Capturing the time-varying drivers of an epidemic using stochastic dynamical systems

Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions, seasonal effects etc). These models assign diffusion processes to the time-varying parameters, and our inferential procedure is based on a suitably adjusted adaptive particle MCMC algorithm. The performance of the proposed computational methods is validated on simulated data and the adopted model is applied to the 2009 H1N1 pandemic in England. In addition to estimating the effective contact rate trajectories, the methodology is applied in real time to provide evidence in related public health decisions. Diffusion driven SEIR-type models with age structure are also introduced.Comment: 21 pages, 5 figure

Influenza interaction with cocirculating pathogens, and its impact on surveillance, pathogenesis and epidemic profile: a key role for mathematical modeling

ABSTRACT Evidence is mounting that influenza virus, a major contributor to the global disease burden, interacts with other pathogens infecting the human respiratory tract. Taking into account interactions with other pathogens may be critical to determining the real influenza burden and the full impact of public health policies targeting influenza. That necessity is particularly true for mathematical modeling studies, which have become critical in public health decision-making, despite their usually focusing on lone influenza virus acquisition and infection, thereby making broad oversimplifications regarding pathogen ecology. Herein, we review evidence of influenza virus interaction with bacteria and viruses, and the modeling studies that incorporated some of these. Despite the many studies examining possible associations between influenza and Streptococcus pneumoniae, Staphylococcus aureus, Haemophilus influenzae, Neisseria meningitides , respiratory syncytial virus, human rhinoviruses, human parainfluenza viruses, etc., very few mathematical models have integrated other pathogens alongside influenza. A notable exception is the recent modeling of the pneumococcus-influenza interaction, which highlighted potential influenza-related increased pneumococcal transmission and pathogenicity. That example demonstrates the power of dynamic modeling as an approach to test biological hypotheses concerning interaction mechanisms and estimate the strength of those interactions. We explore how different interference mechanisms may lead to unexpected incidence trends and misinterpretations. Using simple transmission models, we illustrate how existing interactions might impact public health surveillance systems and demonstrate that the development of multipathogen models is essential to assess the true public health burden of influenza, and help improve planning and evaluation of control measures. Finally, we identify the public health needs, surveillance, modeling and biological challenges, and propose avenues of research for the coming years. Author Summary Influenza is a major pathogen responsible for important morbidity and mortality burdens worldwide. Mathematical models of influenza virus acquisition have been critical to understanding its epidemiology and planning public health strategies of infection control. It is increasingly clear that microbes do not act in isolation but potentially interact within the host. Hence, studying influenza alone may lead to masking effects or misunderstanding information on its transmission and severity. Herein, we review the literature on bacterial and viral species that interact with the influenza virus, interaction mechanisms, and mathematical modeling studies integrating interactions. We report evidence that, beyond the classic secondary bacterial infections, many pathogenic bacteria and viruses probably interact with influenza. Public health relevance of pathogen interactions is detailed, showing how potential misreading or a narrow outlook might lead to mistaken public health decisionmaking. We describe the role of mechanistic transmission models in investigating this complex system and obtaining insight into interactions between influenza and other pathogens. Finally, we highlight benefits and challenges in modeling, and speculate on new opportunities made possible by taking a broader view: including basic science, clinical relevance and public health

Contemporary statistical inference for infectious disease models using Stan

This paper is concerned with the application of recent statistical advances to inference of infectious disease dynamics. We describe the fitting of a class of epidemic models using Hamiltonian Monte Carlo and variational inference as implemented in the freely available Stan software. We apply the two methods to real data from outbreaks as well as routinely collected observations. Our results suggest that both inference methods are computationally feasible in this context, and show a trade-off between statistical efficiency versus computational speed. The latter appears particularly relevant for real-time applications

Evaluating the next generation of RSV intervention strategies: a mathematical modelling study and cost-effectiveness analysis

