Numerical Analysis of Discrete-time Networked Competitive Bivirus SIS Models
Published in Gulf Coast Undergraduate Research Symposium, 2024
Abstract:
The study of epidemics and virus simulations plays a crucial role in understanding and controlling infectious diseases. In a globally connected world, the ability for viruses to spread rapidly across populations has led to public crises like the COVID-19 outbreak. Mathematical modeling and computational simulations provide quantitative tools to predict the course of such epidemics, formulate control strategies, and ultimately save lives. While extensive research has been done on single viruses, we focus on cases where two viruses compete as they propagate through the population. Moreover, unlike most models, our model takes a discrete-time approach, closely matching how virus data are collected - in discrete time frames.
Our research models the epidemic process using the susceptible-infected-susceptible(SIS) framework, which assumes that individuals who recovered from infection may become susceptible again. Firstly, we establish theoretical foundations that give sufficient conditions for the system to reach three main outcomes: the complete eradication of both viruses, the eradication of one virus while the other remains present over time, and the scenario where both viruses coexist in the population over time. Based on the theoretical foundations, we explore these virus-spreading dynamics through computational simulations and numerical results. We generate random infection and healing rates that align well with realistic virus transmission and recovery assumptions. In addition, we simulate the spread of infections over networks of varying structures, such as random graphs or varying connectivity and real-world graphs of population flow, to validate key results from the theory, which includes the conditions for the existence and stability of the outcomes.
Lastly, we use real-life network data such as the Massachusetts County Travel Graph and the New York City Taxi Cab data to gain insights into closely matching how virus competition and coexistence play out in practical settings, which emphasizes the relevance of the model in understanding real-world epidemics. For instance, the model could predict how multiple strains of a single virus, or even multiple viruses, interact within a population, which can then be used to control and suppress their spread.
Future work will focus on improving the model by incorporating the time-varying nature of real-world networks into the simulations, bringing the model even closer to the complexities of real-life virus dynamics.