Hybrid algorithm for efficient simulation of spreading processes on adaptive networks

Abstract

The transmission of different phenomena takes place when individuals interact in ways relevant to the specific transmission route. The definition of "contact" varies depending on the modelled phenomenon. For instance, sexual encounters are relevant for the transmission of sexually transmitted diseases (STDs), while close proximity is significant for airborne infections. To improve the accuracy of the simulation of the spread of phenomena of different origin, researchers have advanced various network models in previous studies. These models aim to better capture the dynamics of disease transmissions and their relationship to contact patterns.

In cases where the contact dynamics occur at a much slower pace than the spreading dynamics, leading to transmission whenever contact is made, it is sufficient to focus exclusively on the contact dynamics. If the network undergoes gradual changes and remains mostly unaffected throughout an outbreak, approximating it as a static network would be suitable. However, there are specific circumstances in which it becomes vital to consider both the dynamic nature of the contact network and the spread of the phenomena. Such consideration becomes particularly relevant when these two processes unfold at comparable timescales, and network modifications can shape the trajectory of the spread. In such circumstances, it is vital to include these changes in the analysis to obtain a comprehensive understanding of the dynamics of the spread. This research work addresses a specific scenario in which the temporal processes of the contact changes and the spreading process are closely interconnected. In this scenario, the occurrence of spreading events directly influences the structure of the network, subsequently influencing the subsequent spread of the disease. This adaptive behaviour enables a more realistic representation of behavioural changes that arise when individuals become aware of their infection and make choices such as self-isolation. This approach allows to capture the interplay between contact patterns and the progression of the spreading process, providing valuable insights into how different phenomena propagate within a population.

The necessity of this work arises from the critical need to balance accuracy and computational efficiency in simulating spreading processes on adaptive, time-evolving networks. The challenge in simulating transmission models on time-evolving adaptive networks stems from the stochastic nature of both spreading processes and contact behaviour. Choosing an appropriate stochastic simulation algorithm is challenging due to this dual stochasticity. While a range of stochastic simulation algorithms exists, selecting a suitable method is not straightforward. Approximate algorithms offer rapid computation but may compromise simulation accuracy and predictive reliability. Conversely, exact simulation algorithms yield accurate predictions but can suffer from computational inefficiency and protracted simulation times. This often hampers research progress and limits the generation of a sufficient amount of simulation trajectories for robust predictions. A distinct category of algorithms is available that allows for the explicit integration of internal dynamics and the evolution of contact network structures within simulations. However, these algorithms predominantly lack the capability to incorporate adaptive responses, a critical aspect of dynamic and responsive modelling in complex systems.

This thesis presents the development and validation of a novel hybrid algorithm, bridging gaps in current methodologies by combining the exact simulation of spreading dynamics with faster, either exact or approximate, simulations of contact dynamics. This methodology focuses on accurately simulating and predicting spreading dynamics while maintaining reliable statistics of contact behaviour, significantly enhancing computational performance for real-world scenarios.