Deterministic epidemic models overestimate the basic reproduction number of observed outbreaks.

The basic reproduction number, R0, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating R0 from incidence data early in the epidemic can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and that, given the same system, some outbreaks may lead to epidemics and some may not. Typically, an observed epidemic that we wish to control is a major outbreak. This amounts to implicit selection for major outbreaks which leads to the over-estimation problem. We formally characterised the split between major and minor outbreaks by using Otsu's method which provides us with a working definition. We show that by conditioning a 'deterministic' model on major outbreaks, we can more reliably estimate the basic reproduction number from an observed epidemic trajectory.

Understanding the infection severity and epidemiological characteristics of mpox in the UK.

In May 2022, individuals infected with the monkeypox virus were detected in the UK without clear travel links to endemic areas. Understanding the clinical characteristics and infection severity of mpox is necessary for effective public health policy. The study period of this paper, from the 1st June 2022 to 30th September 2022, included 3,375 individuals that tested positive for the monkeypox virus. The posterior mean times from infection to hospital admission and length of hospital stay were 14.89 days (95% Credible Intervals (CrI): 13.60, 16.32) and 7.07 days (95% CrI: 6.07, 8.23), respectively. We estimated the modelled Infection Hospitalisation Risk to be 4.13% (95% CrI: 3.04, 5.02), compared to the overall sample Case Hospitalisation Risk (CHR) of 5.10% (95% CrI: 4.38, 5.86). The overall sample CHR was estimated to be 17.86% (95% CrI: 6.06, 33.11) for females and 4.99% (95% CrI: 4.27, 5.75) for males. A notable difference was observed between the CHRs that were estimated for each sex, which may be indicative of increased infection severity in females or a considerably lower infection ascertainment rate. It was estimated that 74.65% (95% CrI: 55.78, 86.85) of infections with the monkeypox virus in the UK were captured over the outbreak.

Identifying employee, workplace and population characteristics associated with COVID-19 outbreaks in the workplace: a population-based study.

OBJECTIVES: To identify risk factors that contribute to outbreaks of COVID-19 in the workplace and quantify their effect on outbreak risk. METHODS: We identified outbreaks of COVID-19 cases in the workplace and investigated the characteristics of the individuals, the workplaces, the areas they work and the mode of commute to work, through data linkages based on Middle Layer Super Output Areas in England between 20 June 2021 and 20 February 2022. We estimated population-level associations between potential risk factors and workplace outbreaks, adjusting for plausible confounders identified using a directed acyclic graph. RESULTS: For most industries, increased physical proximity in the workplace was associated with increased risk of COVID-19 outbreaks, while increased vaccination was associated with reduced risk. Employee demographic risk factors varied across industry, but for the majority of industries, a higher proportion of black/African/Caribbean ethnicities and living in deprived areas, was associated with increased outbreak risk. A higher proportion of employees in the 60-64 age group was associated with reduced outbreak risk. There were significant associations between gender, work commute modes and staff contract type with outbreak risk, but these were highly variable across industries. CONCLUSIONS: This study has used novel national data linkages to identify potential risk factors of workplace COVID-19 outbreaks, including possible protective effects of vaccination and increased physical distance at work. The same methodological approach can be applied to wider occupational and environmental health research.

Forecasting influenza hospital admissions within English sub-regions using hierarchical generalised additive models.

BACKGROUND: Seasonal influenza places a substantial burden annually on healthcare services. Policies during the COVID-19 pandemic limited the transmission of seasonal influenza, making the timing and magnitude of a potential resurgence difficult to ascertain and its impact important to forecast. METHODS: We have developed a hierarchical generalised additive model (GAM) for the short-term forecasting of hospital admissions with a positive test for the influenza virus sub-regionally across England. The model incorporates a multi-level structure of spatio-temporal splines, weekly cycles in admissions, and spatial correlation. Using multiple performance metrics including interval score, coverage, bias, and median absolute error, the predictive performance is evaluated for the 2022-2023 seasonal wave. Performance is measured against autoregressive integrated moving average (ARIMA) and Prophet time series models. RESULTS: Across the epidemic phases the hierarchical GAM shows improved performance, at all geographic scales relative to the ARIMA and Prophet models. Temporally, the hierarchical GAM has overall an improved performance at 7 and 14 day time horizons. The performance of the GAM is most sensitive to the flexibility of the smoothing function that measures the national epidemic trend. CONCLUSIONS: This study introduces an approach to short-term forecasting of hospital admissions for the influenza virus using hierarchical, spatial, and temporal components. The methodology was designed for the real time forecasting of epidemics. This modelling framework was used across the 2022-2023 winter for healthcare operational planning by the UK Health Security Agency and the National Health Service in England.

