Studies On The Transmission Dynamics Of Several Differential Equation Models For Epidemics

The epidemic model is an important approach to understand the disease spreading mechanism,which can reveal main factors and transmission dynamics that provide guidance for controlling disease.In order to study the human immunodeficiency virus,dengue fever and hydatidosis,we propose three epidemic models: an HIV/AIDS epidemic model with unreported cases,a spatiotemporal model of dengue and a hydatidosis transmission model with complex host populations.We calculate the basic reproduction number using the next generation matrix approach,prove the stability via Lyapunov functions,and explore controlling measures.First,we introduce the background of epidemic dynamics and summarize its development.We further present some basic concepts of epidemic models and preliminary knowledge.Second,we analyze the HIV/AIDS epidemic model with unreported cases,and acquire equilibria and the stability.Simulations describe how baseline parameters effect the HIV/AIDS diffusion,and find that higher report rate on patients is more effective than higher recheck rate on unreported cases.Controlling the transmission rate is another safety measure.Third,we study the SEI-SEIR spatiotemporal model for dengue with human mobility.We acquire the basic reproduction number and the stability.Theoretical and numerical analyses indicate that human mobility is the driving force that triggers dengue diffusion.Results also suggest that human should avoid staying in the risky patch and low resident mobility contributes low patchy infections during the prevalent period.Fourth,based on characteristics of the hydatidosis dispersal among multiple intermediate hosts,multiple definitive hosts and humans,we study a new hydatidosis transmission model with complex host populations,and give the unique existence of equilibria and the condition of stability.Finally,we summarize the main results and provide the possible future research directions.