From Particles to People: Vicsek-Inspired Behavioural Modelling Frameworks

Abstract

In this thesis, we develop different modelling frameworks to capture the processes of opinion formation and disease spread. The common theme binding them is a nearest-neighbour-based interaction rule; while the closeness of opinions fosters inter-personal interactions, physical proximity facilitates disease spread. Since the nearest-neighbour rules with dynamic local interactions have been shown to enable consensus about the heading of self-propelled particles in a non-equilibrium system, we adapt the Vicsek model. In the first part of the thesis, we discuss two modelling frameworks that are rendered suitable for the study of opinion formation and influence diffusion. We work on the presumption that the agents' opinions are analogous to directions in the opinion space. We assume that the agents with vectorial opinions related to a common subject form groups. We characterise these groups by the distribution of the initial opinions of the agents, and accordingly, they are either Conservative or Liberal. This modelling aspect exclusive to our work is intended to capture the impact of opinion bias of the group on the eventual behaviour. We also account for the heterogeneity among agents and broadly classify them into rigid and flexible. Although this classification does not seem unique, their characterisation differs from the conventional ones. It is based upon the inclination of agents to update one's opinion and susceptibility to the influence of peers with contrasting opinions. Since the interactions among agents of a group on virtual social platforms are oblivious to the physical distances separating them, we assume them to be arranged on a time-varying and directed influence network. In the first model, the agents are placed on directed influence networks based on opinions, individual tolerance and familiarity. In contrast, the network is generated using Watt-Strogatz's model in the second. This arrangement of agents is unlike the uniform random distribution of particles inside the square box. Additionally, not all interactions are equal; some are more important than others and is quantified using inter-personal weights. The two processes, opinion formation and evolution of the network, in tandem, give rise to several behavioural patterns. We evaluate trends in the behaviour of groups upon varying several model-specific parameters through extensive simulations. In the second part of this thesis, we discuss two other modelling frameworks proposed to capture trends in disease spread due to human mobility. While the opinion models borrow the directional attributes of particles from the original formulation of the Vicsek model, the motion of the self-propelled particles is of interest in the context of the spread of infectious diseases. However, the rules governing the movement of particles cannot describe the human movement straight away, thereby necessitating suitable modifications. We propose an agent-based framework equipped with a population mixing algorithm and stochastic disease transmission and evolutionary dynamics. The population mixing algorithm incorporates the simple rules governing the movement of particles in the Vicsek model, together with collision avoidance and goal following to mimic human motion. This algorithm generates human motion patterns ranging from short-distance and long-distance movement to activity-driven mobility. On the other hand, the disease models characterise the health condition of agents using three crucial traits of the disease, (1) infection status, (2) severity and (3) awareness, endowed with age-dependent probabilities for transmission, progress and recovery of the disease. The representative population, motion model and stochastic age-specific disease transmission dynamics are used to evaluate different scenarios. The scenarios are combinations of different motion patterns of the agents; we have chosen them to reflect restricted human mobility during phases of the COVID-19 outbreak from the past.