Seasonal influenza causes a burden for hospitals and therefore it is useful to be able to accurately predict how many patients might be admitted with the disease. We attempted to predict influenza admissions up to 14 days in the future by creating a computational model that incorporates how the disease is reported and how it spreads. We evaluated our optimised model on data acquired during the winter of 2022-2023 data in England and compared it with previously developed models. Our model was better at modelling how influenza spreads and predicting future hospital admissions than the models we compared it to. Improving how influenza admissions are forecast can enable hospitals to prepare better for increased admissions, enabling improved treatment and reduced death for all patients in hospital over winter.

Bayesian spatial modelling of localised SARS-CoV-2 transmission through mobility networks across England.

In the early phases of growth, resurgent epidemic waves of SARS-CoV-2 incidence have been characterised by localised outbreaks. Therefore, understanding the geographic dispersion of emerging variants at the start of an outbreak is key for situational public health awareness. Using telecoms data, we derived mobility networks describing the movement patterns between local authorities in England, which we have used to inform the spatial structure of a Bayesian BYM2 model. Surge testing interventions can result in spatio-temporal sampling bias, and we account for this by extending the BYM2 model to include a random effect for each timepoint in a given area. Simulated-scenario modelling and real-world analyses of each variant that became dominant in England were conducted using our BYM2 model at local authority level in England. Simulated datasets were created using a stochastic metapopulation model, with the transmission rates between different areas parameterised using telecoms mobility data. Different scenarios were constructed to reproduce real-world spatial dispersion patterns that could prove challenging to inference, and we used these scenarios to understand the performance characteristics of the BYM2 model. The model performed better than unadjusted test positivity in all the simulation-scenarios, and in particular when sample sizes were small, or data was missing for geographical areas. Through the analyses of emerging variant transmission across England, we found a reduction in the early growth phase geographic clustering of later dominant variants as England became more interconnected from early 2022 and public health interventions were reduced. We have also shown the recent increased geographic spread and dominance of variants with similar mutations in the receptor binding domain, which may be indicative of convergent evolution of SARS-CoV-2 variants.

Understanding the leading indicators of hospital admissions from COVID-19 across successive waves in the UK.

Following the end of universal testing in the UK, hospital admissions are a key measure of COVID-19 pandemic pressure. Understanding leading indicators of admissions at the National Health Service (NHS) Trust, regional and national geographies help health services plan for ongoing pressures. We explored the spatio-temporal relationships of leading indicators of hospitalisations across SARS-CoV-2 waves in England. This analysis includes an evaluation of internet search volumes from Google Trends, NHS triage calls and online queries, the NHS COVID-19 app, lateral flow devices (LFDs), and the ZOE app. Data sources were analysed for their feasibility as leading indicators using Granger causality, cross-correlation, and dynamic time warping at fine spatial scales. Google Trends and NHS triages consistently temporally led admissions in most locations, with lead times ranging from 5 to 20 days, whereas an inconsistent relationship was found for the ZOE app, NHS COVID-19 app, and LFD testing, which diminished with spatial resolution, showing cross-correlation of leads between -7 and 7 days. The results indicate that novel surveillance sources can be used effectively to understand the expected healthcare burden within hospital administrative areas though the temporal and spatial heterogeneity of these relationships is a key determinant of their operational public health utility.

Nowcasting the 2022 mpox outbreak in England.

