Estimating Domains Of Attraction Of A Class Of Infectious Disease Model

Over the past decades, there has been a rapid development in the infectious disease dynamics theory, and large numbers of mathematical models are used to analyze a variety of infectious disease. Through the research of infectious disease dynamics model, we can understand the transmission mechanism, which is beneficial for the decision-making departments to take corresponding control measure. Studying deeply about domains of attraction (DOA) of this system can play a key role in directing relevant departments to determine and forecast the development trend of infection. Therefore, it is necessary to explore the domain of attraction of infectious disease model further.In this paper, we study a class of nonlinear autonomous epidemic model that is with a non-constant input, bilinearity contact rate, considering the population density dependent, the incubation period and isolation term. On the basis of analyzing the stability of the equilibrium point, a new method for constructing Lyapunov functional is introduced. By combining the Lyapunov function and the optimization theory, the domain of attraction problem is transformed to a class of constrained optimization problem, and the domain of attraction of the system is obtained with the aid of the GLOPTIPOLY procedures in MATLAB.In this note, a kind of method based on moment theory to solve the attraction domain of the system is investigated. We introduce the basic concepts and some theories in moment theory research, at the same time, the primal optimization algorithm of moment theory are also being given. Thus, the problem of solving the domain of attraction of the system can be transformed to solving constrained optimization problem based on the theory of the moment. And then, with the help of MATLAB LMI toolbox, we get the domain of attraction of the system. Numerical computation and simulation shows that the domain of attraction obtained by this method is significantly greater than the former. It also fully embodies the superiority of this method in estimating the domain of attraction of the system, so it will be a more valuable tool to estimate the domain of attraction.