Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold.

Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as "frailty variation". Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being crucial to protect vulnerable individuals from severe outcomes as the virus becomes endemic.

Herd immunity under individual variation and reinfection.

We study a susceptible-exposed-infected-recovered (SEIR) model considered by Aguas et al. (In: Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics, 2021), Gomes et al. (In: J Theor Biol. 540:111063, 2022) where individuals are assumed to differ in their susceptibility or exposure to infection. Under this heterogeneity assumption, epidemic growth is effectively suppressed when the percentage of the population having acquired immunity surpasses a critical level - the herd immunity threshold - that is lower than in homogeneous populations. We derive explicit formulas to calculate herd immunity thresholds and stable configurations, especially when susceptibility or exposure are gamma distributed, and explore extensions of the model.

Modelling the epidemiology of residual Plasmodium vivax malaria in a heterogeneous host population: A case study in the Amazon Basin.

The overall malaria burden in the Americas has decreased dramatically over the past two decades, but residual transmission pockets persist across the Amazon Basin, where Plasmodium vivax is the predominant infecting species. Current elimination efforts require a better quantitative understanding of malaria transmission dynamics for planning, monitoring, and evaluating interventions at the community level. This can be achieved with mathematical models that properly account for risk heterogeneity in communities approaching elimination, where few individuals disproportionately contribute to overall malaria prevalence, morbidity, and onwards transmission. Here we analyse demographic information combined with routinely collected malaria morbidity data from the town of Mâncio Lima, the main urban transmission hotspot of Brazil. We estimate the proportion of high-risk subjects in the host population by fitting compartmental susceptible-infected-susceptible (SIS) transmission models simultaneously to age-stratified vivax malaria incidence densities and the frequency distribution of P. vivax malaria attacks experienced by each individual over 12 months. Simulations with the best-fitting SIS model indicate that 20% of the hosts contribute 86% of the overall vivax malaria burden. Despite the low overall force of infection typically found in the Amazon, about one order of magnitude lower than that in rural Africa, high-risk individuals gradually develop clinical immunity following repeated infections and eventually constitute a substantial infectious reservoir comprised of asymptomatic parasite carriers that is overlooked by routine surveillance but likely fuels onwards malaria transmission. High-risk individuals therefore represent a priority target for more intensive and effective interventions that may not be readily delivered to the entire community.

The Importance of Heterogeneity to the Epidemiology of Tuberculosis.

Although less well-recognized than for other infectious diseases, heterogeneity is a defining feature of tuberculosis (TB) epidemiology. To advance toward TB elimination, this heterogeneity must be better understood and addressed. Drivers of heterogeneity in TB epidemiology act at the level of the infectious host, organism, susceptible host, environment, and distal determinants. These effects may be amplified by social mixing patterns, while the variable latent period between infection and disease may mask heterogeneity in transmission. Reliance on notified cases may lead to misidentification of the most affected groups, as case detection is often poorest where prevalence is highest. Assuming that average rates apply across diverse groups and ignoring the effects of cohort selection may result in misunderstanding of the epidemic and the anticipated effects of control measures. Given this substantial heterogeneity, interventions targeting high-risk groups based on location, social determinants, or comorbidities could improve efficiency, but raise ethical and equity considerations.

Infectivity of Chronic Malaria Infections and Its Consequences for Control and Elimination.

Assessing the importance of targeting the chronic Plasmodium falciparum malaria reservoir is pivotal as the world moves toward malaria eradication. Through the lens of a mathematical model, we show how, for a given malaria prevalence, the relative infectivity of chronic individuals determines what intervention tools are predicted be the most effective. Crucially, in a large part of the parameter space where elimination is theoretically possible, it can be achieved solely through improved case management. However, there are a significant number of settings where malaria elimination requires not only good vector control but also a mass drug administration campaign. Quantifying the relative infectiousness of chronic malaria across a range of epidemiological settings would provide essential information for the design of effective malaria elimination strategies. Given the difficulties obtaining this information, we also provide a set of epidemiological metrics that can be used to guide policy in the absence of such data.