In May 2022, a cluster of mpox cases were detected in the UK that could not be traced to recent travel history from an endemic region. Over the coming months, the outbreak grew, with over 3000 total cases reported in the UK, and similar outbreaks occurring worldwide. These outbreaks appeared linked to sexual contact networks between gay, bisexual and other men who have sex with men. Following the COVID-19 pandemic, local health systems were strained, and therefore effective surveillance for mpox was essential for managing public health policy. However, the mpox outbreak in the UK was characterised by substantial delays in the reporting of the symptom onset date and specimen collection date for confirmed positive cases. These delays led to substantial backfilling in the epidemic curve, making it challenging to interpret the epidemic trajectory in real-time. Many nowcasting models exist to tackle this challenge in epidemiological data, but these lacked sufficient flexibility. We have developed a nowcasting model using generalised additive models that makes novel use of individual-level patient data to correct the mpox epidemic curve in England. The aim of this model is to correct for backfilling in the epidemic curve and provide real-time characteristics of the state of the epidemic, including the real-time growth rate. This model benefited from close collaboration with individuals involved in collecting and processing the data, enabling temporal changes in the reporting structure to be built into the model, which improved the robustness of the nowcasts generated. The resulting model accurately captured the true shape of the epidemic curve in real time.

Replacement dynamics and the pathogenesis of the Alpha, Delta and Omicron variants of SARS-CoV-2.

New SARS-CoV-2 variants causing COVID-19 are a major risk to public health worldwide due to the potential for phenotypic change and increases in pathogenicity, transmissibility and/or vaccine escape. Recognising signatures of new variants in terms of replacing growth and severity are key to informing the public health response. To assess this, we aimed to investigate key time periods in the course of infection, hospitalisation and death, by variant. We linked datasets on contact tracing (Contact Tracing Advisory Service), testing (the Second-Generation Surveillance System) and hospitalisation (the Admitted Patient Care dataset) for the entire length of contact tracing in the England - from March 2020 to March 2022. We modelled, for England, time delay distributions using a Bayesian doubly interval censored modelling approach for the SARS-CoV-2 variants Alpha, Delta, Delta Plus (AY.4.2), Omicron BA.1 and Omicron BA.2. This was conducted for the incubation period, the time from infection to hospitalisation and hospitalisation to death. We further modelled the growth of novel variant replacement using a generalised additive model with a negative binomial error structure and the relationship between incubation period length and the risk of a fatality using a Bernoulli generalised linear model with a logit link. The mean incubation periods for each variant were: Alpha 4.19 (95% credible interval (CrI) 4.13-4.26) days; Delta 3.87 (95% CrI 3.82-3.93) days; Delta Plus 3.92 (95% CrI 3.87-3.98) days; Omicron BA.1 3.67 (95% CrI 3.61-3.72) days and Omicron BA.2 3.48 (95% CrI 3.43-3.53) days. The mean time from infection to hospitalisation was for Alpha 11.31 (95% CrI 11.20-11.41) days, Delta 10.36 (95% CrI 10.26-10.45) days and Omicron BA.1 11.54 (95% CrI 11.38-11.70) days. The mean time from hospitalisation to death was, for Alpha 14.31 (95% CrI 14.00-14.62) days; Delta 12.81 (95% CrI 12.62-13.00) days and Omicron BA.2 16.02 (95% CrI 15.46-16.60) days. The 95th percentile of the incubation periods were: Alpha 11.19 (95% CrI 10.92-11.48) days; Delta 9.97 (95% CrI 9.73-10.21) days; Delta Plus 9.99 (95% CrI 9.78-10.24) days; Omicron BA.1 9.45 (95% CrI 9.23-9.67) days and Omicron BA.2 8.83 (95% CrI 8.62-9.05) days. Shorter incubation periods were associated with greater fatality risk when adjusted for age, sex, variant, vaccination status, vaccination manufacturer and time since last dose with an odds ratio of 0.83 (95% confidence interval 0.82-0.83) (P value < 0.05). Variants of SARS-CoV-2 that have replaced previously dominant variants have had shorter incubation periods. Conversely co-existing variants have had very similar and non-distinct incubation period distributions. Shorter incubation periods reflect generation time advantage, with a reduction in the time to the peak infectious period, and may be a significant factor in novel variant replacing growth. Shorter times for admission to hospital and death were associated with variant severity - the most severe variant, Delta, led to significantly earlier hospitalisation, and death. These measures are likely important for future risk assessment of new variants, and their potential impact on population health.

