Appropriate models for the management of infectious diseases

Finite mixture models of superspreading in epidemics

Superspreading transmission is usually modeled using the negative binomial distribution, simply because its variance is larger than the mean and it can be long-tailed. However, populations are often partitioned into groups by social, behavioral, or environmental risk factors, particularly in closed settings such as workplaces or care homes. While heterogeneities in infectious histories and contact structure have been considered separately, models for superspreading events that include the joint effects of social and biological risk factors are lacking. To address this need, we developed a mechanistic finite mixture model for the number of secondary infections that unites population partitioning with individual-level heterogeneity in infectious period duration. We showed that the variance in the number of secondary infections is composed of both sources of heterogeneity: risk group structuring and infectiousness. We used the model to construct the outbreak size distribution and to derive critical thresholds for elimination resulting from control activities that differentially target the high-contact subpopulation vs. the population at large. We compared our model with the standard negative binomial distribution and showed that the tail behavior of the outbreak size distribution under a finite mixture model differs substantially. Our results indicate that even if the infectious period follows a bell-shaped distribution, heterogeneity in outbreak sizes may arise due to the influence of population risk structure.

Differentiating Contact with Symptomatic and Asymptomatic Infectious Individuals in a SEIR Epidemic Model

This manuscript introduces a new Erlang-distributed SEIR model. The model incorporates asymptomatic spread through a subdivided exposed class, distinguishing between asymptomatic ( E a ) and symptomatic ( E s ) cases. The model identifies two key parameters: relative infectiousness, β SA , and the percentage of people who become asymptomatic after being infected by a symptomatic individual, κ . Lower values of these parameters reduce the peak magnitude and duration of the infectious period, highlighting the importance of isolation measures. Additionally, the model underscores the need for strategies addressing both symptomatic and asymptomatic transmissions.

Physics-informed deep learning for infectious disease forecasting

Accurate forecasting of contagious illnesses has become increasingly important to public health policymaking, and better prediction could prevent the loss of millions of lives. To better prepare for future pandemics, it is essential to improve forecasting methods and capabilities. In this work, we propose a new infectious disease forecasting model based on physics-informed neural networks (PINNs), an emerging area of scientific machine learning. The proposed PINN model incorporates dynamical systems representations of disease transmission into the loss function, thereby assimilating epidemiological theory and data using neural networks (NNs). Our approach is designed to prevent model overfitting, which often occurs when training deep learning models with observation data alone. In addition, we employ an additional sub-network to account for mobility, vaccination, and other covariates that influence the transmission rate, a key parameter in the compartment model. To demonstrate the capability of the proposed model, we examine the performance of the model using state-level COVID-19 data in California. Our simulation results show that predictions of PINN model on the number of cases, deaths, and hospitalizations are consistent with existing benchmarks. In particular, the PINN model outperforms the basic NN model and naive baseline forecast. We also show that the performance of the PINN model is comparable to a sophisticated Gaussian infection state space with time dependence (GISST) forecasting model that integrates the compartment model with a data observation model and a regression model for inferring parameters in the compartment model. Nonetheless, the PINN model offers a simpler structure and is easier to implement. In summary, our results show that the proposed forecaster could potentially serve as a new computational tool to enhance the current capacity of infectious disease forecasting.

Optimizing contact tracing for avian influenza in poultry flocks

Contact tracing is commonly used to manage infectious diseases of both humans and animals. It aims to detect early and control potentially infected individuals or farms that had contact with infectious cases. Because it is very resource-intensive, contact tracing is usually performed on a pre-defined time window, based on previous knowledge of the duration of the incubation period. However, pre-defined time windows may not be always relevant, reducing the efficiency of contact tracing. In this study, we estimated the day when farms were first infected with highly pathogenic avian influenza viruses, a devastating pathogen causing severe socio-economic damage in domestic poultry. The estimation was performed by fitting a stochastic mechanistic model to observed daily mortality data from 63 infected poultry farms in France and The Netherlands, using approximate Bayesian computation. Independent of the poultry species or country, the estimates of the time of first infection ranged between 3.4 (95% credible interval-CrI: 2.6, 4.6) and 19.9 (95% CrI: 11.9, 31.3) days prior to the last observation. We developed an online application to provide real-time support to policymakers by estimating realistic ranges of dates of first infection to inform contact tracing and improve its efficiency.

An immuno-epidemiological model with non-exponentially distributed disease stage on complex networks

Most of epidemic models assume that duration of the disease phase is distributed exponentially for the simplification of model formulation and analysis. Actually, the exponentially distributed assumption on the description of disease stages is hard to accurately approximate the interplay of drug concentration and viral load within host. In this article, we formulate an immuno-epidemiological epidemic model on complex networks, which is composed of ordinary differential equations and integral equations. The linkage of within- and between-host is connected by setting that the death caused by the disease is an increasing function in viral load within host. Mathematical analysis of the model includes the existence of the solution to the epidemiological model on complex networks, the existence and stability of equilibrium, which are completely determined by the basic reproduction number of the between-host system. Numerical analysis are shown that the non-exponentially distributions and the topology of networks have significant roles in the prediction of epidemic patterns.

Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics

Epidemiological parameters such as the reproduction number, latent period, and infectious period provide crucial information about the spread of infectious diseases and directly inform intervention strategies. These parameters have generally been estimated by mathematical models that involve an unrealistic assumption of history-independent dynamics for simplicity. This assumes that the chance of becoming infectious during the latent period or recovering during the infectious period remains constant, whereas in reality, these chances vary over time. Here, we find that conventional approaches with this assumption cause serious bias in epidemiological parameter estimation. To address this bias, we developed a Bayesian inference method by adopting more realistic history-dependent disease dynamics. Our method more accurately and precisely estimates the reproduction number than the conventional approaches solely from confirmed cases data, which are easy to obtain through testing. It also revealed how the infectious period distribution changed throughout the COVID-19 pandemic during 2020 in South Korea. We also provide a user-friendly package, IONISE, that automates this method.

Characterization and individual-level prediction of cognitive state in the first year after 'mild' stroke

BACKGROUND

Mild stroke affects more than half the stroke population, yet there is limited evidence characterizing cognition over time in this population, especially with predictive approaches applicable at the individual-level. We aimed to identify patterns of recovery and the best combination of demographic, clinical, and lifestyle factors predicting individual-level cognitive state at 3- and 12-months after mild stroke.

