Dynamic Analysis Of HIV/AIDS Patch Model With Sexual Transmission

Acquired Immune Deficiency Syndrome（AIDS）,also known as acquired immunodefi-ciency syndrome,is an infectious disease caused by human immunodeficiency virus（HIV）.HIV/AIDS is mainly transmitted through three ways:sexual contact,blood transmission and mother to child transmission.In recent years,sexual contact has become the most important way of transmission.The number of people infected with HIV/AIDS in China has increased year by year.In the process of population migration and travel,HIV/AIDS can easily spread from one region to another.Therefore,it is of great significance to study the spread of HIV/AIDS among regions.In this paper,HIV/AIDS multi-patch models are established by considering two genders separately to study the impact of population migration and travel on the spread of HIV/AIDS,which is conducive to preventing and controlling the spread of AIDS among regions.Firstly,an HIV/AIDS multi-patch model with Euler movement is established to study the impact of population migration on the spread of HIV/AIDS between patches.The nonnegative and boundedness of the model solutions are given.The basic reproduction number R₀ of the model is calculated by using the next generation matrix.When R₀<1,the disease-free equilibrium is globally asymptotically stable;when R₀>1 and certain conditions are satisfied,the endemic equilibrium is globally asymptotically stable.The model is applied to two patches,Beijing City is regarded as the first patch,and Yunnan Province is regarded as the second patch.Numerical simulations are carried out.Time series diagrams under different conditions are presented,the relationship between R₀ and migration rates is shown by contour plots,the change trend of infected individuals and AIDS individuals with or without migration was compared.The parameters sensitivity of R₀ is analyzed.The results suggest that migration may increase or decrease the spread of disease.Secondly,an HIV/AIDS multi-patch model with Lagrange movement is established to study the impact of travel on the spread of HIV/AIDS between patches.The nonnegative and boundedness of the model solutions are given.The basic reproduction number R₀ of the model is calculated by using the next generation matrix.When R₀<1,the disease-free equilibrium is locally asymptotically stable;when R₀>1,the disease is uniformly persistent.The model is applied to three patches,Yunnan Province is regarded as the first patch,Beijing City is regarded as the second patch,and Tianjin City is regarded as the third patch.Three different connection types are considered and numerical simulations are carried out.Time series diagrams under different conditions are presented,the relationship between R₀ and travel and return rates is shown by contour plots.The parameters sensitivity of R₀ is analyzed.The results suggest that travel may increase or decrease the spread of disease.The travel and return rates have different impact on R₀ for different connection types.Finally,we make a summary and prospect of this paper.