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Model hierarchies in edge-based compartmental modeling for infectious disease spread.

ABSTRACT: We consider the family of edge-based compartmental models for epidemic spread developed in Miller et al. (J R Soc Interface 9(70):890-906, 2012). These models allow for a range of complex behaviors, and in particular allow us to explicitly incorporate duration of a contact into our mathematical models. Our focus here is to identify conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide conditions under which it is appropriate to use the standard mass action SIR model, and we show what happens when these conditions fail. Using our hierarchy, we provide a procedure leading to the choice of the appropriate model for a given population. Our result about the convergence of models to the mass action model gives clear, rigorous conditions under which the mass action model is accurate.

SUBMITTER: Miller JC

PROVIDER: S-EPMC3552133 | biostudies-literature | 2013 Oct

REPOSITORIES: biostudies-literature

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Model hierarchies in edge-based compartmental modeling for infectious disease spread.

Miller Joel C JC Volz Erik M EM

Journal of mathematical biology 20120822 4

We consider the family of edge-based compartmental models for epidemic spread developed in Miller et al. (J R Soc Interface 9(70):890-906, 2012). These models allow for a range of complex behaviors, and in particular allow us to explicitly incorporate duration of a contact into our mathematical models. Our focus here is to identify conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide ...[more]

PMID: 22911242

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Project description:The world is continuously urbanising, resulting in clusters of densely populated urban areas and more sparsely populated rural areas. We propose a method for generating spatial fields with controllable levels of clustering of the population. We build a synthetic country, and use this method to generate versions of the country with different clustering levels. Combined with a metapopulation model for infectious disease spread, this allows us to in silico explore how urbanisation affects infectious disease spread. In a baseline scenario with no interventions, the underlying population clustering seems to have little effect on the final size and timing of the epidemic. Under within-country restrictions on non-commuting travel, the final size decreases with increased population clustering. The effect of travel restrictions on reducing the final size is larger with higher clustering. The reduction is larger in the more rural areas. Within-country travel restrictions delay the epidemic, and the delay is largest for lower clustering levels. We implemented three different vaccination strategies-uniform vaccination (in space), preferentially vaccinating urban locations and preferentially vaccinating rural locations. The urban and uniform vaccination strategies were most effective in reducing the final size, while the rural vaccination strategy was clearly inferior. Visual inspection of some European countries shows that many countries already have high population clustering. In the future, they will likely become even more clustered. Hence, according to our model, within-country travel restrictions are likely to be less and less effective in delaying epidemics, while they will be more effective in decreasing final sizes. In addition, to minimise final sizes, it is important not to neglect urban locations when distributing vaccines. To our knowledge, this is the first study to systematically investigate the effect of urbanisation on infectious disease spread and in particular, to examine effectiveness of prevention measures as a function of urbanisation.

Project description:BackgroundThe spread of SARS-CoV-2, originating in Wuhan, China, was classified as a pandemic by the World Health Organization on March 11, 2020. The governments of affected countries have implemented various measures to limit the spread of the virus. The starting point of this paper is the different government approaches, in terms of promulgating new legislative regulations to limit the virus diffusion and to contain negative effects on the populations.ObjectiveThis paper aims to study how the spread of SARS-CoV-2 is linked to government policies and to analyze how different policies have produced different results on public health.MethodsConsidering the official data provided by 4 countries (Italy, Germany, Sweden, and Brazil) and from the measures implemented by each government, we built an agent-based model to study the effects that these measures will have over time on different variables such as the total number of COVID-19 cases, intensive care unit (ICU) bed occupancy rates, and recovery and case-fatality rates. The model we implemented provides the possibility of modifying some starting variables, and it was thus possible to study the effects that some policies (eg, keeping the national borders closed or increasing the ICU beds) would have had on the spread of the infection.ResultsThe 4 considered countries have adopted different containment measures for COVID-19, and the forecasts provided by the model for the considered variables have given different results. Italy and Germany seem to be able to limit the spread of the infection and any eventual second wave, while Sweden and Brazil do not seem to have the situation under control. This situation is also reflected in the forecasts of pressure on the National Health Services, which see Sweden and Brazil with a high occupancy rate of ICU beds in the coming months, with a consequent high number of deaths.ConclusionsIn line with what we expected, the obtained results showed that the countries that have taken restrictive measures in terms of limiting the population mobility have managed more successfully than others to contain the spread of COVID-19. Moreover, the model demonstrated that herd immunity cannot be reached even in countries that have relied on a strategy without strict containment measures.

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Model hierarchies in edge-based compartmental modeling for infectious disease spread.

Publications

Model hierarchies in edge-based compartmental modeling for infectious disease spread.

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