Improvement And Stability Analysis Of Two Types Of Infectious Disease Models

Treatment is a crucial step for infectious diseases.Chapter 2 of this paper considers treatment for the AIDS model.According to the four stages of HIV infection,the population is divided into five categories:susceptible population,asymptomatic HIV-positive population,pre-HIV HIV positive patients who have not received treatment,and untreated full-blown AIDS patients.AIDS patients,those receiving treatment.At the same time,we consider that some of the asymptomatic HIV-positive people enter the pre-HIV-positive but untreated HIV patients,while the other part enters the full-blown AIDS patients but does not receive treatment.HIV model of AIDS patients is analyzed.The existence and stability of disease-free equilibrium and endemic equilibrium are discussed by using basic regeneration number,qualitative and stability theory of differential equation.Conclusion:When R₀<1,the disease disappears,and when R₀.1,the positive equilibrium is globally asymptotically stable.Diseases are widespread.Finally,numerical simulation is used to verify the correctness of the results.In the third chapter,we study the model of hepatitis C,and consider the primary infection and reinfection.The characteristics of primary infection and reinfection are very different.We use the qualitative and stability theory of differential equation to analyze the dynamic behavior of the system.The results show that in the case of distinguishing primary infection from reinfection,the system will produce backward branches when R₀=1 and R_C>1.