Migration to middle-income countries and tuberculosis-global policies for global economies.

BACKGROUND: International migration to middle-income countries is increasing and its health consequences, in particular increasing transmission rates of tuberculosis (TB), deserve consideration. Migration and TB are a matter of concern in high-income countries and targeted screening of migrants for active and latent TB infection is a main strategy to manage risk and minimize transmission. In this paper, we discuss some aspects of TB control and migration in the context of middle-income countries, together with the prospect of responding with equitable and comprehensive policies. MAIN BODY: TB rates in middle-income countries remain disproportionally high among the poorest and most vulnerable groups in large cities where most migrant populations are concentrated. Policies that tackle migrant TB in high-income countries may be inadequate for middle-income countries because of their different socio-economic and cultural scenarios. Strategies to control TB in these settings must take into account the characteristics of middle-income countries and the complexity of TB as a disease of poverty. Intersectoral policies of social protection such as cash-transfer programs help reducing poverty and improving health in vulnerable populations. We address the development of new approaches to improve well-established strategies including contact tracing and active and latent TB screening as an 'add on' to the existing health care guidelines of conditional cash transfer programs. In addition, we discuss how it might improve health and welfare among both poor migrants and locally-born populations. Authorities from middle-income countries should recognise that migrants are a vulnerable social group and promote cooperation efforts between sending and receiving countries for mitigation of poverty and prevention of disease in this group. CONCLUSIONS: Middle-income countries have long sent migrants overseas. However, the influx of large migrant populations into their societies is relatively new and a growing phenomenon and it is time to set comprehensive goals to improve health among these communities. Conditional cash transfer policies with TB screening and strengthening of DOTS are some strategies that deserve attention. Reduction of social and health inequality among migrants should be incorporated into concerted actions to meet TB control targets.

How direct competition shapes coexistence and vaccine effects in multi-strain pathogen systems.

We describe an integrated modeling framework for understanding strain coexistence in polymorphic pathogen systems. Previous studies have debated the utility of neutral formulations and focused on cross-immunity between strains as a major stabilizing mechanism. Here we convey that direct competition for colonization mediates stable coexistence only when competitive abilities amongst pathogen clones satisfy certain pairwise asymmetries. We illustrate our ideas with nested SIS models of single and dual colonization, applied to polymorphic pneumococcal bacteria. By fitting the models to cross-sectional prevalence data from Portugal (before and after the introduction of a seven-valent pneumococcal conjugate vaccine), we are able to not only statistically compare neutral and non-neutral epidemiological formulations, but also estimate vaccine efficacy, transmission and competition parameters simultaneously. Our study highlights that the response of polymorphic pathogen populations to interventions holds crucial information about strain interactions, which can be extracted by suitable nested modeling.

A theoretical framework to identify invariant thresholds in infectious disease epidemiology.

Setting global strategies and targets for disease prevention and control often involves mathematical models. Model structure is typically subject to intense scrutiny, such as confrontation with empirical data and alternative formulations, while a less frequently challenged aspect is the widely adopted reduction of parameters to their average values. Focusing on endemic diseases, we use a general transmission model to explain how mean field approximations decrease the estimated R0 from prevalence data, while threshold phenomena - such as the epidemic and reinfection thresholds - remain invariant. This results in an underestimation of the effort required to control disease, which may be particularly severe when the approximation inappropriately places transmission estimates below important thresholds. These concepts are widely applicable across endemic pathogen systems.

End TB strategy: the need to reduce risk inequalities.

BACKGROUND: Diseases occur in populations whose individuals differ in essential characteristics, such as exposure to the causative agent, susceptibility given exposure, and infectiousness upon infection in the case of infectious diseases. DISCUSSION: Concepts developed in demography more than 30 years ago assert that variability between individuals affects substantially the estimation of overall population risk from disease incidence data. Methods that ignore individual heterogeneity tend to underestimate overall risk and lead to overoptimistic expectations for control. Concerned that this phenomenon is frequently overlooked in epidemiology, here we feature its significance for interpreting global data on human tuberculosis and predicting the impact of control measures. We show that population-wide interventions have the greatest impact in populations where all individuals face an equal risk. Lowering variability in risk has great potential to increase the impact of interventions. Reducing inequality, therefore, empowers health interventions, which in turn improves health, further reducing inequality, in a virtuous circle.

