Epidemic Spreading On Complex Networks

Complex networks are all around us. Neural networks, food web networks, socialinteraction networks, Internet and World Wide Web are only few examples of complexnetworks. Networks can represent systems composed by a large number of highlyinterconnected dynamical units. Apparently, these networks are different; however, theyhave some important common features, for example, small-world effect, scale-freeproperty, community structure and so on. These properties of networks play an importantrole in spreading processes taking place on networks. The spread of computer virus,human disease outbreak, and rumor and information transmission are typical spreadingprocesses, which can be modeled by spreading epidemics on complex networks.Firstly, the impact of scale-free properties and community structure on the spread ofepidemics on networks has been considered in this article. Considering the stochasticnature of epidemic spreading, we proposed a stochastic epidemic model. In this model,there are two types of infectious contacts, namely, local contacts and global contacts. Allthese contacts are modeled by Possion processes. Different infectious contacts can resultin different types of offspring. At early stages of epidemic spreading, the change of thenumber of infected individuals can be approximated with a two-type branching process.By this approximation, the basic reproduction number can be derived. We also performedindividual-based simulations to study the impact of community sizes and communitystrength on the spreading of epidemics on scale-free networks with different degreedistributions.Moreover, the infection awareness of individuals in networks and their behavioralchanges have been considered. An epidemic spreading model incorporating behavioralchanges has been proposed. In this model, individuals are divided into households andthe defensive action toward epidemic spreading is taken by the household as the basic unit. The results show that the behavioral changes can reduce the prevalence size ofepidemic outbreaks and slow down the epidemic spreading. Also, the number of infectedhouseholds has been introduced to measure the epidemic outbreaks. It has been shownthat the adaptive behavior patterns can lead to the decrease of resource needed in thecontrol of epidemics.