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.

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.

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.

The impact of active case finding on transmission dynamics of tuberculosis: A modelling study.

BACKGROUND: In the last decade, active case finding (ACF) strategies for tuberculosis (TB) have been implemented in many diverse settings, with some showing large increases in case detection and reporting at the sub-national level. There have also been several studies which seek to provide evidence for the benefits of ACF to individuals and communities in the broader context. However, there remains no quantification of the impact of ACF with regards to reducing the burden of transmission. We sought to address this knowledge gap and quantify the potential impact of active case finding on reducing transmission of TB at the national scale and further, to determine the intensification of intervention efforts required to bring the reproduction number (R0) below 1 for TB. METHODS: We adopt a dynamic transmission model that incorporates heterogeneity in risk to TB to assess the impact of an ACF programme (IMPACT TB) on reducing TB incidence in Vietnam and Nepal. We fit the models to country-level incidence data using a Bayesian Markov Chain Monte Carlo approach. We assess the impact of ACF using a parameter in our model, which we term the treatment success rate. Using programmatic data, we estimate how much this parameter has increased as a result of IMPACT TB in the implementation districts of Vietnam and Nepal and quantify additional efforts needed to eliminate transmission of TB in these countries by 2035. RESULTS: Extending the IMPACT TB programme to national coverage would lead to moderate decreases in TB incidence and would not be enough to interrupt transmission by 2035. Decreasing transmission sufficiently to bring the reproduction number (R0) below 1, would require a further intensification of current efforts, even at the sub-national level. CONCLUSIONS: Active case finding programmes are effective in reducing TB in the short term. However, interruption of transmission in high-burden countries, like Vietnam and Nepal, will require comprehensive incremental efforts. Complementary measures to reduce progression from infection to disease, and reactivation of latent infection, are needed to meet the WHO End TB incidence targets.

Investigating extradomiciliary transmission of tuberculosis: An exploratory approach using social network patterns of TB cases and controls and the genotyping of Mycobacterium tuberculosis.

Extradomiciliary contacts have been overlooked in the study of TB transmission due to difficulties in identifying actual contacts in large populations. Complex network analysis provides a framework to model the structure of contacts, specially extradomiciliary ones. We conducted a study of incident sputum-positive TB cases and healthy controls occurring in a moderate TB burden city. Cases and controls were interviewed to obtain data regarding the usual locations of residence, work, study, and leisure. Mycobacterium tuberculosis isolated from sputum was genotyped. The collected data were used to build networks based on a framework of putative social interactions indicating possible TB transmission. A user-friendly open source environment (GraphTube) was setup to extract information from the collected data. Networks based on the likelihood of patient-patient, patient-healthy, and healthy-healthy contacts were setup, depending on a constraint of geographical distance of places attended by the volunteers. Using a threshold for the geographical distance of 300 m, the differences between TB cases and controls are revealed. Several clusters formed by social network nodes with high genotypic similarity were characterized. The developed framework provided consistent results and can be used to support the targeted search of potentially infected individuals and to help to understand the TB transmission.

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 effects of individual nonheritable variation on fitness estimation and coexistence.

Demographic theory and data have emphasized that nonheritable variation in individual frailty enables selection within cohorts, affecting the dynamics of a population while being invisible to its evolution. Here, we include the component of individual variation in longevity or viability which is nonheritable in simple bacterial growth models and explore its ecological and evolutionary impacts. First, we find that this variation produces consistent trends in longevity differences between bacterial genotypes when measured across stress gradients. Given that direct measurements of longevity are inevitably biased due to the presence of this variation and ongoing selection, we propose the use of the trend itself for obtaining more exact inferences of genotypic fitness. Second, we show how species or strain coexistence can be enabled by nonheritable variation in longevity or viability. These general conclusions are likely to extend beyond bacterial systems.

Introducing risk inequality metrics in tuberculosis policy development.