Unveiling time in dose-response models to infer host susceptibility to pathogens.

The biological effects of interventions to control infectious diseases typically depend on the intensity of pathogen challenge. As much as the levels of natural pathogen circulation vary over time and geographical location, the development of invariant efficacy measures is of major importance, even if only indirectly inferrable. Here a method is introduced to assess host susceptibility to pathogens, and applied to a detailed dataset generated by challenging groups of insect hosts (Drosophila melanogaster) with a range of pathogen (Drosophila C Virus) doses and recording survival over time. The experiment was replicated for flies carrying the Wolbachia symbiont, which is known to reduce host susceptibility to viral infections. The entire dataset is fitted by a novel quantitative framework that significantly extends classical methods for microbial risk assessment and provides accurate distributions of symbiont-induced protection. More generally, our data-driven modeling procedure provides novel insights for study design and analyses to assess interventions.

On the correlation between variance in individual susceptibilities and infection prevalence in populations.

The hypothesis that infection prevalence in a population correlates negatively with variance in the susceptibility of its individuals has support from experimental, field, and theoretical studies. However, its generality has never been formally demonstrated. Here we formulate an endemic SIS model with individual susceptibility distributed according to a discrete or continuous probability function to assess the generality of such hypothesis. We introduce an ordering among susceptibility distributions with the same mean, analogous to that considered in Katriel (J Math Biol 65:237-262, 2012) to order the attack rates in an epidemic SIR model with heterogeneity. It turns out that if one distribution dominates another in this order then it has greater variance and corresponds to a lower infection prevalence for R0 varying in a suitable maximal interval of the form ]1, R0*]. We show that in both the discrete and continuous frameworks R0* can be finite, so that the expected correlation among variance and prevalence does not always hold. For discrete distributions this fact is demonstrated analytically, and the proof introduces a constructive procedure to find ordered pairs for which R0* is arbitrarily close to 1. For continuous distributions our conclusion is based on numerical studies with the beta distribution. Finally, we present explicit partial orderings among discrete susceptibility distributions and among symmetric beta distributions which guarantee that R0* = +∞.

Utilizing syndromic surveillance data for estimating levels of influenza circulation.

The availability of weekly Web-based participatory surveillance data on self-reported influenza-like illness (ILI), defined here as self-reported fever and cough/sore throat, over several influenza seasons allows for estimation of the incidence of influenza infection in population cohorts. We demonstrate this using syndromic data reported through the Influenzanet surveillance platform in the Netherlands. We used the 2011-2012 influenza season, a low-incidence season that began late, to assess the baseline rates of self-reported ILI during periods of low influenza circulation, and we used ILI rates above that baseline level from the 2012-1013 season, a major influenza season, to estimate influenza attack rates for that period. The latter conversion required estimates of age-specific probabilities of self-reported ILI given influenza (Flu) infection (P(ILI | Flu)), which were obtained from separate data (extracted from Hong Kong, China, household studies). For the 2012-2013 influenza season in the Netherlands, we estimated combined influenza A/B attack rates of 29.2% (95% credible interval (CI): 21.6, 37.9) among survey participants aged 20-49 years, 28.3% (95% CI: 20.7, 36.8) among participants aged 50-60 years, and 5.9% (95% CI: 0.4, 11.8) among participants aged ≥61 years. Estimates of influenza attack rates can be obtained in other settings using analogous, multiseason surveillance data on self-reported ILI together with separate, context-specific estimates of P(ILI | Flu).

Interpreting measures of tuberculosis transmission: a case study on the Portuguese population.