Transmission dynamics of monkeypox in the United Kingdom: contact tracing study.

OBJECTIVE: To analyse the transmission dynamics of the monkeypox outbreak in the UK, declared a Public Health Emergency of International Concern in July 2022. DESIGN: Contact tracing study, linking data on case-contact pairs and on probable exposure dates. SETTING: Case questionnaires from the UK Health Security Agency (UKHSA), United Kingdom. PARTICIPANTS: 2746 people with polymerase chain reaction confirmed monkeypox virus in the UK between 6 May and 1 August 2022. MAIN OUTCOME MEASURES: The incubation period and serial interval of a monkeypox infection using two bayesian time delay models-one corrected for interval censoring (ICC-interval censoring corrected) and one corrected for interval censoring, right truncation, and epidemic phase bias (ICRTC-interval censoring right truncation corrected). Growth rates of cases by reporting date, when monkeypox virus was confirmed and reported to UKHSA, were estimated using generalised additive models. RESULTS: The mean age of participants was 37.8 years and 95% reported being gay, bisexual, and other men who have sex with men (1160 out of 1213 reporting). The mean incubation period was estimated to be 7.6 days (95% credible interval 6.5 to 9.9) using the ICC model and 7.8 days (6.6 to 9.2) using the ICRTC model. The estimated mean serial interval was 8.0 days (95% credible interval 6.5 to 9.8) using the ICC model and 9.5 days (7.4 to 12.3) using the ICRTC model. Although the mean serial interval was longer than the incubation period for both models, short serial intervals were more common than short incubation periods, with the 25th centile and the median of the serial interval shorter than the incubation period. For the ICC and ICRTC models, the corresponding estimates ranged from 1.8 days (95% credible interval 1.5 to 1.8) to 1.6 days (1.4 to 1.6) shorter at the 25th centile and 1.6 days (1.5 to 1.7) to 0.8 days (0.3 to 1.2) shorter at the median. 10 out of 13 linked patients had documented pre-symptomatic transmission. Doubling times of cases declined from 9.07 days (95% confidence interval 12.63 to 7.08) on the 6 May, when the first case of monkeypox was reported in the UK, to a halving time of 29 days (95% confidence interval 38.02 to 23.44) on 1 August. CONCLUSIONS: Analysis of the instantaneous growth rate of monkeypox incidence indicates that the epidemic peaked in the UK as of 9 July and then started to decline. Short serial intervals were more common than short incubation periods suggesting considerable pre-symptomatic transmission, which was validated through linked patient level records. For patients who could be linked through personally identifiable data, four days was the maximum time that transmission was detected before symptoms manifested. An isolation period of 16 to 23 days would be required to detect 95% of people with a potential infection. The 95th centile of the serial interval was between 23 and 41 days, suggesting long infectious periods.

Novel methods for estimating the instantaneous and overall COVID-19 case fatality risk among care home residents in England.

The COVID-19 pandemic has had high mortality rates in the elderly and frail worldwide, particularly in care homes. This is driven by the difficulty of isolating care homes from the wider community, the large population sizes within care facilities (relative to typical households), and the age/frailty of the residents. To quantify the mortality risk posed by disease, the case fatality risk (CFR) is an important tool. This quantifies the proportion of cases that result in death. Throughout the pandemic, CFR amongst care home residents in England has been monitored closely. To estimate CFR, we apply both novel and existing methods to data on deaths in care homes, collected by Public Health England and the Care Quality Commission. We compare these different methods, evaluating their relative strengths and weaknesses. Using these methods, we estimate temporal trends in the instantaneous CFR (at both daily and weekly resolutions) and the overall CFR across the whole of England, and dis-aggregated at regional level. We also investigate how the CFR varies based on age and on the type of care required, dis-aggregating by whether care homes include nursing staff and by age of residents. This work has contributed to the summary of measures used for monitoring the UK epidemic.

EpiBeds: Data informed modelling of the COVID-19 hospital burden in England.

