Epidemic models and their use

In the last 40 years, humanity has struggled with an “epidemic of epidemics” which triggered a huge advance in the field of epidemic models. The emergence of HIV challenged the homogeneous mixing assumption, very common until then. The cholera epidemics in the 1990s fostered the inclusion of environmental reservoirs in models. The emergence of H5N1 and H1N1 influenza strains led to the development of immuno-ecological models, dengue fever led to the development of models combining environmental and immunological components. Meanwhile, models that were originally created as hypothetico-deductive tools, to build scenarios, assess counterfacts, and identify knowledge gaps, were increasingly challenged to become tools for inductive use, that is, to make quantitative predictions. The success of this new use of epidemic models is controversial, as shown through multiple applications to the COVID-19 pandemic [1].

“Essentially all models are wrong, but some are useful” is a popular quote [2]. But how useful a model is? G.R. Conway [3] proposes a classification of models as strategic, tactic or policy, distinguishing them primarily in terms of their geographic scale and the timespan over which they operate. We propose to use these definitions to understand the multitude of dengue models found in the literature, as reviewed by Aguiar et al. [4]. In their search of the literature, the authors found 225 publications, out of which 56 concern multi-strain models. Within this group, these models vary in how they deal with stochasticity, spatial and temporal heterogeneities, and by whether they include mosquitos as state variables.

One of the main contributions of multi-strain models has been the identification of deterministic chaos as a possible explanation for the highly variable long-term dynamics of dengue. This result provides important consequences for public health decisions, thus constituting a use as a policy model. They indicate that long-term prediction of dengue is not feasible, especially in the context of poor data quality. As such, the development of models for short-term predictions or within season predictions seem to be more useful for decision-making. For short term predictions, we argue that multi-strain models may not be required, as epidemics tend to be dominated by a single strain. However, any strategic or tactical use of these models, both single or multi-strain ones, will require good estimations of initial conditions.

Fig. 2(a) of Aguiar et al. shows that single-strain models, according to their multi-strain focused search criteria, outnumber multi-strain ones approximately 4 to 1. Perhaps this higher dominance of single-strain models reflects a difficulty in properly parameterizing multi-strain models. Currently, the most commonly available testing protocols based on antigen (NS1) and antibody detection do not allow for strain identification. This lack of information, combined with the difficulties in clinical differentiation between DENV and other arboviruses, makes it extremely challenging to properly measure the size of dengue epidemics [5]. Meanwhile, in endemic regions with historical exposure to all viruses, assessing the size of the immune population is also a barrier to the application of these models for prediction. From a public health perspective, to model dengue epidemics (through single-strain models) may be an efficient way to inform short term disease control actions.

As new technologies for multiple viral detection are developed, the gap between models and data tends to decrease. Still, discriminating between chaotic behavior and stochastic behavior is still an intriguing question not completely addressed by the current models, with important consequences for their use in dengue surveillance [6]. Another important application of a multi-strain model, for policy and strategy, is the design of vaccine campaigns. As new vaccines become available, multi-strain models become fundamental tools to assess their cost-benefits and define targets for vaccination campaigns.

Lastly, Aguiar et al. argue that multi-stain dengue models could be used as reference for the development of models for COVID and other diseases characterized by multiple strains. To our understanding, the similarities between COVID and dengue dynamics should be considered only in very broad terms. The main contribution of multi-strain models for dengue is to understand the interferences between the dengue virus serotypes (DENV-1, -2, -3 and -4) and their effect on the overall population dynamics. These are genetically related viruses that produce antigenically distinct immune responses in humans. Phylogenetic analyses indicate that these four dengue serotypes evolved independently of sylvatic reservoirs in a series of divergence events that occurred at least centuries ago [7]. This complex of four virus types justify the development of population models such as those found in the review, where the dynamics of each strain is tracked separately and strains are assumed to be stable. The models provide explanations for cycling of serotypes, and the role of co-circulating serotypes on the emergence of chaotic behaviors. But the approach is not necessarily useful for a virus with many strains, as influenza [8] or sars-cov-2 [9] that evolve at a much faster rate. For these, models that combine evolutionary and ecological processes may be a better option.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Communicated by J. Fontanari