METHODS

In this prospective cohort study, the Montreal Cognitive Assessment (MoCA) was administered at 3-7 days, 3- and 12-months post-stroke. Raw changes in MoCA and impairment rates (defined as MoCA<24 points) were compared between assessment time-points. Trajectory clusters were identified using variations of ≥1 point in MoCA scores. To further compare clusters, additional assessments administered at 3- and 12-months were included. Gamma and Quantile mixed-effects regression were used to predict individual MoCA scores over time, using baseline clinical and demographic variables. Model predictions were fitted for each stroke survivor and evaluated using model cross-validation to identify the overall best predictors of cognitive recovery.

RESULTS

Participants' (n = 119) MoCA scores improved from baseline to 3-months (p<0.001); and decreased from 3- to 12-months post-stroke (p = 0.010). Cognitive impairment rates decreased significantly from baseline to 3-months (p<0.001), but not between 3- and 12-months (p = 0.168). Nine distinct trajectory clusters were identified. Clinical characteristics between clusters at each time-point varied in cognitive outcomes but not in clinical and/or activity participation outcomes. Cognitive performance at 3- and 12-months was best predicted by younger age, higher physical activity levels, and left-hemisphere lesion side.

CONCLUSION

More than half of mild-stroke survivors are at risk of cognitive decline one year after stroke, even when preceded by a significantly improving pattern in the first 3-months of recovery. Physical activity was the only modifiable factor independently associated with cognitive recovery. Individual-level prediction methods may inform the timing and personalized application of future interventions to maximize cognitive recovery post-stroke.

Optimization and performance analytics of global aircraft-based wastewater surveillance networks

Aircraft wastewater surveillance has been proposed as a novel approach to monitor the global spread of pathogens. Here we develop a computational framework to provide actionable information for designing and estimating the effectiveness of global aircraft-based wastewater surveillance networks (WWSNs). We study respiratory diseases of varying transmission potentials and find that networks of 10 to 20 strategically placed wastewater sentinel sites can provide timely situational awareness and function effectively as an early warning system. The model identifies potential blind spots and suggests optimization strategies to increase WWSNs effectiveness while minimizing resource use. Our findings highlight that increasing the number of sentinel sites beyond a critical threshold does not proportionately improve WWSNs capabilities, stressing the importance of resource optimization. We show through retrospective analyses that WWSNs can significantly shorten the detection time for emerging pathogens. The presented approach offers a realistic analytic framework for the analysis of WWSNs at airports.

Transoceanic pathogen transfer in the age of sail and steam

In the centuries following Christopher Columbus's 1492 voyage to the Americas, transoceanic travel opened unprecedented pathways in global pathogen circulation. Yet no biological transfer is a single, discrete event. We use mathematical modeling to quantify historical risk of shipborne pathogen introduction, exploring the respective contributions of journey time, ship size, population susceptibility, transmission intensity, density dependence, and pathogen biology. We contextualize our results using port arrivals data from San Francisco, 1850 to 1852, and from a selection of historically significant voyages, 1492 to 1918. We offer numerical estimates of introduction risk across historically realistic ranges of journey time and ship population size, and show that both steam travel and shipping regimes that involved frequent, large-scale movement of people substantially increased risk of transoceanic pathogen circulation.

When should lockdown be implemented? Devising cost-effective strategies for managing epidemics amid vaccine uncertainty

During an infectious disease outbreak, public health policy makers are tasked with strategically implementing interventions whilst balancing competing objectives. To provide a quantitative framework that can be used to guide these decisions, it is helpful to devise a clear and specific objective function that can be evaluated to determine the optimal outbreak response. In this study, we have developed a mathematical modelling framework representing outbreaks of a novel emerging pathogen for which non-pharmaceutical interventions (NPIs) are imposed or removed based on thresholds for hospital occupancy. These thresholds are set at different levels to define four unique strategies for disease control. We illustrate that the optimal intervention strategy is contingent on the choice of objective function. Specifically, the optimal strategy depends on the extent to which policy makers prioritise reducing health costs due to infection over the costs associated with maintaining interventions. Motivated by the scenario early in the COVID-19 pandemic, we incorporate the development of a vaccine into our modelling framework and demonstrate that a policy maker's belief about when a vaccine will become available in future, and its eventual coverage (and/or effectiveness), affects the optimal strategy to adopt early in the outbreak. Furthermore, we show how uncertainty in these quantities can be accounted for when deciding which interventions to introduce. This research highlights the benefits of policy makers being explicit about the precise objectives of introducing interventions.

Structural network characteristics affect epidemic severity and prediction in social contact networks

Understanding and mitigating epidemic spread in complex networks requires the measurement of structural network properties associated with epidemic risk. Classic measures of epidemic thresholds like the basic reproduction number (R0) have been adapted to account for the structure of social contact networks but still may be unable to capture epidemic potential relative to more recent measures based on spectral graph properties. Here, we explore the ability of R0 and the spectral radius of the social contact network to estimate epidemic susceptibility. To do so, we simulate epidemics on a series of constructed (small world, scale-free, and random networks) and a collection of over 700 empirical biological social contact networks. Further, we explore how other network properties are related to these two epidemic estimators (R0 and spectral radius) and mean infection prevalence in simulated epidemics. Overall, we find that network properties strongly influence epidemic dynamics and the subsequent utility of R0 and spectral radius as indicators of epidemic risk.

Evaluation of vaccine rollout strategies for emerging infectious diseases: A model-based approach including protection attitudes

Vaccine allocation strategies become crucial during vaccine shortages, especially in the face of potential outbreaks of new infectious diseases, as witnessed during the COVID-19 pandemic. To address this, a specialized compartmental model is created, which simulates an emerging infectious disease similar to COVID-19. This model divides the population into different age groups and is used to compare various vaccine prioritisation approaches, aiming to minimize the total number of fatalities. The model is an improvement upon previous ones as it incorporates essential behavioural factors and is adapted to account for the protective effects of vaccination against both disease infection and transmission. It takes into account human behaviors such as mask-wearing and social distancing by utilizing specific parameters related to self-protection, awareness levels, and the frequency of daily person-to-person interactions within each age group. Furthermore, a novel method for dynamic vaccine prioritisation was introduced in this study. This approach is model-independent and relies on the dynamic R number. It is the first time such a method has been developed, offering a decision-making approach that is not tied to any specific model. This innovation provides a flexible and adaptable strategy for determining vaccine priorities based on real-time data and the current state of the outbreak. Our findings reveal crucial insights into vaccine allocation strategies. When the daily rollout rates are fast (0.75% or higher) and children are eligible for vaccination, prioritising groups with high daily person-to-person interactions can lead to substantial reductions in total fatalities (up to approximately 40% lower). On the other hand, if rollout rates are slower and overall vaccination coverage is high, focusing on vaccinating elders emerges as the most effective strategy, resulting in up to approximately 10% fewer fatalities. However, the scenario changes significantly when children are not eligible for vaccination, as they constitute a highly interactive population group. In this case, the differences between priority strategies become smaller. With fast daily rollout rates, prioritisation based on interactions achieves only a 7% reduction in total fatalities, while a slower rollout with vaccination of elders first leads to an approximately 11% reduction in fatalities compared to the scenario where children are eligible for vaccination. The impact of behavioural parameters is equally critical. When the self-protection levels exercised by the population are low, it significantly affects the optimal vaccine prioritisation strategy to be followed, making it essential to consider behavioural factors in decision-making.

