| One of the most concerned issues is the prevention and control of infectious diseases in human.The study found that many factors influence disease transmission,including effective contact rates,media coverage,and vaccination etc.With the economic globalization and technological progress,media plays an increasingly important role in controlling the spread of infectious diseases.Therefore,two eco-epidemiological models are considered and discussed with media influence in this paper.In Chapter 2,a stage-structure eco-epidemiological model with the non-linear media influence is considered.First,the positivity and boundedness of solutions are discussed.Then,the basic reproductive number is given,and the local stability of the trivial equilibrium and disease-free equilibrium is discussed.Next,by taking the infection delay as a bifurcation parameter,the condition of stability switching is given due to the stability switching criterion,which shows that the delay can generate instability and oscillation of the population through the Hopf bifurcation.Further,by using normal form theory and center manifold theory,we obtain some explicit expressions for the stability and direction of periodic solutions.Finally,the correctness of the theoretical analysis is verified by numerical simulation,and the biological explanations are also given.In Chapter 3,an eco-epidemiological model of adulterated food with awareness programs and two time delays is proposed.First,the stability of disease-free equilibrium and the endemic equilibrium without delay is discussed.Secondly,by taking time delay as the bifurcation parameters,the existence of Hopf bifurcation of this model at the endemic equilibrium is given.Next,by using normal form theory and central manifold theory,the expressions of stability and direction of periodic solutions are obtain.Finally,some numerical simulations are given to check the correctness and feasibility of the theoretical results.The obtained results show that both media influence and awareness programs reduce people’s consumption of adulterated food,which plays an important role in the control of diseases. |