The first year of the COVID-19 pandemic put considerable strain on healthcare systems worldwide. In order to predict the effect of the local epidemic on hospital capacity in England, we used a variety of data streams to inform the construction and parameterisation of a hospital progression model, EpiBeds, which was coupled to a model of the generalised epidemic. In this model, individuals progress through different pathways (e.g. may recover, die, or progress to intensive care and recover or die) and data from a partially complete patient-pathway line-list was used to provide initial estimates of the mean duration that individuals spend in the different hospital compartments. We then fitted EpiBeds using complete data on hospital occupancy and hospital deaths, enabling estimation of the proportion of individuals that follow the different clinical pathways, the reproduction number of the generalised epidemic, and to make short-term predictions of hospital bed demand. The construction of EpiBeds makes it straightforward to adapt to different patient pathways and settings beyond England. As part of the UK response to the pandemic, EpiBeds provided weekly forecasts to the NHS for hospital bed occupancy and admissions in England, Wales, Scotland, and Northern Ireland at national and regional scales.

Adjusting for time of infection or positive test when estimating the risk of a post-infection outcome in an epidemic.

When comparing the risk of a post-infection binary outcome, for example, hospitalisation, for two variants of an infectious pathogen, it is important to adjust for calendar time of infection. Typically, the infection time is unknown and positive test time used as a proxy for it. Positive test time may also be used when assessing how risk of the outcome changes over calendar time. We show that if time from infection to positive test is correlated with the outcome, the risk conditional on positive test time is a function of the trajectory of infection incidence. Hence, a risk ratio adjusted for positive test time can be quite different from the risk ratio adjusted for infection time. We propose a simple sensitivity analysis that indicates how risk ratios adjusted for positive test time and infection time may differ. This involves adjusting for a shifted positive test time, shifted to make the difference between it and infection time uncorrelated with the outcome. We illustrate this method by reanalysing published results on the relative risk of hospitalisation following infection with the Alpha versus pre-existing variants of SARS-CoV-2. Results indicate the relative risk adjusted for infection time may be lower than that adjusted for positive test time.

The rapid replacement of the SARS-CoV-2 Delta variant by Omicron (B.1.1.529) in England.

The emergence of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) B.1.1.529 (Omicron) variant caused international concern due to its rapid spread in Southern Africa. It was unknown whether this variant would replace or coexist with (either transiently or long term) the then-dominant Delta variant on its introduction to England. We developed a set of hierarchical logistic growth models to describe changes in the frequency of S gene target failure (SGTF) PCR tests, a proxy for Omicron. The doubling time of SGTF cases peaked at 1.56 days (95% CI: 1.49 to 1.63) on 5 December, whereas triple-positive cases were halving every 5.82 days (95% CI: 5.11 to 6.67) going into Christmas 2021. We were unable to characterize the replacement of Delta by Omicron with a single rate. The replacement rate decreased by 53.56% (95% CrI: 45.38 to 61.01) between 14 and 15 December, meaning the competitive advantage of Omicron approximately halved. Preceding the changepoint, Omicron was replacing Delta 16.24% (95% CrI: 9.72 to 23.41) faster in those with two or more vaccine doses, indicative of vaccine escape being a substantial component of competitive advantage. Despite the slowdown, Delta was almost entirely replaced in England within a month of the first sequenced domestic case. The synchrony of changepoints across regions at various stages of Omicron epidemics suggests that the growth rate advantage was not attenuated because of biological mechanisms related to strain competition. The step change in replacement could have resulted from behavioral changes, potentially elicited by public health messaging or policies, that differentially affected Omicron.

Effectiveness of the BNT162b2 (Pfizer-BioNTech) and the ChAdOx1 nCoV-19 (Oxford-AstraZeneca) vaccines for reducing susceptibility to infection with the Delta variant (B.1.617.2) of SARS-CoV-2.