Reproduction number projection for the COVID-19 pandemic

The recently derived Hybrid-Incidence Susceptible-Transmissible-Removed (HI-STR) prototype is a deterministic compartment model for epidemics and an alternative to the Susceptible-Infected-Removed (SIR) model. The HI-STR predicts that pathogen transmission depends on host population characteristics including population size, population density and social behaviour common within that population.

The HI-STR prototype is applied to the ancestral Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2) to show that the original estimates of the Coronavirus Disease 2019 (COVID-19) basic reproduction number $\mathcal{R}_{0}$ R 0 for the United Kingdom (UK) could have been projected onto the individual states of the United States of America (USA) prior to being detected in the USA.

The Imperial College London (ICL) group’s estimate of $\mathcal{R}_{0}$ R 0 for the UK is projected onto each USA state. The difference between these projections and the ICL’s estimates for USA states is either not statistically significant on the paired Student t-test or not epidemiologically significant.

The SARS-CoV2 Delta variant’s $\mathcal{R}_{0}$ R 0 is also projected from the UK to the USA to prove that projection can be applied to a Variant of Concern (VOC). Projection provides both a localised baseline for evaluating the implementation of an intervention policy and a mechanism for anticipating the impact of a VOC before local manifestation.

Modeling the XBB strain of SARS-CoV-2: Competition between variants and impact of reinfection

XBB, an Omicron subvariant of SARS-CoV-2 that began to circulate in late 2022, has been dominant in the US since early 2023. To quantify the impact of XBB on the progression of COVID-19, we propose a new mathematical model which describes the interplay between XBB and other SARS-CoV-2 variants at the population level and which incorporates the effects of reinfection. We apply the model to COVID-19 data in the US that include surveillance data on the cases and variant proportions from the New York City, the State of New York, and the State of Washington. Our fitting and simulation results show that the transmission rate of XBB is significantly higher than that of other variants and the reinfection from XBB may play an important role in shaping the pandemic/epidemic pattern in the US.

Replicating superspreader dynamics with compartmental models

Infectious disease outbreaks often exhibit superspreader dynamics, where most infected people generate no, or few secondary cases, and only a small fraction of individuals are responsible for a large proportion of transmission. Although capturing this heterogeneity is critical for estimating outbreak risk and the effectiveness of group-specific interventions, it is typically neglected in compartmental models of infectious disease transmission-which constitute the most common transmission dynamic modeling framework. In this study we propose different classes of compartmental epidemic models that incorporate transmission heterogeneity, fit them to a number of real outbreak datasets, and benchmark their performance against the canonical superspreader model (i.e., the negative binomial branching process model). We find that properly constructed compartmental models can capably reproduce observed superspreader dynamics and we provide the pathogen-specific parameter settings required to do so. As a consequence, we also show that compartmental models parameterized according to a binary clinical classification have limited support.

Anchoring the mean generation time in the SEIR to mitigate biases in ℜ0 estimates due to uncertainty in the distribution of the epidemiological delays

The basic reproduction number, ℜ 0 , is of paramount importance in the study of infectious disease dynamics. Primarily, ℜ 0 serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ℜ 0 and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ℜ 0 estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ℜ 0 .

Swift and extensive Omicron outbreak in China after sudden exit from 'zero-COVID' policy

In late 2022, China transitioned from a strict 'zero-COVID' policy to rapidly abandoning nearly all interventions and data reporting. This raised great concern about the presumably-rapid but unreported spread of the SARS-CoV-2 Omicron variant in a very large population of very low pre-existing immunity. By modeling a combination of case count and survey data, we show that Omicron spread extremely rapidly, at a rate of 0.42/day (95% credibility interval: [0.35, 0.51]/day), translating to an epidemic doubling time of 1.6 days ([1.6, 2.0] days) after the full exit from zero-COVID on Dec. 7, 2022. Consequently, we estimate that the vast majority of the population (97% [95%, 99%], sensitivity analysis lower limit of 90%) was infected during December, with the nation-wide epidemic peaking on Dec. 23. Overall, our results highlight the extremely high transmissibility of the variant and the importance of proper design of intervention exit strategies to avoid large infection waves.

The relationship between controllability, optimal testing resource allocation, and incubation-latent period mismatch as revealed by COVID-19

The severe shortfall in testing supplies during the initial COVID-19 outbreak and ensuing struggle to manage the pandemic have affirmed the critical importance of optimal supply-constrained resource allocation strategies for controlling novel disease epidemics. To address the challenge of constrained resource optimization for managing diseases with complications like pre- and asymptomatic transmission, we develop an integro partial differential equation compartmental disease model which incorporates realistic latent, incubation, and infectious period distributions along with limited testing supplies for identifying and quarantining infected individuals. Our model overcomes the limitations of typical ordinary differential equation compartmental models by decoupling symptom status from model compartments to allow a more realistic representation of symptom onset and presymptomatic transmission. To analyze the influence of these realistic features on disease controllability, we find optimal strategies for reducing total infection sizes that allocate limited testing resources between 'clinical' testing, which targets symptomatic individuals, and 'non-clinical' testing, which targets non-symptomatic individuals. We apply our model not only to the original, delta, and omicron COVID-19 variants, but also to generically parameterized disease systems with varying mismatches between latent and incubation period distributions, which permit varying degrees of presymptomatic transmission or symptom onset before infectiousness. We find that factors that decrease controllability generally call for reduced levels of non-clinical testing in optimal strategies, while the relationship between incubation-latent mismatch, controllability, and optimal strategies is complicated. In particular, though greater degrees of presymptomatic transmission reduce disease controllability, they may increase or decrease the role of non-clinical testing in optimal strategies depending on other disease factors like transmissibility and latent period length. Importantly, our model allows a spectrum of diseases to be compared within a consistent framework such that lessons learned from COVID-19 can be transferred to resource constrained scenarios in future emerging epidemics and analyzed for optimality.