© 2020, The Author(s). Background: With a suite of promising new RSV prophylactics on the horizon, including long-acting monoclonal antibodies and new vaccines, it is likely that one or more of these will replace the current monoclonal Palivizumab programme. However, choosing the optimal intervention programme will require balancing the costs of the programmes with the health benefits accrued. Methods: To compare the next generation of RSV prophylactics, we integrated a novel transmission model with an economic analysis. We estimated key epidemiological parameters by calibrating the model to 7 years of historical epidemiological data using a Bayesian approach. We determined the cost-effective and affordable maximum purchase price for a comprehensive suite of intervention programmes. Findings: Our transmission model suggests that maternal protection of infants is seasonal, with 38–62% of infants born with protection against RSV. Our economic analysis found that to cost-effectively and affordably replace the current monoclonal antibody Palivizumab programme with long-acting monoclonal antibodies, the purchase price per dose would have to be less than around £4350 but dropping to £200 for vaccinated heightened risk infants or £90 for all infants. A seasonal maternal vaccine would have to be priced less than £85 to be cost-effective and affordable. While vaccinating pre-school and school-age children is likely not cost-effective relative to elderly vaccination programmes, vaccinating the elderly is not likely to be affordable. Conversely, vaccinating infants at 2 months seasonally would be cost-effective and affordable if priced less than £80. Conclusions: In a setting with seasonal RSV epidemiology, maternal protection conferred to newborns is also seasonal, an assumption not previously incorporated in transmission models of RSV. For a country with seasonal RSV dynamics like England, seasonal programmes rather than year-round intervention programmes are always optimal

Age-specific incidence of A/H1N1 2009 influenza infection in England from sequential antibody prevalence data using likelihood-based estimation.

Estimating the age-specific incidence of an emerging pathogen is essential for understanding its severity and transmission dynamics. This paper describes a statistical method that uses likelihoods to estimate incidence from sequential serological data. The method requires information on seroconversion intervals and allows integration of information on the temporal distribution of cases from clinical surveillance. Among a family of candidate incidences, a likelihood function is derived by reconstructing the change in seroprevalence from seroconversion following infection and comparing it with the observed sequence of positivity among the samples. This method is applied to derive the cumulative and weekly incidence of A/H1N1 pandemic influenza in England during the second wave using sera taken between September 2009 and February 2010 in four age groups (1-4, 5-14, 15-24, 25-44 years). The highest cumulative incidence was in 5-14 year olds (59%, 95% credible interval (CI): 52%, 68%) followed by 1-4 year olds (49%, 95% CI: 38%, 61%), rates 20 and 40 times higher respectively than estimated from clinical surveillance. The method provides a more accurate and continuous measure of incidence than achieved by comparing prevalence in samples grouped by time period

Influenza Interaction with Cocirculating Pathogens, and Its Impact on Surveillance, Pathogenesis and Epidemic Profile: A Key Role for Mathematical Modeling

