Models of spreading processes over nontrivial networks are commonly motivated by modeling and analysis of biological networks, computer networks, and human contact networks. However, learning the spread parameters of such models has not yet been explored in detail, and the models have not been validated by real data. In this paper, we present several different spread models from the literature and explore their relationships to each other; for one of these processes, we present a sufficient condition for asymptotic stability of the healthy equilibrium, show that the condition is necessary and sufficient for uniqueness of the healthy equilibrium, and present necessary and sufficient conditions for estimating the spread parameters. Finally, we employ two real data sets, one from John Snow's seminal work on cholera epidemics in London in the 1850s and the other one from the United States Department of Agriculture, to validate an approximation of a well-studied network-dependent susceptible-infected-susceptible model. Index Terms-Epidemic processes, John Snow's cholera data set, networked control systems, nonlinear systems, system identification in biomedical applications, validation of networked systems. S PREADING processes have been studied in many fields. In the systems and control community, the main interest has been on susceptible-infected-susceptible (SIS) spread models over nontrivial networks. These models have been proposed for discrete time [1]-[8] and continuous time [4] , [9]-[13] and are based on an infection parameter β and a healing rate δ. A virus model is called homogeneous if the infection and healing rates are the same for every agent, and heterogeneous if they are different for each agent. In this paper, we will focus on discrete-time SIS models, mainly for the more general, heterogeneous models, but exploring estimating the spread parameters of homogeneous models as well.
To the best our knowledge, there exist no results on the stability of the endemic equilibrium of the networked discrete-time SIS model in REF for general initial conditions.
Analysis, Estimation, and Validation of Discrete-Time Epidemic Processes
IEEE Transactions on Control Systems Technology
IEEE Transactions on Control Systems Technology
Computer Science Mathematics