Lessons from a decade of individual-based models for infectious disease transmission: a systematic review (2006-2015)

The number of published IBMs for infectious disease transmission and the diversity of disease topics are increasing. Our systematic search identified 698 unique papers between 2006 and 2015. Most included articles were applied to unspecified close-contact infections or to influenza, though IBMs for other air-, saliva-, vector-borne and sexually transmitted infections are emerging. Methods for vector-borne diseases have been described for malaria and dengue and could guide future research. Especially, IBM applications on chikungunya and zika are expected over the next decade given the growing geographical expansion of their common vectors [49, 105]. Also screening and (non-)pharmaceutical intervention strategies have not been fully explored with IBMs for many diseases. Given the heterogeneous nature of bio-medical and socioeconomic data and the accelerating health care expenditures, IBMs become progressively useful to inform policy makers, particularly in combination with efficiency and equity analyses [106, 107]. There are relatively few papers with an IBM for stochastic outbreak analysis under high vaccination coverage, for example for vaccine-preventable childhood diseases. For measles, it was shown that stochastic fluctuations around the endemic equilibrium in populations with high vaccination coverage could cause recurrent epidemics [84]. We expect future research to focus more on these topics with IBMs in combination with increasing global mobility, urbanization, climate change, disease elimination efforts and vaccine skepticism [2]. Customization of health care is one way to mitigate these stochastic epidemics with medical interventions tailored to the individual patient. The rising transition towards precision medicine needs to be informed with studies on the individual-level to capture spatio-temporal heterogeneity.

Modeling frameworks, such as STDSIM [71], EMOD [73] and EPISIMS [72] exist but are limited in that their application depends heavily on specific input data. Indeed, it is difficult to create or maintain generic models that incorporate many modeling options and still manage the computational burden. Nonetheless, given the high programming burden, transparent reuse of models increases confidence in their approach and generated results. Making IBM code open-source (e.g., FluTE [36] and FRED [76]) is also useful to validate model outcomes, to inspire future modeling projects [55] and to expand model exploration [108]. Consistent “branding” of the IBM, with a proper acronym, is practical to link studies and consolidate intellectual ownership of freely accessible source code.

Regarding the simulation platform, mathematical software (e.g., MATLAB^®;) enables many embedded features and is user-friendly but currently lacks specific modules for IBMs. Integrated platforms such as RepastS [109] and Netlogo [25, 110], are used by others and can be practical and straightforward but cannot fulfill all requirements of the inherent heterogeneity and computational burden of IBMs. A third option is the low-level programming language C++, which enables high-performance code but requires high-level programming skills to efficiently manage the model logic and memory usage. Given the computational and implementation burden [84, 89], close interaction with computer sciences is required. Nonetheless, good-practice programming with version control, regression testing and benchmarking is rarely described [108, 111].

Although runtimes are inherent to model implementation and computer hardware, presenting the order of magnitude of runtimes and memory requirements could be useful for other researchers. Details on model performance and computational burden were usually lacking in our selection of full-text papers. In our total set of IBM papers, we found 2 examples on the computational burden of their IBM in C++ [36, 76]. An influenza simulation with FLUTE [36] uses approximately 80 megabytes of memory per million simulated individuals. Simulating an epidemic in a population of 10 million people can take up to two hours (on a single processor on an Intel^®; Core Duo T9400), but it may take only seconds if the virus is not highly transmissible or if there are effective interventions [36]. With 750 - 1000 megabytes of memory required per million simulated individuals, FRED’s computational burden [76] is about ten times larger. Simulations for the H1N1 pandemic in a population of 1 million people takes less than two minutes on a typical dual-core laptop computer (in 2013) but the runtime will vary depending on the number of individuals infected during the epidemic and depending on which optional features are activated. Unfortunately, computational performance is a significant aspect of a simulator’s usefulness. Investment in performance optimization is required to achieve the full potential of current high-performance workstations [108]. This seems most feasible using open-source software, as it allows more researchers to contribute to optimization and to leverage on the existing - and ever expanding - IBM knowledge base, thus enabling a cyclic process of innovation and optimization.