BACKGROUND: Tuberculosis remains a high burden for Human society despite considerable investments in its control. Unique features in the history of infection and transmission dynamics of tuberculosis pose serious limitations on the direct interpretation of surveillance data and call for models that incorporate latent processes and simulate specific interventions. METHODS: A transmission model was adjusted to the dataset of active tuberculosis cases reported in Portugal between 2002 and 2009. We estimated key transmission parameters from the data (i.e. time to diagnosis, treatment length, default proportion, proportion of pulmonary TB cases). Using the adjusted model to the Portuguese case, we estimated the total burden of tuberculosis in Portugal. We further performed sensitivity analysis to heterogeneities in susceptibility to infection and exposure intensity. RESULTS: We calculated a mean time to diagnose of 2.81 months and treatment length of 8.80 months in Portugal. The proportion defaulting treatment was calculated as 0.04 and the proportion of pulmonary cases as 0.75. Using these values, we estimated a TB burden of 1.6 million infected persons, corresponding to more than 15% of the Portuguese population. We further described the sensitivity of these estimates to heterogeneity. CONCLUSIONS: We showed that the model reproduces well the observed dynamics of the Portuguese data, thus demonstrating its adequacy for devising control strategies for TB and predicting the effects of interventions.

inTB - a data integration platform for molecular and clinical epidemiological analysis of tuberculosis.

BACKGROUND: Tuberculosis is currently the second highest cause of death from infectious diseases worldwide. The emergence of multi and extensive drug resistance is threatening to make tuberculosis incurable. There is growing evidence that the genetic diversity of Mycobacterium tuberculosis may have important clinical consequences. Therefore, combining genetic, clinical and socio-demographic data is critical to understand the epidemiology of this infectious disease, and how virulence and other phenotypic traits evolve over time. This requires dedicated bioinformatics platforms, capable of integrating and enabling analyses of this heterogeneous data. RESULTS: We developed inTB, a web-based system for integrated warehousing and analysis of clinical, socio-demographic and molecular data for Mycobacterium sp. isolates. As a database it can organize and display data from any of the standard genotyping methods (SNP, MIRU-VNTR, RFLP and spoligotype), as well as an extensive array of clinical and socio-demographic variables that are used in multiple countries to characterize the disease. Through the inTB interface it is possible to insert and download data, browse the database and search specific parameters. New isolates are automatically classified into strains according to an internal reference, and data uploaded or typed in is checked for internal consistency. As an analysis framework, the system provides simple, point and click analysis tools that allow multiple types of data plotting, as well as simple ways to download data for external analysis. Individual trees for each genotyping method are available, as well as a super tree combining all of them. The integrative nature of inTB grants the user the ability to generate trees for filtered subsets of data crossing molecular and clinical/socio-demografic information. inTB is built on open source software, can be easily installed locally and easily adapted to other diseases. Its design allows for use by research laboratories, hospitals or public health authorities. The full source code as well as ready to use packages is available at http://www.evocell.org/inTB. CONCLUSIONS: To the best of our knowledge, this is the only system capable of integrating different types of molecular data with clinical and socio-demographic data, empowering researchers and clinicians with easy to use analysis tools that were not possible before.

Successes and shortcomings of polio eradication: a transmission modeling analysis.

Polio eradication is on the cusp of success, with only a few regions still maintaining transmission. Improving our understanding of why some regions have been successful and others have not will help with both global eradication of polio and development of more effective vaccination strategies for other pathogens. To examine the past 25 years of eradication efforts, we constructed a transmission model for wild poliovirus that incorporates waning immunity (which affects both infection risk and transmissibility of any resulting infection), age-mediated vaccination rates, and transmission of oral polio vaccine. The model produces results consistent with the 4 country categories defined by the Global Polio Eradication Program: elimination with no subsequent outbreaks; elimination with subsequent transient outbreaks; elimination with subsequent outbreaks and transmission detected for more than 12 months; and endemic polio transmission. Analysis of waning immunity rates and oral polio vaccine transmissibility reveals that higher waning immunity rates make eradication more difficult because of increasing numbers of infectious adults, and that higher oral polio vaccine transmission rates make eradication easier as adults become reimmunized. Given these dynamic properties, attention should be given to intervention strategies that complement childhood vaccination. For example, improvement in sanitation can reduce the reproduction number in problematic regions, and adult vaccination can lower adult transmission.

