Stability Analysis Of Two Infectious Disease Models

Most infectious diseases have complex stages of transmission after infection,and establish appropriate mathematical models could to study how to control disease transmission.The full text includes two models,the first model is a multistage model of syphilis,which studies the effects of changes in cure rate on the spread of syphilis in different populations,the second is a mathematical model established based on the life history and the transmission route of toxoplasma gondii.First of all,a multistage infectious disease model that divides the population into injecting drug users,female sex workers,clients of the female sex workers,and MSM were established.Through the theoretical analysis and research of the whole model,the basic reproduction number R₀ is calculated.When R₀<1,the disease-free equilibriumE₀ is the globally asymptotically stable,when the R₀>1,the disease-free equilibrium E₀ is unstable and shown that disease is uniform persistence.The part of numerical simulation studies the influence of the change in the cure rate of primary and second of syphilis patients on the basic regeneration number in each group,concludes that improving the cure rate of the primary and second of syphilis patients at the same time,and paying attention to the high-risk population is the key to fundamentally controlling the spread of syphilis.Second,due to no suitable vaccine for toxoplasmosis at present,prevention is important of control disease.Therefore,the chapter establishes the mathematical model based on the life history and transmission route of toxoplasma gondii,and calculate the basic reproduction number R₀ of the model.When R₀<1,the disease-free equilibrium E₀ is the globally asympto-tically stable and the disease will gradually disappear,when R₀>1,the endemic equilibrium E^*is the globally asymptotically stable and the disease will continue to spread.