Time horizons and modeling step sizes in the full-text articles were diverse and are subject to disease characteristics and research objectives. There is no standard approach on the number of stochastic realizations, which seems model specific and requires sensitivity analysis. Models focusing on key factors of between-host dynamics in large populations with homogeneous mixing [87] will not produce much stochastic variability and require fewer realizations compared to simulations combining complex social mixing clusters, adaptive behavior, within-host dynamics and medical backgrounds [80, 91, 92]. One of the most frequent criticisms of IBMs is that “they can be calibrated to say anything” [25]. This is partly a result of not capturing the difference between the calibration of IBMs and equation-based models. The latter have usually fewer parameters, which have to be evaluated by calibrating the full model to observed data [25]. IBMs, in contrast, are constructed bottom-up, which allows to select parameters independently based on census data, mobility patterns, serotype distribution, social contact behavior, natural history of a disease, etc. As such, a limited number of particularly uncertain parameters has to be calibrated by fitting the model to observed prevalence and/or incidence of disease states [25]. IBM calibration has been performed with genetic algorithms [86], maximum likelihood [88] or Bayesian procedures with Markov Chain Monte Carlo sampling [53]. A limitation of the IBM approach is that the basic reproduction number (R₀), corresponding to the number of secondary cases caused by a single (typical) infection in a totally susceptible population, cannot be attributed directly but has to be derived from model output. R₀ has been estimated in IBM studies [23, 36, 76, 88, 108, 112] by the average number of secondary cases from a randomly selected individual in a fully susceptible model population based on multiple realizations. Parameterization and calibration needs to be documented well. Model presentation should preferably be accompanied by an assessment of the goodness of fit to observed data [4]. Another convincing way to show that your ABM has been calibrated without bias and produces useful general results is to analyze it thoroughly after calibration [25]. Ideally, each model should be analyzed systematically to understand the impact of model assumptions and parameters on the results [55]. Parameter values can be drawn from a pre-computed design (e.g., Latin Hypercube) or at random from a distribution. Emulation techniques are promising to capture complex simulators’ behavior in order to improve engaged and perhaps more rapid policy making [55–58]. Given the lack of standards, it is crucial to fully describe the methods and experimental design in the context of the model [4]. Unfortunately, we were not able to recapture all model characteristics and study designs from our full-text subset. This stresses the need for the ODD protocol with shorthand conventions and a syntax that modelers can understand intuitively such that the methodology can be converted directly into an executable simulator [28].

The terminology to describe individual-level models and infectious diseases was inconsistent and curtail efficient knowledge transfer. For example, a systematic review in 2015 on IBMs for non-communicable diseases [33] searched only with the terms “agent-based” and “individual-based” to dramatically reduce the number of false positive hits. To assist future research, it is crucial to use the same semantics for IBM studies across disciplines. The introduction of the Medical Subject Headings (MeSH) controlled vocabulary [113] is a huge step forward but is limited to PubMed and does not (yet) contain fixed terms for simulation models at the individual-level. With this review, we seek to provide keywords to the IBM community and a definition for individual-based modeling as “computer simulation for the creation, disappearance and movement of a finite collection of interacting individuals or agents with unique attributes regarding spatial location, physiological traits and/or social behavior” [8–11, 25, 33]. The overall term IBM refers to the individual-level approach based on a fundamental philosophy of methodological individualism, which advocates a focus on the uniqueness of individuals and their interactions. Further subcategories can be used according to whether locations are static (as in CAs) or individuals act autonomously (as in ABMs). The standard incorporation of the overarching term “individual-based model” in the abstract or keywords would greatly improve current and future systematic searches in large electronic databases.

One could argue that our recommendations are constrained since they are based on title, abstract and keyword screening. For example, a frequently cited article on pandemic influenza by Ferguson et al. [114] was not retrieved by our search since it has none of the IBM terms in its title, abstract or keywords. The model is described as a “large-scale epidemic simulation” in the abstract although the first sentence of the introduction reads “We parameterize an individual-based model of pandemic influenza transmission...”. This example could be seen as a confirmation of the inconsistencies and limitations of current article archiving practice. A similar remark can be made for our disease related search terms but we believe we used the most relevant keywords and can only recommend future research to include also general disease-related terminology. If our selection was identifiable by searching on “infectious AND disease AND transmission”, this would be a substantial improvement, in contrast to the current 40% of our selection. The restriction to only include papers published between 2006 and 2015 might be considered a minor limitation by the time the current paper is published. The final fully included year was chosen mainly for practical reasons, at the time of completing this labour-intensive review in early 2016. We are convinced that a review over a decade (an intuitively appealing period for review) is highly informative to understand the evolution of this field and to adequately guide future research. We had no intention to present a complete review of all the IBM papers we systematically identified, but we provide all included references in a searchable database enabling others to conduct more specific literature reviews. Clearly, our database can be updated using the discussed insights on search methodology and keywords.