Introduction. Effectively modeling SARS-CoV-2/COVID-19 dynamics requires careful integration of population health (public health motivation) and recovery dynamics (medical interventions motivation). This manuscript proposes a minimal pandemic model, which conceptually separates "complex adaptive systems" (CAS) associated with social behavior and infrastructure (e.g., tractable input events modulating exposure) from idealized bio-CAS (e.g., the immune system). The proposed model structure extends the classic simple SEIR (susceptible, exposed, infected, resistant/recovered) uni-causal compartmental model, widely used in epidemiology, into an 8th-order functional network SEI3R2S-Nrec model structure, with infection partitioned into three severity states (e.g., starts in I1 [mostly asymptomatic], then I2 if notable symptoms, then I3 if ideally hospitalized) that connect via a lattice of fluxes to two "resistant" (R) states. Here Nrec ("not recovered") represents a placeholder for better tying emerging COVID-19 medical research findings with those from epidemiology.
Methods. Borrowing from fuzzy logic, a given model represents a "Universe of Discourse" (UoD) that is based on assumptions. Nonlinear flux rates are implemented using the classic Hill function, widely used in the biochemical and pharmaceutical fields and intuitive for inclusion within differential equations. There is support for "encounter" input events that modulate ongoing E (exposures) fluxes via S↔I1 and other I1/2/3 encounters, partitioned into a "social/group" (uSG(t)) behavioral subgroup (e.g., ideally informed by evolving science best-practices), and a smaller uTB(t) subgroup with added "spreader" lifestyle and event support. In addition to signal and flux trajectories (e.g., plotted over 300 days), key cumulative output metrics include fluxes such as I3→D deaths, I2→I3 hospital admittances, I1→I2 related to "cases" and R1+R2 resistant. The code, currently available as a well-commented Matlab Live Script file, uses a common modeling framework developed for a portfolio of other physiological models that tie to a planned textbook; an interactive web-based version will follow.
Results. Default population results are provided for the USA as a whole, three states in which this author has lived (Arizona, Wisconsin, Oregon), and several special hypothetical cases of idealized UoDs (e.g., nursing home; healthy lower-risk mostly on I1→R1 path to evaluate reinfection possibilities). Often known events were included (e.g., pulses for holiday weekends; Trump/governor-inspired summer outbreak in Arizona). Runs were mildly tuned by the author, in two stages: i) mild model-tuning (e.g., for risk demographics such as obesity), then ii) iterative input tuning to obtain similar overall March-thru-November curve shapes and appropriate cumulative numbers (recognizing limitations of data like "cases"). Predictions are consistent deaths, and CDC estimates of actual cases and immunity (e.g., antibodies). Results could be further refined by groups with more resources (human, data access, computational). It is hoped that its structure and causal predictions might prove helpful to policymakers, medical professionals, and "on the ground" managers of science-based interventions.
Discussion and Future Directions. These include: i) sensitivity of the model to parameters; ii) possible next steps for this SEI3R2S-Nrec framework such as dynamic sub-models to better address compartment-specific forms of population diversity (e.g., for E [host-parasite biophysics], I's [infection diversity], and/or R's [immune diversity]); iii) model's potential utility as a framework for applying optimal/feedback control engineering to help manage the ongoing pandemic response in the context of competing subcriteria and emerging new tools (e.g., more timely testing, vaccines); and iv) ways in which the Nrec medical submodel could be expanded to provide refined estimates of the types of tissue damage, impairments and dysfunction that are known byproducts of the COVID-19 disease process, including as a function of existing comorbidities.
Aggregation and Controlled Interaction: Automated Mechanisms for Managing Design Complexity