BACKGROUND: From January to May 2021 the alpha variant (B.1.1.7) of SARS-CoV-2 was the most commonly detected variant in the UK. Following this, the Delta variant (B.1.617.2) then became the predominant variant. The UK COVID-19 vaccination programme started on 8th December 2020. Prior to the Delta variant, most vaccine effectiveness studies focused on the alpha variant. We therefore aimed to estimate the effectiveness of the BNT162b2 (Pfizer-BioNTech) and the ChAdOx1 nCoV-19 (Oxford-AstraZeneca) vaccines in preventing symptomatic and asymptomatic infection with respect to the Delta variant in a UK setting. METHODS: We used anonymised public health record data linked to infection data (PCR) using the Combined Intelligence for Population Health Action resource. We then constructed an SIR epidemic model to explain SARS-CoV-2 infection data across the Cheshire and Merseyside region of the UK. Vaccines were assumed to be effective after 21 days for 1 dose and 14 days for 2 doses. RESULTS: We determined that the effectiveness of the Oxford-AstraZeneca vaccine in reducing susceptibility to infection is 39% (95% credible interval [34, 43]) and 64% (95% credible interval [61, 67]) for a single dose and a double dose respectively. For the Pfizer-BioNTech vaccine, the effectiveness is 20% (95% credible interval [10, 28]) and 84% (95% credible interval [82, 86]) for a single-dose and a double dose respectively. CONCLUSION: Vaccine effectiveness for reducing susceptibility to SARS-CoV-2 infection shows noticeable improvement after receiving two doses of either vaccine. Findings also suggest that a full course of the Pfizer-BioNTech provides the optimal protection against infection with the Delta variant. This reinforces the need to complete the full course programme to maximise individual protection and reduce transmission.

Challenges for modelling interventions for future pandemics.

Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross-disciplinary collaboration together with close communication between scientists and policy makers.

Challenges in estimation, uncertainty quantification and elicitation for pandemic modelling.

The estimation of parameters and model structure for informing infectious disease response has become a focal point of the recent pandemic. However, it has also highlighted a plethora of challenges remaining in the fast and robust extraction of information using data and models to help inform policy. In this paper, we identify and discuss four broad challenges in the estimation paradigm relating to infectious disease modelling, namely the Uncertainty Quantification framework, data challenges in estimation, model-based inference and prediction, and expert judgement. We also postulate priorities in estimation methodology to facilitate preparation for future pandemics.

Estimation of reproduction numbers in real time: Conceptual and statistical challenges.

The reproduction number R has been a central metric of the COVID-19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations of R , the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulating R becomes increasingly complicated and inevitably model-dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Visible Light-Activated Carbon Dots for Inhibiting Biofilm Formation and Inactivating Biofilm-Associated Bacterial Cells.

This study aimed to address the significant problems of bacterial biofilms found in medical fields and many industries. It explores the potential of classic photoactive carbon dots (CDots), with 2,2'-(ethylenedioxy)bis (ethylamine) (EDA) for dot surface functionalization (thus, EDA-CDots) for their inhibitory effect on B. subtilis biofilm formation and the inactivation of B. subtilis cells within established biofilm. The EDA-CDots were synthesized by chemical functionalization of selected small carbon nanoparticles with EDA molecules in amidation reactions. The inhibitory efficacy of CDots with visible light against biofilm formation was dependent significantly on the time point when CDots were added; the earlier the CDots were added, the better the inhibitory effect on the biofilm formation. The evaluation of antibacterial action of light-activated EDA-CDots against planktonic B. subtilis cells versus the cells in biofilm indicate that CDots are highly effective for inactivating planktonic cells but barely inactivate cells in established biofilms. However, when coupling with chelating agents (e.g., EDTA) to target the biofilm architecture by breaking or weakening the EPS protection, much enhanced photoinactivation of biofilm-associated cells by CDots was achieved. The study demonstrates the potential of CDots to prevent the initiation of biofilm formation and to inhibit biofilm growth at an early stage. Strategic combination treatment could enhance the effectiveness of photoinactivation by CDots to biofilm-associated cells.

Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics.

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour. We develop a system of ordinary differential equations that approximate the number of infected individuals in the QSD for arbitrary contact networks and parameter values. When the epidemic level is high, these QSD approximations coincide with the existing approximation methods. However, as we approach the epidemic threshold, the models deviate, with these models following the QSD and the existing methods approaching the all susceptible state. Through consistently approximating the QSD, the proposed methods provide a more robust link to the stochastic models.