Evaluations of heterogeneous epidemic models with exponential and non-exponential distributions for latent period: the Case of COVID-19

Most of heterogeneous epidemic models assume exponentially distributed sojourn times in infectious states, which may not be practical in reality and could affect the dynamics of the epidemic. This paper investigates the potential discrepancies between exponential and non-exponential distribution models in analyzing the transmission patterns of infectious diseases and evaluating control measures. Two SEIHR models with multiple subgroups based on different assumptions for latency are established: Model Ⅰ assumes an exponential distribution of latency, while Model Ⅱ assumes a gamma distribution. To overcome the challenges associated with the high dimensionality of GDM, we derive the basic reproduction number ($ R_{0} $) of the model theoretically, and apply numerical simulations to evaluate the effect of different interventions on EDM and GDM. Our results show that considering a more realistic gamma distribution of latency can change the peak numbers of infected and the timescales of an epidemic, and GDM may underestimate the infection eradication time and overestimate the peak value compared to EDM. Additionally, the two models can produce inconsistent predictions in estimating the time to reach the peak. Our study contributes to a more accurate understanding of disease transmission patterns, which is crucial for effective disease control and prevention.

Heterogeneity is a key factor describing the initial outbreak of COVID-19

Assessing the transmission potential of emerging infectious diseases, such as COVID-19, is crucial for implementing prompt and effective intervention policies. The basic reproduction number is widely used to measure the severity of the early stages of disease outbreaks. The basic reproduction number of standard ordinary differential equation models is computed for homogeneous contact patterns; however, realistic contact patterns are far from homogeneous, specifically during the early stages of disease transmission. Heterogeneity of contact patterns can lead to superspreading events that show a significantly high level of heterogeneity in generating secondary infections. This is primarily due to the large variance in the contact patterns of complex human behaviours. Hence, in this work, we investigate the impacts of heterogeneity in contact patterns on the basic reproduction number by developing two distinct model frameworks: 1) an SEIR-Erlang ordinary differential equation model and 2) an SEIR stochastic agent-based model. Furthermore, we estimated the transmission probability of both models in the context of COVID-19 in South Korea. Our results highlighted the importance of heterogeneity in contact patterns and indicated that there should be more information than one quantity (the basic reproduction number as the mean quantity), such as a degree-specific basic reproduction number in the distributional sense when the contact pattern is highly heterogeneous.

Maximizing the cost-effectiveness of cervical screening in the context of routine HPV vaccination by optimizing screening strategies with respect to vaccine uptake: a modeling analysis

BACKGROUND

Regarding primary and secondary cervical cancer prevention, the World Health Organization proposed the cervical cancer elimination strategy that requires countries to achieve 90% uptake of human papillomavirus (HPV) vaccines and 70% screening uptake. The optimal cervical screening strategy is likely different for unvaccinated and vaccinated cohorts upon national HPV immunization. However, health authorities typically only provide a one-size-fits-all recommendation for the general population. We aimed to evaluate the cost-effectiveness for determining the optimal screening strategies for vaccinated and unvaccinated cohorts.

METHODS

We considered the women population in Hong Kong which has a unique HPV infection and cervical cancer epidemiology compared to other regions in China and Asia. We used mathematical models which comprise a deterministic age-structured compartmental dynamic component and a stochastic individual-based cohort component to evaluate the cost-effectiveness of screening strategies for cervical screening. Following the recommendations in local guidelines in Hong Kong, we considered strategies that involved cytology, HPV testing, or co-testing as primary cervical screening. We also explored the impacts of adopting alternative de-intensified strategies for vaccinated cohorts. The 3-year cytology screening was used as the base comparator while no screening was also considered for vaccinated cohorts. Women's lifetime life years, quality-adjusted life years, and costs of screening and treatment were estimated from the societal perspective based on the year 2022 and were discounted by 3% annually. Incremental cost-effectiveness ratios (ICERs) were compared to a willingness to pay (WTP) threshold of one gross domestic product per capita (US $47,792). Probabilistic and one-way sensitivity analyses were conducted.

RESULTS

Among unvaccinated cohorts, the strategy that adds reflex HPV to triage mild cytology abnormality generated more life years saved than cytology-only screening and could be a cost-effective alternative. Among vaccinated cohorts, when vaccine uptake was 85% (based on the uptake in 2022), all guideline-based strategies (including the cytology-only screening) had ICERs above the WTP threshold when compared with no screening if the vaccine-induced protection duration was 20 years or longer. Under the same conditions, HPV testing with genotyping triage had ICERs (compared with no screening) below the WTP threshold if the routine screening interval was lengthened to 10 and 15 years or screening was initiated at ages 30 and 35 years.

CONCLUSIONS

HPV testing is a cost-effective alternative to cytology for vaccinated cohorts, and the associated optimal screening frequency depends on vaccine uptake. Health authorities should optimize screening recommendations by accounting for population vaccine uptake.

Uncertainty and error in SARS-CoV-2 epidemiological parameters inferred from population-level epidemic models

During the SARS-CoV-2 pandemic, epidemic models have been central to policy-making. Public health responses have been shaped by model-based projections and inferences, especially related to the impact of various non-pharmaceutical interventions. Accompanying this has been increased scrutiny over model performance, model assumptions, and the way that uncertainty is incorporated and presented. Here we consider a population-level model, focusing on how distributions representing host infectiousness and the infection-to-death times are modelled, and particularly on the impact of inferred epidemic characteristics if these distributions are mis-specified. We introduce an SIR-type model with the infected population structured by 'infected age', i.e. the number of days since first being infected, a formulation that enables distributions to be incorporated that are consistent with clinical data. We show that inference based on simpler models without infected age, which implicitly mis-specify these distributions, leads to substantial errors in inferred quantities relevant to policy-making, such as the reproduction number and the impact of interventions. We consider uncertainty quantification via a Bayesian approach, implementing this for both synthetic and real data focusing on UK data in the period 15 Feb-14 Jul 2020, and emphasising circumstances where it is misleading to neglect uncertainty. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Disentangling the causes of mumps reemergence in the United States

Over the past two decades, multiple countries with high vaccine coverage have experienced resurgent outbreaks of mumps. Worryingly, in these countries, a high proportion of cases have been among those who have completed the recommended vaccination schedule, raising alarm about the effectiveness of existing vaccines. Two putative mechanisms of vaccine failure have been proposed as driving observed trends: 1) gradual waning of vaccine-derived immunity (necessitating additional booster doses) and 2) the introduction of novel viral genotypes capable of evading vaccinal immunity. Focusing on the United States, we conduct statistical likelihood-based hypothesis testing using a mechanistic transmission model on age-structured epidemiological, demographic, and vaccine uptake time series data. We find that the data are most consistent with the waning hypothesis and estimate that 32.8% (32%, 33.5%) of individuals lose vaccine-derived immunity by age 18 y. Furthermore, we show using our transmission model how waning vaccine immunity reproduces qualitative and quantitatively consistent features of epidemiological data, namely 1) the shift in mumps incidence toward older individuals, 2) the recent recurrence of mumps outbreaks, and 3) the high proportion of mumps cases among previously vaccinated individuals.

The impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants

Introduction

A key feature of the COVID-19 pandemic has been the emergence of SARS-CoV-2 variants with different transmission characteristics. However, when a novel variant arrives in a host population, it will not necessarily lead to many cases. Instead, it may fade out, due to stochastic effects and the level of immunity in the population. Immunity against novel SARS-CoV-2 variants may be influenced by prior exposures to related viruses, such as other SARS-CoV-2 variants and seasonal coronaviruses, and the level of cross-reactive immunity conferred by those exposures.

Methods

Here, we investigate the impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants in a simplified scenario in which a novel SARS-CoV-2 variant is introduced after an antigenically related virus has spread in the population. We use mathematical modelling to explore the risk that the novel variant invades the population and causes a large number of cases, as opposed to fading out with few cases.

Results

We find that, if cross-reactive immunity is complete (i.e. someone infected by the previously circulating virus is not susceptible to the novel variant), the novel variant must be more transmissible than the previous virus to invade the population. However, in a more realistic scenario in which cross-reactive immunity is partial, we show that it is possible for novel variants to invade, even if they are less transmissible than previously circulating viruses. This is because partial cross-reactive immunity effectively increases the pool of susceptible hosts that are available to the novel variant compared to complete cross-reactive immunity. Furthermore, if previous infection with the antigenically related virus assists the establishment of infection with the novel variant, as has been proposed following some experimental studies, then even variants with very limited transmissibility are able to invade the host population.

Discussion

Our results highlight that fast assessment of the level of cross-reactive immunity conferred by related viruses against novel SARS-CoV-2 variants is an essential component of novel variant risk assessments.

A comparison of COVID-19 outbreaks across US Combined Statistical Areas using new methods for estimating R0 and social distancing behaviour

We investigated the initial outbreak rates and subsequent social distancing behaviour over the initial phase of the COVID-19 pandemic across 29 Combined Statistical Areas (CSAs) of the United States. We used the Numerus Model Builder Data and Simulation Analysis (NMB-DASA) web application to fit the exponential phase of a SCLAIV+D (Susceptible, Contact, Latent, Asymptomatic infectious, symptomatic Infectious, Vaccinated, Dead) disease classes model to outbreaks, thereby allowing us to obtain an estimate of the basic reproductive number R₀ for each CSA. Values of R₀ ranged from 1.9 to 9.4, with a mean and standard deviation of 4.5±1.8. Fixing the parameters from the exponential fit, we again used NMB-DASA to estimate a set of social distancing behaviour parameters to compute an epidemic flattening index c_flatten. Finally, we applied hierarchical clustering methods using this index to divide CSA outbreaks into two clusters: those presenting a social distancing response that was either weaker or stronger. We found c_flatten to be more influential in the clustering process than R₀. Thus, our results suggest that the behavioural response after a short initial exponential growth phase is likely to be more determinative of the rise of an epidemic than R₀ itself.

A contact tracing SIR model for randomly mixed populations

Contact tracing is an important intervention measure to control infectious diseases. We present a new approach that borrows the edge dynamics idea from network models to track contacts included in a compartmental SIR model for an epidemic spreading in a randomly mixed population. Unlike network models, our approach does not require statistical information of the contact network, data that are usually not readily available. The model resulting from this new approach allows us to study the effect of contact tracing and isolation of diagnosed patients on the control reproduction number and number of infected individuals. We estimate the effects of tracing coverage and capacity on the effectiveness of contact tracing. Our approach can be extended to more realistic models that incorporate latent and asymptomatic compartments.

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

The reproduction numberR 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 ofR , 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, formulatingR 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.

Omitting age-dependent mosquito mortality in malaria models underestimates the effectiveness of insecticide-treated nets

Mathematical models of vector-borne infections, including malaria, often assume age-independent mortality rates of vectors, despite evidence that many insects senesce. In this study we present survival data on insecticide-resistant Anopheles gambiae s.l. from experiments in Côte d’Ivoire. We fit a constant mortality function and two age-dependent functions (logistic and Gompertz) to the data from mosquitoes exposed (treated) and not exposed (control) to insecticide-treated nets (ITNs), to establish biologically realistic survival functions. This enables us to explore the effects of insecticide exposure on mosquito mortality rates, and the extent to which insecticide resistance might impact the effectiveness of ITNs. We investigate this by calculating the expected number of infectious bites a mosquito will take in its lifetime, and by extension the vectorial capacity. Our results show that the predicted vectorial capacity is substantially lower in mosquitoes exposed to ITNs, despite the mosquitoes in the experiment being highly insecticide-resistant. The more realistic age-dependent functions provide a better fit to the experimental data compared to a constant mortality function and, hence, influence the predicted impact of ITNs on malaria transmission potential. In models with age-independent mortality, there is a great reduction for the vectorial capacity under exposure compared to no exposure. However, the two age-dependent functions predicted an even larger reduction due to exposure, highlighting the impact of incorporating age in the mortality rates. These results further show that multiple exposures to ITNs had a considerable effect on the vectorial capacity. Overall, the study highlights the importance of including age dependency in mathematical models of vector-borne disease transmission and in fully understanding the impact of interventions.