Comparative analysis of Streptococcus pneumoniae transmission in Portuguese and Finnish day-care centres.

BACKGROUND: Day-care centre (DCC) attendees play a central role in maintaining the circulation of Streptococcus pneumoniae (pneumococcus) in the population. The prevalence of pneumococcal carriage is highest in DCC attendees but varies across countries and is found to be consistently lower in Finland than in Portugal. We compared key parameters underlying pneumococcal transmission in DCCs to understand which of these contributed to the observed differences in carriage prevalence. METHODS: Longitudinal data about serotype-specific carriage in DCC attendees in Portugal (47 children in three rooms; mean age 2 years; range 1-3 years) and Finland (91 children in seven rooms; mean age 4 years; range 1-7 years) were analysed with a continuous-time event history model in a Bayesian framework. The monthly rates of within-room transmission, community acquisition and clearing carriage were estimated. RESULTS: The posterior mean of within-room transmission rate was 1.05 per month (Portugal) vs. 0.63 per month (Finland). The smaller rate of clearance in Portugal (0.57 vs. 0.73 per month) is in accordance with the children being younger. The overall community rate of acquisition was larger in the Portuguese setting (0.25 vs. 0.11 per month), in agreement with that the groups belonged to a larger DCC. The model adequately predicted the observed levels of carriage prevalence and longitudinal patterns in carriage acquisition and clearance. CONCLUSIONS: The difference in prevalence of carriage (61% in Portuguese vs. 26% among Finnish DCC attendees) was assigned to the longer duration of carriage in younger attendees and a significantly higher rate of within-room transmission and community acquisition in the Portuguese setting.

How host heterogeneity governs tuberculosis reinfection?

Recurrent episodes of tuberculosis (TB) can be due to relapse of latent infection or exogenous reinfection, and discrimination is crucial for control planning. Molecular genotyping of Mycobacterium tuberculosis isolates offers concrete opportunities to measure the relative contribution of reinfection in recurrent disease. Here, a mathematical model of TB transmission is fitted to data from 14 molecular epidemiology studies, enabling the estimation of relevant epidemiological parameters. Meta-analysis reveals that rates of reinfection after successful treatment are higher than rates of new TB, raising an important question about the underlying mechanism. We formulate two alternative mechanisms within our model framework: (i) infection increases susceptibility to reinfection or (ii) infection affects individuals differentially, thereby recruiting high-risk individuals to the group at risk for reinfection. The second mechanism is better supported by the fittings to the data, suggesting that reinfection rates are inflated through a population phenomenon that occurs in the presence of heterogeneity in individual risk of infection. As a result, rates of reinfection are higher when measured at the population level even though they might be lower at the individual level. Finally, differential host recruitment is modulated by transmission intensity, being less pronounced when incidence is high.

The role of weather on the relation between influenza and influenza-like illness.

Influenza epidemics, enabled by viral antigenic drift, occur invariably each winter in temperate climates. However, attempts to correlate the magnitude of virus change and epidemic size have been unsatisfactory. The incidence of influenza is not typically measured directly, but rather derived from the incidence of influenza-like illness (ILI), a clinical syndrome. Weather factors have been shown to influence the manifestation of influenza-like symptoms. We fitted an influenza transmission model to time series of influenza-like illness as monitored from 2003 to 2010 by two independent symptomatic surveillance systems (Influenzanet and EISN) in three European countries. By assuming that seasonality only acts upon the manifestation of symptoms, the model shows a significant correlation between the absolute humidity and temperature at the time of infection, and the proportion of influenza infections fulfilling the clinical ILI case definition, the so-called ILI factor. When a weather-dependent ILI factor is included in the model, the epidemic size of influenza-like illness becomes dependent not only on the susceptibility of the population at the beginning of the epidemic season but also on the weather conditions during which the epidemic unfolds. The combination reduces season-to-season variation in epidemic size and, interestingly, leads to a non-monotonic trend whereby the largest ILI epidemic occurs for moderate initial susceptibility.

Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold.

Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as "frailty variation". Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being critical to protect vulnerable individuals from severe outcomes as the virus becomes endemic.