The Qualitative Analysis Of Epidemic Disease With Vertical Transmission On Static Networks

Complex network has been rapidly developed as an emerging discipline in recent decades,many practical problems can be studied as a complex network model in the real world.For example,a lot of the spread process of infectious disease can be studied by the method of complex dynamic network,etc.The transmission dynamics are static network without birth and death in most of the existing network,but for infectious disease model with birth and death of the network,because born will lead to the growth of the network,and death can cause the attenuation of the network,it will affect the structure of the network.The research results is not substantial,at present there are mainly two forms,one kind is to join the empty node,degree distribution is still given,the sum of population node and empty node remains unchanged,and its essence is still a static network.The other is a complete dynamic network,whose network structure,including the degree distribution is changeable dynamically.This paper gives infectious disease dynamics modeling and analysis in the first form,the research model is as follows:In this paper,the conclusion is as follows:If R₀<1,the disease-free equilibrium of the system is globally asymptotically stable,and diseases will be eradicated;if R₀>1,the system exists a unique endemic equilibrium,and if there is a positive initial value,the disease may continue to exist in the population.Throughwe know that R₀ is monotone decreasing function of vaccinal parameters of m₀,so vaccinal parameters is crucial adjective for controlling R₀.At the same time,by the definition of R₀,it is defined as the ideal coverage level of vaccination of disease eradication.It shows that the disease will be eradicated if m₀>m_c.