Building resilience into today’s complex infrastructures is critical to the daily functioning of society and its ability to withstand and recover from natural disasters, epidemics, and cyber-threats. This study proposes quantitative measures that capture and implement the definition of engineering resilience advanced by the National Academy of Sciences. The approach is applicable across physical, information, and social domains. It evaluates the critical functionality, defined as a performance function of time set by the stakeholders. Critical functionality is a source of valuable information, such as the integrated system resilience over a time interval, and its robustness. The paper demonstrates the formulation on two classes of models: 1) multi-level directed acyclic graphs, and 2) interdependent coupled networks. For both models synthetic case studies are used to explore trends. For the first class, the approach is also applied to the Linux operating system. Results indicate that desired resilience and robustness levels are achievable by trading off different design parameters, such as redundancy, node recovery time, and backup supply available. The nonlinear relationship between network parameters and resilience levels confirms the utility of the proposed approach, which is of benefit to analysts and designers of complex systems and networks.

People who inject drugs (PWID) are at high risk for blood-borne pathogens transmitted during the sharing of contaminated injection equipment, particularly hepatitis C virus (HCV). HCV prevalence is influenced by a complex interplay of drug-use behaviors, social networks, and geography, as well as the availability of interventions, such as needle exchange programs. To adequately address this complexity in HCV epidemic forecasting, we have developed a computational model, the Agent-based Pathogen Kinetics model (APK). APK simulates the PWID population in metropolitan Chicago, including the social interactions that result in HCV infection. We used multiple empirical data sources on Chicago PWID to build a spatial distribution of an in silico PWID population and modeled networks among the PWID by considering the geography of the city and its suburbs. APK was validated against 2012 empirical data (the latest available) and shown to agree with network and epidemiological surveys to within 1%. For the period 2010–2020, APK forecasts a decline in HCV prevalence of 0.8% per year from 44(±2)% to 36(±5)%, although some sub-populations would continue to have relatively high prevalence, including Non-Hispanic Blacks, 48(±5)%. The rate of decline will be lowest in Non-Hispanic Whites and we find, in a reversal of historical trends, that incidence among non-Hispanic Whites would exceed incidence among Non-Hispanic Blacks (0.66 per 100 per years vs 0.17 per 100 person years). APK also forecasts an increase in PWID mean age from 35(±1) to 40(±2) with a corresponding increase from 59(±2)% to 80(±6)% in the proportion of the population >30 years old. Our studies highlight the importance of analyzing subpopulations in disease predictions, the utility of computer simulation for analyzing demographic and health trends among PWID and serve as a tool for guiding intervention and prevention strategies in Chicago, and other major cities.

The major route of hepatitis C virus (HCV) transmission in the United States is injection drug use. We hypothesized that if an HCV vaccine were available, vaccination could affect HCV transmission among people who inject drugs by reducing HCV titers after viral exposure without necessarily achieving sterilizing immunity. To investigate this possibility, we developed a mathematical model to determine transmission probabilities relative to the HCV RNA titers of needle/syringe-sharing donors. We simulated sharing of two types of syringes fitted with needles that retain either large or small amounts of fluid after expulsion. Using previously published viral kinetics data from both naïve subjects infected with HCV and reinfected individuals who had previously cleared an HCV infection, we estimated transmission risk between pairs of serodiscordant injecting drug users, accounting for syringe type, rinsing, and sharing frequency. We calculated that the risk of HCV transmission through syringe sharing increased ~10-fold as viral titers (log IU/ml) increased ~25-fold. Cumulative analyses showed that, assuming sharing episodes every 7 days, the mean transmission risk over the first 6 months was >90% between two people sharing syringes when one had an HCV RNA titer >5 log IU/ml. For those with preexisting immunity that rapidly controlled HCV, the cumulative risk decreased to 1 to 25% depending on HCV titer and syringe type. Our modeling approach demonstrates that, even with transient viral replication after exposure during injection drug use, HCV transmission among people sharing syringes could be reduced through vaccination if an HCV vaccine were available.