Coupled Evolutionary Behavioral and Disease Dynamics under Reinfection Risk

We study the interplay between epidemic dynamics and human decision making for epidemics that involve reinfection risk; in particular, the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered-infected (SIRI) epidemic models. In the proposed game-theoretic setting, individuals choose whether to adopt protection or not based on the trade-off between the cost of adopting protection and the risk of infection; the latter depends on the current prevalence of the epidemic and the fraction of individuals who adopt protection in the entire population. We define the coupled epidemic-behavioral dynamics by modeling the evolution of individual protection adoption behavior according to the replicator dynamics. For the SIS epidemic, we fully characterize the equilibria and their stability properties. We further analyze the coupled dynamics under timescale separation when individual behavior evolves faster than the epidemic, and characterize the equilibria of the resulting discontinuous hybrid dynamical system for both SIS and SIRI models. Numerical results illustrate how the coupled dynamics exhibits oscillatory behavior and convergence to sliding mode solutions under suitable parameter regimes.Comment: arXiv admin note: text overlap with arXiv:2203.1027

A Game Theoretical Method for Cost-Benefit Analysis of Malware Dissemination Prevention

Copyright © Taylor & Francis Group, LLC. Literature in malware proliferation focuses on modeling and analyzing its spread dynamics. Epidemiology models, which are inspired by the characteristics of biological disease spread in human populations, have been used against this threat to analyze the way malware spreads in a network. This work presents a modified version of the commonly used epidemiology models Susceptible Infected Recovered (SIR) and Susceptible Infected Susceptible (SIS), which incorporates the ability to capture the relationships between nodes within a network, along with their effect on malware dissemination process. Drawing upon a model that illustrates the network’s behavior based on the attacker’s and the defender’s choices, we use game theory to compute optimal strategies for the defender to minimize the effect of malware spread, at the same time minimizing the security cost. We consider three defense mechanisms: patch, removal, and patch and removal, which correspond to the defender’s strategy and use probabilistically with a certain rate. The attacker chooses the type of attack according to its effectiveness and cost. Through the interaction between the two opponents we infer the optimal strategy for both players, known as Nash Equilibrium, evaluating the related payoffs. Hence, our model provides a cost-benefit risk management framework for managing malware spread in computer networks