BackgroundMathematical modelling of infectious diseases transmitted by the respiratory or close-contact route (e.g., pandemic influenza) is increasingly being used to determine the impact of possible interventions. Although mixing patterns are known to be crucial determinants for model outcome, researchers often rely on a priori contact assumptions with little or no empirical basis. We conducted a population-based prospective survey of mixing patterns in eight European countries using a common paper-diary methodology.Methods and Findings7,290 participants recorded characteristics of 97,904 contacts with different individuals during one day, including age, sex, location, duration, frequency, and occurrence of physical contact. We found that mixing patterns and contact characteristics were remarkably similar across different European countries. Contact patterns were highly assortative with age: schoolchildren and young adults in particular tended to mix with people of the same age. Contacts lasting at least one hour or occurring on a daily basis mostly involved physical contact, while short duration and infrequent contacts tended to be nonphysical. Contacts at home, school, or leisure were more likely to be physical than contacts at the workplace or while travelling. Preliminary modelling indicates that 5- to 19-year-olds are expected to suffer the highest incidence during the initial epidemic phase of an emerging infection transmitted through social contacts measured here when the population is completely susceptible.ConclusionsTo our knowledge, our study provides the first large-scale quantitative approach to contact patterns relevant for infections transmitted by the respiratory or close-contact route, and the results should lead to improved parameterisation of mathematical models used to design control strategies.

When analysing new emerging infectious disease outbreaks, one typically has observational data over a limited period of time and several parameters to estimate, such as growth rate, the basic reproduction number R0, the case fatality rate and distributions of serial intervals, generation times, latency and incubation times and times between onset of symptoms, notification, death and recovery/discharge. These parameters form the basis for predicting a future outbreak, planning preventive measures and monitoring the progress of the disease outbreak. We study inference problems during the emerging phase of an outbreak, and point out potential sources of bias, with emphasis on: contact tracing backwards in time, replacing generation times by serial intervals, multiple potential infectors and censoring effects amplified by exponential growth. These biases directly affect the estimation of, for example, the generation time distribution and the case fatality rate, but can then propagate to other estimates such as R0 and growth rate. We propose methods to remove or at least reduce bias using statistical modelling. We illustrate the theory by numerical examples and simulations.

BackgroundIndividual-based models can provide the most reliable estimates of the spread of infectious diseases. In the present study, we evaluated the diffusion of pandemic influenza in Italy and the impact of various control measures, coupling a global SEIR model for importation of cases with an individual based model (IBM) describing the Italian epidemic.Methodology/Principal FindingsWe co-located the Italian population (57 million inhabitants) to households, schools and workplaces and we assigned travel destinations to match the 2001 census data. We considered different R0 values (1.4; 1.7; 2), evaluating the impact of control measures (vaccination, antiviral prophylaxis -AVP-, international air travel restrictions and increased social distancing). The administration of two vaccine doses was considered, assuming that first dose would be administered 1-6 months after the first world case, and different values for vaccine effectiveness (VE). With no interventions, importation would occur 37–77 days after the first world case. Air travel restrictions would delay the importation of the pandemic by 7–37 days. With an R0 of 1.4 or 1.7, the use of combined measures would reduce clinical attack rates (AR) from 21–31% to 0.3–4%. Assuming an R0 of 2, the AR would decrease from 38% to 8%, yet only if vaccination were started within 2 months of the first world case, in combination with a 90% reduction in international air traffic, closure of schools/workplaces for 4 weeks and AVP of household and school/work close contacts of clinical cases. Varying VE would not substantially affect the results.ConclusionsThis IBM, which is based on country-specific demographic data, could be suitable for the real-time evaluation of measures to be undertaken in the event of the emergence of a new pandemic influenza virus. All preventive measures considered should be implemented to mitigate the pandemic.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute ‘Models for an exit strategy’ workshop (11–15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

This paper considers metapopulation models in the general sense, i.e. where the population is partitioned into sub-populations (groups, patches,...), irrespective of the biological interpretation they have, e.g. spatially segregated large sub-populations, small households or hosts themselves modelled as populations of pathogens. This framework has traditionally provided an attractive approach to incorporating more realistic contact structure into epidemic models, since it often preserves analytic tractability (in stochastic as well as deterministic models) but also captures the most salient structural inhomogeneity in contact patterns in many applied contexts. Despite the progress that has been made in both the theory and application of such metapopulation models, we present here several major challenges that remain for future work, focusing on models that, in contrast to agent-based ones, are amenable to mathematical analysis. The challenges range from clarifying the usefulness of systems of weakly-coupled large sub-populations in modelling the spread of specific diseases to developing a theory for endemic models with household structure. They include also developing inferential methods for data on the emerging phase of epidemics, extending metapopulation models to more complex forms of human social structure, developing metapopulation models to reflect spatial population structure, developing computationally efficient methods for calculating key epidemiological model quantities, and integrating within- and between-host dynamics in models.