Interventions against malaria are most commonly targeted on the adult mosquitoes, which transmit the infection from person to person. One of the most important interventions are bed-nets, treated with insecticides. Unfortunately, extensive exposure of mosquitoes to insecticide has led to widespread evolution of insecticide resistance, which might threaten control strategies. Piecing together the overall impact of resistance on the efficacy of insecticide-treated nets is complex, but can be informed by the use of mathematical models. However, there are some assumptions that the models frequently use which are not realistic in terms of the mosquito biology. In this paper, we formulate a model that includes age-dependent mortality rates, an important parameter in vector control since control strategies most commonly aim to reduce the lifespan of the mosquitoes. By using novel data collected using field-derived insecticide-resistant mosquitoes, we explore the effects that the presence of insecticides on nets have on the mortality rates, as well as the difference incorporating age dependency in the model has on the results. We find that including age-dependent mortality greatly alters the anticipated effects of insecticide-treated nets on mosquito transmission potential, and that ignoring this realism potentially overestimates the negative impact of insecticide resistance.

Importation, Local Transmission, and Model Selection in Estimating the Transmissibility of COVID-19: The Outbreak in Shaanxi Province of China as a Case Study

Background: Since the emergence of the COVID-19 pandemic, many models have been applied to understand its epidemiological characteristics. However, the ways in which outbreak data were used in some models are problematic, for example, importation was mixed up with local transmission. Methods: In this study, five models were proposed for the early Shaanxi outbreak in China. We demonstrated how to select a reasonable model and correctly use the outbreak data. Bayesian inference was used to obtain parameter estimates. Results: Model comparison showed that the renewal equation model generates the best model fitting and the Susceptible-Exposed-Diseased-Asymptomatic-Recovered (SEDAR) model is the worst; the performance of the SEEDAR model, which divides the exposure into two stages and includes the pre-symptomatic transmission, and SEEDDAAR model, which further divides infectious classes into two equally, lies in between. The Richards growth model is invalidated by its continuously increasing prediction. By separating continuous importation from local transmission, the basic reproduction number of COVID-19 in Shaanxi province ranges from 0.45 to 0.61, well below the unit, implying that timely interventions greatly limited contact between people and effectively contained the spread of COVID-19 in Shaanxi. Conclusions: The renewal equation model provides the best modelling; mixing continuous importation with local transmission significantly increases the estimate of transmissibility.

The importance of the generation interval in investigating dynamics and control of new SARS-CoV-2 variants

Inferring the relative strength (i.e. the ratio of reproduction numbers) and relative speed (i.e. the difference between growth rates) of new SARS-CoV-2 variants is critical to predicting and controlling the course of the current pandemic. Analyses of new variants have primarily focused on characterizing changes in the proportion of new variants, implicitly or explicitly assuming that the relative speed remains fixed over the course of an invasion. We use a generation-interval-based framework to challenge this assumption and illustrate how relative strength and speed change over time under two idealized interventions: a constant-strength intervention like idealized vaccination or social distancing, which reduces transmission rates by a constant proportion, and a constant-speed intervention like idealized contact tracing, which isolates infected individuals at a constant rate. In general, constant-strength interventions change the relative speed of a new variant, while constant-speed interventions change its relative strength. Differences in the generation-interval distributions between variants can exaggerate these changes and modify the effectiveness of interventions. Finally, neglecting differences in generation-interval distributions can bias estimates of relative strength.

Dynamic survival analysis for non-Markovian epidemic models

We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method's versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach.

A wastewater-based epidemic model for SARS-CoV-2 with application to three Canadian cities

The COVID-19 pandemic has stimulated wastewater-based surveillance, allowing public health to track the epidemic by monitoring the concentration of the genetic fingerprints of SARS-CoV-2 shed in wastewater by infected individuals. Wastewater-based surveillance for COVID-19 is still in its infancy. In particular, the quantitative link between clinical cases observed through traditional surveillance and the signals from viral concentrations in wastewater is still developing and hampers interpretation of the data and actionable public-health decisions. We present a modelling framework that includes both SARS-CoV-2 transmission at the population level and the fate of SARS-CoV-2 RNA particles in the sewage system after faecal shedding by infected persons in the population. Using our mechanistic representation of the combined clinical/wastewater system, we perform exploratory simulations to quantify the effect of surveillance effectiveness, public-health interventions and vaccination on the discordance between clinical and wastewater signals. We also apply our model to surveillance data from three Canadian cities to provide wastewater-informed estimates for the actual prevalence, the effective reproduction number and incidence forecasts. We find that wastewater-based surveillance, paired with this model, can complement clinical surveillance by supporting the estimation of key epidemiological metrics and hence better triangulate the state of an epidemic using this alternative data source.

The source of individual heterogeneity shapes infectious disease outbreaks

There is known heterogeneity between individuals in infectious disease transmission patterns. The source of this heterogeneity is thought to affect epidemiological dynamics but studies tend not to control for the overall heterogeneity in the number of secondary cases caused by an infection. To explore the role of individual variation in infection duration and transmission rate in parasite emergence and spread, while controlling for this potential bias, we simulate stochastic outbreaks with and without parasite evolution. As expected, heterogeneity in the number of secondary cases decreases the probability of outbreak emergence. Furthermore, for epidemics that do emerge, assuming more realistic infection duration distributions leads to faster outbreaks and higher epidemic peaks. When parasites require adaptive mutations to cause large epidemics, the impact of heterogeneity depends on the underlying evolutionary model. If emergence relies on within-host evolution, decreasing the infection duration variance decreases the probability of emergence. These results underline the importance of accounting for realistic distributions of transmission rates to anticipate the effect of individual heterogeneity on epidemiological dynamics.

A hybrid stochastic model and its Bayesian identification for infectious disease screening in a university campus with application to massive COVID-19 screening at the University of Liège

Amid the COVID-19 pandemic, universities are implementing various prevention and mitigation measures. Identifying and isolating infectious individuals by using screening testing is one such a measure that can contribute to reducing spread. Here, we propose a hybrid stochastic model for infectious disease transmission in a university campus with screening testing and its surrounding community. Based on a compartmental modeling strategy, this hybrid stochastic model represents the evolution of the infectious disease and its transmission using continuous-time stochastic dynamics, and it represents the screening testing as discrete stochastic events. We also develop, in a Bayesian framework, the identification of parameters of this hybrid stochastic model, including transmission rates. These parameters were identified from the screening test data for the university population and observed incidence counts for the surrounding community. We implement the exploration of the Bayesian posterior using a machine-learning simulation-based inference approach. The proposed methodology was applied in a retrospective modeling study of a massive COVID-19 screening conducted at the University of Liège in Fall 2020. The emphasis of the paper is on the development of the hybrid stochastic model to assess the impact of screening testing as a measure to reduce spread. The hybrid stochastic model allows various factors to be represented and examined, such as interplay with the surrounding community, variability of the transmission dynamics, the rate of participation in the screening testing, the test sensitivity, the test frequency, the diagnosis delay, and compliance with isolation. The application in the retrospective modeling study suggests that a high rate of participation and a high test frequency are important factors to reduce spread.

