Modeling Infectious Disease Dynamics Among Structured Hospital and Community Population Interactions

Matthew Mietchen

doi:10.7273/000005239

Mathematical models are important tools to further our understanding of infectious disease dynamics and to provide insight into public health interventions. Disease transmission models vary on a broad scale of complexity, often balancing issues pertaining to tractability and generalizability. More simplified compartmental models are useful when contact networks are not available, or when computationally expensive models are not feasible. The random mixing assumptions of compartment models, however, ignore contact heterogeneities and thus potentially conceal vastly different subpopulation transmission dynamics. By incorporating a population’s interaction structure, using non-spatial metapopulation frameworks, we explore the infection dynamics of two pathogens in small populations of different magnitudes. SARS-CoV-2, a viral respiratory infection that causes COVID-19, spreads rapidly from person to person, primarily via aerosolization. Using surveillance data of reported cases within a rural county, we developed a two-population compartmental model to estimate transmission parameters within and between university-associated individuals and the surrounding community to evaluate cross-transmission using particle Markov Chain Monte Carlo (pMCMC) simulation-based methods. Compared to the cross-transmission estimate (BM), the university estimate (BU) and community estimate (BC) were considerably higher (1,225 and 72 times, respectively). This finding suggests that random mixing assumptions, even in small rural counties, should be reconsidered, and interaction heterogeneity should be applied to disease models in spatially overlapping subpopulations. Considering methicillin-resistant Staphylococcus aureus (MRSA) as a motivating example, we developed three stochastic compartmental models of an 18-bed intensive care unit (ICU) to compare patient-staff interaction structures and rates of MRSA acquisitions, in addition to parameter sensitivity. From simple to complex, the model structures (complete random mixing, separation of staff types, and assigned patient groups) revealed that mean acquisitions decreased by 52%, and parameters were less sensitive when the model captured the contact heterogeneity within the ICU. Compartmental models remain a valuable method for understanding the infectious disease dynamics of a system; however, simplifying assumptions of population interactions, even among small, spatially-constrained populations, should be reconsidered, as shown by these results. Establishing some level of contact heterogeneity within the model allows for random mixing but provides a more accurate representation of overlapping subpopulations where potential intervention and infection control efforts could be implemented more effectively.

Modeling Infectious Disease Dynamics Among Structured Hospital and Community Population Interactions

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