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During its first two years, the SARS-CoV-2 pandemic manifested as multiple waves shaped by complex interactions between variants of concern, non-pharmaceutical interventions, and the immunological landscape of the population. Understanding how the age-specific epidemiology of SARS-CoV-2 has evolved throughout the pandemic is crucial for informing policy decisions. We developed an inference-based modelling approach to reconstruct the burden of true infections and hospital admissions in children, adolescents and adults over the seven waves of four variants (wild-type, Alpha, Delta, Omicron BA.1) during the first two years of the pandemic, using the Netherlands as the motivating example. We find that reported cases are a considerable underestimate and a generally poor predictor of true infection burden, especially because case reporting differs by age. The contribution of children and adolescents to total infection and hospitalization burden increased with successive variants and was largest during the Omicron BA.1 period. Before the Delta period, almost all infections were primary infections occurring in naive individuals. During the Delta and Omicron BA.1 periods, primary infections were common in children but relatively rare in adults who experienced either re-infections or breakthrough infections. Our approach can be used to understand age-specific epidemiology through successive waves in other countries where random community surveys uncovering true SARS-CoV-2 dynamics are absent but basic surveillance and statistics data are available., Comment: 23 pages, 5 figures, 1 table; supplementary materials to the main text available at https://github.com/oboldea/COVID_age_regions

We use a stochastic metapopulation model to study the combined effects of seasonality and spatial heterogeneity on disease persistence. We find a pronounced effect of enhanced persistence associated with strong heterogeneity, intermediate coupling strength and moderate seasonal forcing. Analytic calculations show that this effect is not related with the phase lag between epidemic bursts in different patches, but rather with the linear stability properties of the attractor that describes the steady state of the system in the large population limit., Comment: main text (8 pages, 5 figures); supplementary material (17 pages, 3 figures) and electronic supplementary material (ESM.mov)

Rubella is a completely immunizing and mild infection in children. Understanding its behavior is of considerable public health importance because of Congenital Rubella Syndrome, which results from infection with rubella during early pregnancy and may entail a variety of birth defects. The recurrent dynamics of rubella are relatively poorly resolved, and appear to show considerable diversity globally. Here, we investigate the behavior of a stochastic seasonally forced susceptible-infected-recovered model to characterize the determinants of these dynamics and illustrate patterns by comparison with measles. We perform a systematic analysis of spectra of stochastic fluctuations around stable attractors of the corresponding deterministic model and compare them with spectra from full stochastic simulations in large populations. This approach allows us to quantify the effects of demographic stochasticity and to give a coherent picture of measles and rubella dynamics, explaining essential differences in the recurrent patterns exhibited by these diseases. We discuss the implications of our findings in the context of vaccination and changing birth rates as well as the persistence of these two childhood infections., Comment: 20 pages, 9 figures

The dynamics of strongly immunizing childhood infections is still not well understood. Although reports of successful modeling of several incidence data records can be found in the literature, the key determinants of the observed temporal patterns have not been clearly identified. In particular, different models of immunity waning and degree of protection applied to disease and vaccine induced immunity have been debated in the literature on pertussis. Here we study the effect of disease acquired immunity on the long term patterns of pertussis prevalence. We compare five minimal models, all of which are stochastic, seasonally forced, well-mixed models of infection based on susceptible-infective-recovered dynamics in a closed population. These models reflect different assumptions about the immune response of naive hosts, namely total permanent immunity, immunity waning, immunity waning together with immunity boosting, reinfection of recovered, and repeat infection after partial immunity waning. The power spectra of the output prevalence time series characterize the long term dynamics of the models. For epidemiological parameters consistent with published data for pertussis, the power spectra show quantitative and even qualitative differences that can be used to test their assumptions by comparison with ensembles of several decades long pre-vaccination data records. We illustrate this strategy on two publicly available historical data sets., Comment: paper (31 pages, 11 figures, 1 table) and supplementary material (19 pages, 5 figures, 2 tables)

The interplay of seasonality, the system's nonlinearities and intrinsic stochasticity is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns., Comment: 13 pages, 9 figures, 3 tables

In this paper, we consider a simple stochastic epidemic model on large regular random graphs and the stochastic process that corresponds to this dynamics in the standard pair approximation. Using the fact that the nodes of a pair are unlikely to share neighbors, we derive the master equation for this process and obtain from the system size expansion the power spectrum of the fluctuations in the quasi-stationary state. We show that whenever the pair approximation deterministic equations give an accurate description of the behavior of the system in the thermodynamic limit, the power spectrum of the fluctuations measured in long simulations is well approximated by the analytical power spectrum. If this assumption breaks down, then the cluster approximation must be carried out beyond the level of pairs. We construct an uncorrelated triplet approximation that captures the behavior of the system in a region of parameter space where the pair approximation fails to give a good quantitative or even qualitative agreement. For these parameter values, the power spectrum of the fluctuations in finite systems can be computed analytically from the master equation of the corresponding stochastic process., Comment: the notation has been changed; Ref. [26] and a new paragraph in Section IV have been added

We study the phase diagram of the standard pair approximation equations for two different models in population dynamics, the susceptible-infective-recovered-susceptible model of infection spread and a predator-prey interaction model, on a network of homogeneous degree $k$. These models have similar phase diagrams and represent two classes of systems for which noisy oscillations, still largely unexplained, are observed in nature. We show that for a certain range of the parameter $k$ both models exhibit an oscillatory phase in a region of parameter space that corresponds to weak driving. This oscillatory phase, however, disappears when $k$ is large. For $k=3, 4$, we compare the phase diagram of the standard pair approximation equations of both models with the results of simulations on regular random graphs of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. We discuss this failure of the standard pair approximation model to capture even the qualitative behavior of the simulations on large regular random graphs and the relevance of the oscillatory phase in the pair approximation diagrams to explain the cycling behavior found in real populations., Comment: 8 pages, 5 figures; we have expanded and rewritten the introduction, slightly modified the abstract and the text in other sections; also, several new references have been added in the revised manuscript (Refs. [17-25,30,35])

The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree $k$ predict a thin phase of sustained oscillations for parameter values that correspond to diseases that confer long lasting immunity. Here we present a study of the dependence of this oscillatory phase on the parameter $k$ and of its relevance to understand the behaviour of simulations on networks. For $k=4$, we compare the phase diagram of the PA model with the results of simulations on regular random graphs (RRG) of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. This failure of the standard PA model to capture the qualitative behaviour of the simulations on large RRGs is currently being investigated., Comment: 6 pages, 3 figures, WIPP to be published in Conference proceedings Complex'2009 February 23-25, Shanghai, China

We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behaviour in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of stochastic fluctuations, a general mechanism first reported for predator-prey dynamics. In a narrow range of parameters that includes many infectious diseases which confer long lasting immunity the oscillations persist for infinite populations. This effect is apparent in simulations of the stochastic process in systems of variable size, and can be understood from the phase diagram of the deterministic pair approximation equations. The two mechanisms combined play a central role in explaining the ubiquity of oscillatory behaviour in real data and in simulation results of epidemic and other related models., Comment: acknowledgments added; a typo in the discussion that follows Eq. (3) is corrected