and give the voluntary vaccination rate combining with the game theory and the logistic function.Furthermore,we calculate the basic reproductive number of the model and prove the existence and uniqueness of the endemic equilibrium.Finally,the impact of voluntary vaccination rate on disease transmission is demonstrated through the numerical simulation.The numerical results show that,it is easier to cause the outbreak of disease when the individual preventive awareness is weak or the assessment about vaccination benefits is more accurate.Simultaneously,we should control the spread of disease information,in order to avoid that too much information prevents the control of disease.