Estimating the Number of COVID-19 Cases and Impact of New COVID-19 Variants and Vaccination on the Population in Kerman, Iran: A Mathematical Modeling Study

COVID-19 is spreading all over Iran, and Kerman is one of the most affected cities. We conducted this study to predict COVID-19-related deaths, hospitalization, and infected cases under different scenarios (scenarios A, B, and C) by 31 December 2021 in Kerman. We also aimed to assess the impact of new COVID-19 variants and vaccination on the total number of COVID-19 cases, deaths, and hospitalizations (scenarios D, E, and F) using the modified susceptible-exposed-infected-removed (SEIR) model. We calibrated the model using deaths reported from the start of the epidemic to August 30, 2021. A Monte Carlo Markov Chain (MCMC) uncertainty analysis was used to estimate 95% uncertainty intervals (UI). We also calculated the time-varying reproductive number (R_t) following time-dependent methods. Under the worst-case scenario (scenario A; contact rate = 10, self‐isolation rate = 30%, and average vaccination shots per day = 5,000), the total number of infections by December 31, 2021, would be 1,625,000 (95% UI: 1,112,000–1,898,000) with 6,700 deaths (95% UI: 5,200–8,700). With the presence of alpha and delta variants without vaccine (scenario D), the total number of infected cases and the death toll were estimated to be 957,000 (95% UI: 208,000–1,463,000) and 4,500 (95% UI: 1,500–7,000), respectively. If 70% of the population were vaccinated when the alpha variant was dominant (scenario E), the total number of infected cases and deaths would be 608,000 (95% UI: 122,000–743,000) and 2,700 (95% UI: 700–4,000), respectively. The R_t was ≥1 almost every day during the epidemic. Our results suggest that policymakers should concentrate on improving vaccination and interventions, such as reducing social contacts, stricter limitations for gathering, public education to promote social distancing, incensing case finding and contact tracing, effective isolation, and quarantine to prevent more COVID-19 cases, hospitalizations, and deaths in Kerman.

Planning as Inference in Epidemiological Dynamics Models

In this work we demonstrate how to automate parts of the infectious disease-control policy-making process via performing inference in existing epidemiological models. The kind of inference tasks undertaken include computing the posterior distribution over controllable, via direct policy-making choices, simulation model parameters that give rise to acceptable disease progression outcomes. Among other things, we illustrate the use of a probabilistic programming language that automates inference in existing simulators. Neither the full capabilities of this tool for automating inference nor its utility for planning is widely disseminated at the current time. Timely gains in understanding about how such simulation-based models and inference automation tools applied in support of policy-making could lead to less economically damaging policy prescriptions, particularly during the current COVID-19 pandemic.

Mathematical Modeling to Study Optimal Allocation of Vaccines against COVID-19 Using an Age-Structured Population

Vaccination against the coronavirus disease 2019 (COVID-19) started in early December of 2020 in the USA. The efficacy of the vaccines vary depending on the SARS-CoV-2 variant. Some countries have been able to deploy strong vaccination programs, and large proportions of their populations have been fully vaccinated. In other countries, low proportions of their populations have been vaccinated, due to different factors. For instance, countries such as Afghanistan, Cameroon, Ghana, Haiti and Syria have less than 10% of their populations fully vaccinated at this time. Implementing an optimal vaccination program is a very complex process due to a variety of variables that affect the programs. Besides, science, policy and ethics are all involved in the determination of the main objectives of the vaccination program. We present two nonlinear mathematical models that allow us to gain insight into the optimal vaccination strategy under different situations, taking into account the case fatality rate and age-structure of the population. We study scenarios with different availabilities and efficacies of the vaccines. The results of this study show that for most scenarios, the optimal allocation of vaccines is to first give the doses to people in the 55+ age group. However, in some situations the optimal strategy is to first allocate vaccines to the 15–54 age group. This situation occurs whenever the SARS-CoV-2 transmission rate is relatively high and the people in the 55+ age group have a transmission rate 50% or less that of those in the 15–54 age group. This study and similar ones can provide scientific recommendations for countries where the proportion of vaccinated individuals is relatively small or for future pandemics.

Estimating COVID-19-Related Infections, Deaths, and Hospitalizations in Iran Under Different Physical Distancing and Isolation Scenarios

BACKGROUND

Iran is one of the first few countries that was hit hard with the coronavirus disease 2019 (COVID-19) pandemic. We aimed to estimate the total number of COVID-19 related infections, deaths, and hospitalizations in Iran under different physical distancing and isolation scenarios.

METHODS

We developed a susceptible-exposed-infected/infectious-recovered/removed (SEIR) model, parameterized to the COVID-19 pandemic in Iran. We used the model to quantify the magnitude of the outbreak in Iran and assess the effectiveness of isolation and physical distancing under five different scenarios (A: 0% isolation, through E: 40% isolation of all infected cases). We used Monte-Carlo simulation to calculate the 95% uncertainty intervals (UIs).

RESULTS

Under scenario A, we estimated 5 196 000 (UI 1 753 000-10 220 000) infections to happen till mid-June with 966 000 (UI 467 800-1 702 000) hospitalizations and 111 000 (UI 53 400-200 000) deaths. Successful implantation of scenario E would reduce the number of infections by 90% (ie, 550 000) and change the epidemic peak from 66 000 on June 9, to 9400 on March 1, 2020. Scenario E also reduces the hospitalizations by 92% (ie, 74 500), and deaths by 93% (ie, 7800).

CONCLUSION

With no approved vaccination or therapy available, we found physical distancing and isolation that include public awareness and case-finding and isolation of 40% of infected people could reduce the burden of COVID-19 in Iran by 90% by mid-June.