ABSTRACTEvidence is mounting that influenza virus, a major contributor to the global disease burden, interacts with other pathogens infecting the human respiratory tract. Taking into account interactions with other pathogens may be critical to determining the real influenza burden and the full impact of public health policies targeting influenza. That necessity is particularly true for mathematical modeling studies, which have become critical in public health decision-making, despite their usually focusing on lone influenza virus acquisition and infection, thereby making broad oversimplifications regarding pathogen ecology. Herein, we review evidence of influenza virus interaction with bacteria and viruses, and the modeling studies that incorporated some of these. Despite the many studies examining possible associations between influenza andStreptococcus pneumoniae, Staphylococcus aureus, Haemophilus influenzae, Neisseria meningitides, respiratory syncytial virus, human rhinoviruses, human parainfluenza viruses, etc., very few mathematical models have integrated other pathogens alongside influenza. A notable exception is the recent modeling of the pneumococcus-influenza interaction, which highlighted potential influenza-related increased pneumococcal transmission and pathogenicity. That example demonstrates the power of dynamic modeling as an approach to test biological hypotheses concerning interaction mechanisms and estimate the strength of those interactions. We explore how different interference mechanisms may lead to unexpected incidence trends and misinterpretations. Using simple transmission models, we illustrate how existing interactions might impact public health surveillance systems and demonstrate that the development of multipathogen models is essential to assess the true public health burden of influenza, and help improve planning and evaluation of control measures. Finally, we identify the public health needs, surveillance, modeling and biological challenges, and propose avenues of research for the coming years.Author SummaryInfluenza is a major pathogen responsible for important morbidity and mortality burdens worldwide. Mathematical models of influenza virus acquisition have been critical to understanding its epidemiology and planning public health strategies of infection control. It is increasingly clear that microbes do not act in isolation but potentially interact within the host. Hence, studying influenza alone may lead to masking effects or misunderstanding information on its transmission and severity. Herein, we review the literature on bacterial and viral species that interact with the influenza virus, interaction mechanisms, and mathematical modeling studies integrating interactions. We report evidence that, beyond the classic secondary bacterial infections, many pathogenic bacteria and viruses probably interact with influenza. Public health relevance of pathogen interactions is detailed, showing how potential misreading or a narrow outlook might lead to mistaken public health decisionmaking. We describe the role of mechanistic transmission models in investigating this complex system and obtaining insight into interactions between influenza and other pathogens. Finally, we highlight benefits and challenges in modeling, and speculate on new opportunities made possible by taking a broader view: including basic science, clinical relevance and public health.</jats:sec

Modelling the impact of local reactive school closures on critical care provision during an influenza pandemic

Despite the fact that the 2009 H1N1 pandemic influenza strain was less severe than had been feared, both seasonal epidemics of influenza-like-illness and future influenza pandemics have the potential to place a serious burden on health services. The closure of schools has been postulated as a means of reducing transmission between children and hence reducing the number of cases at the peak of an epidemic; this is supported by the marked reduction in cases during school holidays observed across the world during the 2009 pandemic. However, a national policy of long-duration school closures could have severe economic costs. Reactive short-duration closure of schools in regions where health services are close to capacity offers a potential compromise, but it is unclear over what spatial scale and time frame closures would need to be made to be effective. Here, using detailed geographical information for England, we assess how localized school closures could alleviate the burden on hospital intensive care units (ICUs) that are reaching capacity. We show that, for a range of epidemiologically plausible assumptions, considerable local coordination of school closures is needed to achieve a substantial reduction in the number of hospitals where capacity is exceeded at the peak of the epidemic. The heterogeneity in demand per hospital ICU bed means that even widespread school closures are unlikely to have an impact on whether demand will exceed capacity for many hospitals. These results support the UK decision not to use localized school closures as a control mechanism, but have far wider international public-health implications. The spatial heterogeneities in both population density and hospital capacity that give rise to our results exist in many developed countries, while our model assumptions are sufficiently general to cover a wide range of pathogens. This leads us to believe that when a pandemic has severe implications for ICU capacity, only widespread school closures (with their associated costs and organizational challenges) are sufficient to mitigate the burden on the worst-affected hospitals

Tooling-up for infectious disease transmission modelling.

In this introduction to the Special Issue on methods for modelling of infectious disease epidemiology we provide a commentary and overview of the field. We suggest that the field has been through three revolutions that have focussed on specific methodological developments; disease dynamics and heterogeneity, advanced computing and inference, and complexity and application to the real-world. Infectious disease dynamics and heterogeneity dominated until the 1980s where the use of analytical models illustrated fundamental concepts such as herd immunity. The second revolution embraced the integration of data with models and the increased use of computing. From the turn of the century an emergence of novel datasets enabled improved modelling of real-world complexity. The emergence of more complex data that reflect the real-world heterogeneities in transmission resulted in the development of improved inference methods such as particle filtering. Each of these three revolutions have always kept the understanding of infectious disease spread as its motivation but have been developed through the use of new techniques, tools and the availability of data. We conclude by providing a commentary on what the next revoluition in infectious disease modelling may be