Individual-Behavior Based Epidemic Spreading in Complex Networks

Abstract

This thesis mainly addresses the problem of modelling and analysing the epidemic spreading processes based on a two-infectious-state epidemic model, i.e. the generalized Susceptible-Exposed-Infected-Vigilant (SEIV) model. We consider several problems in this area, such as taking human behaviors into consideration to refine the epidemic model, where the interaction between human awareness design and epidemic dynamics over complex networks can be properly analysed. We also looked into the problem of state-dependent network structure design based on SEIV model, where the epidemic states are capable to influence people's communication and interaction and hence affect the epidemic spreading process. Finally, the equilibrium and stability analysis of epidemic systems with two different parameter control design are presented.

In the first part of the thesis, we propose a method to represent the effect of human communication and interactions in our daily lives. We assume that people change their behaviors due to the awareness of the epidemics and the awareness comes from the fear of being infected. People gain awareness and fear of the disease from three information sources and a novel awareness design upon two infectious states is proposed to reduce the susceptibility of people, which in turn could affect the threshold and outbreak of the epidemic spreading system. The novel awareness response design is then applied to a continuous mean-field SEIV model to illustrate the effectiveness of restraining the epidemics propagation. The system global exponential stability analysis and epidemic threshold embedded with human awareness are proposed.

The second part considers an adaptive network problem in the epidemic spreading process, however, here the adaptive network is not the same meaning as in the automation control field, the adaptive network in this thesis is used to describe the complex network structure which is adaptive to human interactions and hence influence epidemic transition. A novel adaptive network structure, more precisely a state-dependent network structure, is designed and applied to the mean-field SEIV epidemic model which represents the changing communication behaviors along with the epidemic spreading process. As a consequence and as reflected in our adaptive network design, an individual obtains more protection by reducing the direct contact with infected neighbors due to the fear of the disease, and probably rebuilds connections with neighbors as soon as they are recovered. The adaptive network structure makes the model more consistent with the real epidemic spreading and is illustrated to be effective in curbing the spread of the disease in our simulation.

The last part of the thesis considers the parameter control techniques where different kinds of control method will be applied to the epidemic spreading model and reasonably control the system parameter based on real epidemic spreading processes to achieve good disease suppression performance. We first propose a state-feedback control design to the awareness SEIV epidemic model where only the recovery rate is considered to be controllable. The controller uses one of the epidemic states, i.e. the infected state, as the control input and works for the infected people to effectively cure the disease. Secondly, we propose an integral parameter control scheme based on the effect of medical treatment. The recovery rate and the disease prevention rate are chosen as the controllable parameters in the epidemic spreading system, both of which are closely associated with medical resources allocation in our real lives. The controller is applied to the mean-field SEIV epidemic model with our adaptive network structure design. Both of the control methods are proved to satisfy the exponential stability of the epidemic system and are effective in reducing the epidemic outbreak and inhibiting the epidemic dissemination. Show more