Pathogen transfer through environment-host contact: an agent-based queueing theoretic framework

Abstract

Queueing theory studies the properties of waiting queues and has been applied to investigate direct host-to-host transmitted disease dynamics, but its potential in modelling environmentally transmitted pathogens has not been fully explored. In this study, we provide a flexible and customizable queueing theory modelling framework with three major subroutines to study the in-hospital contact processes between environments and hosts and potential nosocomial pathogen transfer, where environments are servers and hosts are customers. Two types of servers with different parameters but the same utilization are investigated. We consider various forms of transfer functions that map contact duration to the amount of pathogen transfer based on existing literature. We propose a case study of simulated in-hospital contact processes and apply stochastic queues to analyse the amount of pathogen transfer under different transfer functions, and assume that pathogen amount decreases during the inter-arrival time. Different host behaviour (feedback and non-feedback) as well as initial pathogen distribution (whether in environment and/or in hosts) are also considered and simulated. We assess pathogen transfer and circulation under these various conditions and highlight the importance of the nonlinear interactions among contact processes, transfer functions and pathogen demography during the contact process. Our modelling framework can be readily extended to more complicated queueing networks to simulate more realistic situations by adjusting parameters such as the number and type of servers and customers, and adding extra subroutines.

Fig. 1.

ABM diagram and subroutine description. Note: the three hierarchical subroutines (QUS, TDS, and TRS) together form the ABM in this study. Different initial pathogen distributions and feedback/non-feedback queues are not shown in this illustrative diagram, but will be incorporated into the ABM.

Fig. 2.

Simulated and theoretical server utilization under low- and high-touch systems. Note: Both systems have the same theoretical utilization (0.2), and simulated means (from 100 realizations) are very good approximation of the theoretical value.

Fig. 3.

Distribution of percent of pathogen transfer per contact–-low-touch system (). Note: Vertical bar represents the mean value. The three functions have exactly the same inputs (contact durations). The outputs are significantly different for the three functions.

Fig. 4.

Distribution of percent of pathogen transfer per contact—high-touch system (). Note: Vertical bar represents the mean value. The three functions have exactly the same inputs (contact durations). The outputs are significantly different for the three functions.

Fig. 5.

Comparison of mean pathogen in environment, total pathogen transfer to hosts, and total pathogen transfer to environment in all simulated conditions. Low-touch (LT) vs high-touch (HT); Non-feedback (NF) vs Feedback (F); Initial pathogen on both hosts and environment (BOTH) vs no initial pathogen on hosts (NULL HOSTS) vs no initial pathogen on environment (NULL ENV). 1–3 are for linear, convex, and concave functions. And this sequence is the same for all conditions hereafter (e.g., 4–6, 7–9 are linear, convex, concave, linear, convex, concave). Conditions 1–3: LT/NF/BOTH; conditions 4–6: HT/NF/BOTH; conditions 7–9: LT/F/BOTH; conditions 10–12: HT/F/BOTH; conditions 13–15: LT/NF/ NULL HOSTS; conditions 16–18: HT/NF/NULL HOSTS; conditions 19–21: LT/F/ NULL HOSTS; conditions 22–24: HT/F/ NULL HOSTS; conditions 25–27: LT/NF/ NULL ENV; conditions 28–30: HT/NF/NULL ENV; conditions 31–33: LT/F/NULL ENV; conditions 34–36: HT/F/NULL ENV.

Fig. 6.

Relationship between mean pathogen in environment and total pathogen transfer to hosts and to environment. Note: Left panel: total pathogen transfer from environment to hosts; right panel: total pathogen transfer from hosts to environment. Note the high correlation between these two panels (despite the range/scale differences in -axis).