The role of a programmatic immune response on the evolution of pathogen traits

In modelling pathogen evolution during epidemics, it is important to understand the interactions between within-host infection dynamics and between-host pathogen transmission. Multiscale models often assume an immune response that is highly responsive to pathogen dynamics. Empirical evidence, however, suggests that the immune response in acute infections is triggered and programmatic. This leads to somewhat more predictable infection trajectories where transition times and, consequently, the infectious window are non-exponentially distributed. Here, we develop a within-host model where the immune response is triggered by pathogen growth but otherwise develops independently, and use this to obtain analytic expressions for the infectious period and peak pathogen load. This allows us to model the basic reproductive number in terms of explicit functional relationships among within-host traits including the growth rate of the pathogen. We find that the dependence of pathogen load and the infectious window on within-host parameters constrains the evolution of the pathogen growth rate. At low growth rate, selection favours a higher pathogen load and therefore increasing pathogen growth rate. At high growth rates, selection for a longer infectious window trades off against selection against the effects of virulence. At intermediate growth rates the basic reproductive number is relatively insensitive to changes in the growth rate. The resulting "flat" region of the pathogen fitness landscape is due to the stability of the programmatic immune response in clearing the infection.

Dynamical Modeling as a Tool for Inferring Causation

Dynamical models, commonly used in infectious disease epidemiology, are formal mathematical representations of time-changing systems or processes. For many chronic disease epidemiologists, the link between dynamical models and predominant causal inference paradigms is unclear. In this commentary, we explain the use of dynamical models for representing causal systems and the relevance of dynamical models for causal inference. In certain simple settings, dynamical modeling and conventional statistical methods (e.g., regression-based methods) are equivalent, but dynamical modeling has advantages over conventional statistical methods for many causal inference problems. Dynamical models can be used to transparently encode complex biological knowledge, interference and spillover, effect modification, and variables that influence each other in continuous time. As our knowledge of biological and social systems and access to computational resources increases, there will be growing utility for a variety of mathematical modeling tools in epidemiology.

Estimating the impact of influenza on the epidemiological dynamics of SARS-CoV-2

As in past pandemics, co-circulating pathogens may play a role in the epidemiology of coronavirus disease 2019 (COVID-19), caused by the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In particular, experimental evidence indicates that influenza infection can up-regulate the expression of ACE2-the receptor of SARS-CoV-2 in human cells-and facilitate SARS-CoV-2 infection. Here we hypothesized that influenza impacted the epidemiology of SARS-CoV-2 during the early 2020 epidemic of COVID-19 in Europe. To test this hypothesis, we developed a population-based model of SARS-CoV-2 transmission and of COVID-19 mortality, which simultaneously incorporated the impact of non-pharmaceutical control measures and of influenza on the epidemiological dynamics of SARS-CoV-2. Using statistical inference methods based on iterated filtering, we confronted this model with mortality incidence data in four European countries (Belgium, Italy, Norway, and Spain) to systematically test a range of assumptions about the impact of influenza. We found consistent evidence for a 1.8-3.4-fold (uncertainty range across countries: 1.1 to 5.0) average population-level increase in SARS-CoV-2 transmission associated with influenza during the period of co-circulation. These estimates remained robust to a variety of alternative assumptions regarding the epidemiological traits of SARS-CoV-2 and the modeled impact of control measures. Although further confirmatory evidence is required, our results suggest that influenza could facilitate the spread and hamper effective control of SARS-CoV-2. More generally, they highlight the possible role of co-circulating pathogens in the epidemiology of COVID-19.

The impact of infection-derived immunity on disease dynamics

When modeling infectious diseases, it is common to assume that infection-derived immunity is either (1) non-existent or (2) perfect and lifelong. However there are many diseases in which infection-derived immunity is known to be present but imperfect. There are various ways in which infection-derived immunity can fail, which can ultimately impact the probability that an individual be reinfected by the same pathogen, as well as the long-run population-level prevalence of the pathogen. Here we discuss seven different models of imperfect infection-derived immunity, including waning, leaky and all-or-nothing immunity. For each model we derive the probability that an infected individual becomes reinfected during their lifetime, given that the system is at endemic equilibrium. This can be thought of as the impact that each of these infection-derived immunity failures have on reinfection. This measure is useful because it provides us with a way to compare different modes of failure of infection-derived immunity.

Inferring within-flock transmission dynamics of highly pathogenic avian influenza H5N8 virus in France, 2020

Following the emergence of highly pathogenic avian influenza (H5N8) in France in early December 2020, we used duck mortality data from the index farm to investigate within-flock transmission dynamics. A stochastic epidemic model was fitted to the daily mortality data and model parameters were estimated using an approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithm. The model predicted that the first bird in the flock was infected 5 days (95% credible interval, CI: 3-6) prior to the day of suspicion and that the transmission rate was 4.1 new infections per day (95% CI: 2.8-5.8). On average, ducks became infectious 4.1 h (95% CI: 0.7-9.1) after infection and remained infectious for 4.3 days (95% CI: 2.8-5.7). The model also predicted that 34% (50% prediction interval: 8%-76%) of birds would already be infectious by the day of suspicion, emphasizing the substantial latent threat this virus could pose to other poultry farms and to neighbouring wild birds. This study illustrates how mechanistic models can help provide rapid relevant insights that contribute to the management of infectious disease outbreaks of farmed animals. These methods can be applied to future outbreaks and the resulting parameter estimates made available to veterinary services within a few hours.

Importance of untested infectious individuals for interventions to suppress COVID-19

The impact of the extent of testing infectious individuals on suppression of COVID-19 is illustrated from the early stages of outbreaks in Germany, the Hubei province of China, Italy, Spain and the UK. The predicted percentage of untested infected individuals depends on the specific outbreak but we found that they typically represent 60-80% of all infected individuals during the early stages of the outbreaks. We propose that reducing the underlying transmission from untested cases is crucial to suppress the virus. This can be achieved through enhanced testing in combination with social distancing and other interventions that reduce transmission such as wearing face masks. Once transmission from silent carriers is kept under control by these means, the virus could have been fully suppressed through fast isolation and contact tracing of tested cases.

On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies

Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a major simplification consists in assuming that the infectious period is exponentially distributed, then implying that the chance of recovery is independent on the time since infection. Here, we first attempt to investigate the consequences of relaxing this assumption on the performances of time-variant disease control strategies by using optimal control theory. In the framework of a basic susceptible–infected–removed (SIR) model, an Erlang distribution of the infectious period is considered and optimal isolation strategies are searched for. The objective functional to be minimized takes into account the cost of the isolation efforts per time unit and the sanitary costs due to the incidence of the epidemic outbreak. Applying the Pontryagin’s minimum principle, we prove that the optimal control problem admits only bang–bang solutions with at most two switches. In particular, the optimal strategy could be postponing the starting intervention time with respect to the beginning of the outbreak. Finally, by means of numerical simulations, we show how the shape of the optimal solutions is affected by the different distributions of the infectious period, by the relative weight of the two cost components, and by the initial conditions.