The Study Of Epidemics In Multi-Agent Dynamical Networking Systems

As one mainstream of the early research of theoretical biology/ecology, the study of epidemic dynamics has a long history and has borne fruitful outcomes. It goes without saying that the reason why epidemic dynamics attracts many researchers'persistent attention lies in potential jeopardy caused by the object that prevails in the spreading processes: Infectious diseases contaminate among biological entities, computer viruses proliferate hosts on the Internet, rumors spread among the crowd, to name a few examples of epidemic dynamical behaviors. As recent years step into the so-called'Age of Network Science', researchers turn to the study of complex networks, where epidemic spreading on networks proceeds to be one focus of their researches. However, complicated spreading behaviors in the real world are far beyond what existing models could describe. This presses for a more appropriate model on which a more in-depth exploration of the epidemic dynamics in the real world, its dynamical characteristics and the control strategy can be carried.The dissertation introduced some basic concepts of the complex network, surveys a wide range of related works and current situation of epidemic dynamics on complex networks, and discusses the effects of network topology on the spreading critical value, taking into consideration both time-varying topology and non-constant spreading rates. The dissertation thereafter proposes and studies a model of epidemic spreading on mobile multi-agent systems and its control strategy. Finally, the dissertation studies the epidemic threshold of self-driven particle systems with non-constant spreading rates. The main contributions of the dissertation are summarized as follows. 1. Based on Vicsek model, we propose and study a model of epidemic spreading on mobile multi-agent systems, where each moving agent can spread the infectivity to (or be spread by) any other agents that it encounters in its path. We introduce infectious expressivity (the probability that an infectious agent in system expresses its state, i.e., other agents can recognize the infectious one). We reveal the effects of the infectious expressivity as well as other system parameters such as sensing radius and agent density on the spreading process.2. We propose a spreading control strategy for mobile multi-agent systems aforementioned, where each susceptible agent avoids the infected agents in his sensing neighborhood. The simulation results show that the strategy can enhance the epidemic threshold and is validated for spreading control. Beside, the increase of the infectious expressivity also avails to control the epidemical prevalence.3. We study the epidemic spreading process on self-driven particle systems with non-constant spreading rates. To model the differences among individuals in abilities (like the resistibility to viruses), we introduce susceptibility and infectivity, and prove that there exists the epidemic threshold for the systems under the assumption of the spreading rate in form of multiply of the susceptibility and infectivity, the threshold showing that if the average spreading rate(the average value of multiply of the susceptibility and infectivity over all particles) is larger than the inverse of the average number of a particle's collisions that spread infectivity during one of its infectious periods, then the epidemic will prevail, and otherwise extinct finally. We also illustrate through numerical method the epidemic dynamical behaviors of self-driven particle systems with the mobility and heterogeneity of individuals.