Global stakeholders including the World Health Organization rely on predictive models for developing strategies and setting targets for tuberculosis care and control programs. Failure to account for variation in individual risk leads to substantial biases that impair data interpretation and policy decisions. Anticipated impediments to estimating heterogeneity for each parameter are discouraging despite considerable technical progress in recent years. Here we identify acquisition of infection as the single process where heterogeneity most fundamentally impacts model outputs, due to selection imposed by dynamic forces of infection. We introduce concrete metrics of risk inequality, demonstrate their utility in mathematical models, and pack the information into a risk inequality coefficient (RIC) which can be calculated and reported by national tuberculosis programs for use in policy development and modeling.

Limited available evidence supports theoretical predictions of reduced vaccine efficacy at higher exposure dose.

Understanding the causes of vaccine failure is important for predicting disease dynamics in vaccinated populations and planning disease interventions. Pathogen exposure dose and heterogeneity in host susceptibility have both been implicated as important factors that may reduce overall vaccine efficacy and cause vaccine failure. Here, we explore the effect of pathogen dose and heterogeneity in host susceptibility in reducing efficacy of vaccines. Using simulation-based methods, we find that increases in pathogen exposure dose decrease vaccine efficacy, but this effect is modified by heterogeneity in host susceptibility. In populations where the mode of vaccine action is highly polarized, vaccine efficacy decreases more slowly with exposure dose than in populations with less variable protection. We compared these theoretical results to empirical estimates from a systematic literature review of vaccines tested over multiple exposure doses. We found that few studies (nine of 5,389) tested vaccine protection against infection over multiple pathogen challenge doses, with seven studies demonstrating a decrease in vaccine efficacy with increasing exposure dose. Our research demonstrates that pathogen dose has potential to be an important determinant of vaccine failure, although the limited empirical data highlight a need for additional studies to test theoretical predictions on the plausibility of reduced host susceptibility and high pathogen dose as mechanisms responsible for reduced vaccine efficacy in high transmission settings.

Tuberculosis in Brazil and cash transfer programs: A longitudinal database study of the effect of cash transfer on cure rates.

INTRODUCTION: Tuberculosis incidence is disproportionately high among people in poverty. Cash transfer programs have become an important strategy in Brazil fight inequalities as part of comprehensive poverty alleviation policies. This study was aimed at assessing the effect of being a beneficiary of a governmental cash transfer program on tuberculosis (TB) treatment cure rates. METHODS: We conducted a longitudinal database study including people ≥18 years old with confirmed incident TB in Brazil in 2015. We treated missing data with multiple imputation. Poisson regression models with robust variance were carried out to assess the effect of TB determinants on cure rates. The average effect of being beneficiary of cash transfer was estimated by propensity-score matching. RESULTS: In 2015, 25,084 women and men diagnosed as new tuberculosis case, of whom 1,714 (6.8%) were beneficiaries of a national cash transfer. Among the total population with pulmonary tuberculosis several determinants were associated with cure rates. However, among the cash transfer group, this association was vanished in males, blacks, region of residence, and people not deprived of their freedom and who smoke tobacco. The average treatment effect of cash transfers on TB cure rates, based on propensity score matching, found that being beneficiary of cash transfer improved TB cure rates by 8% [Coefficient 0.08 (95% confidence interval 0.06-0.11) in subjects with pulmonary TB]. CONCLUSION: Our study suggests that, in Brazil, the effect of cash transfer on the outcome of TB treatment may be achieved by the indirect effect of other determinants. Also, these results suggest the direct effect of being beneficiary of cash transfer on improving TB cure rates.

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.

Variation in Wolbachia effects on Aedes mosquitoes as a determinant of invasiveness and vectorial capacity.

Wolbachia has been introduced into Aedes aegypti mosquitoes to control the spread of arboviruses, such as dengue, chikungunya and Zika. Studies showed that certain Wolbachia strains (such as wMel) reduce replication of dengue viruses in the laboratory, prompting the release of mosquitoes carrying the bacterium into the field, where vectorial capacity can be realistically assessed in relation to native non-carriers. Here we apply a new analysis to two published datasets, and show that wMel increases the mean and the variance in Ae. aegypti susceptibility to dengue infection when introgressed into Brazil and Vietnam genetic backgrounds. In the absence of other processes, higher mean susceptibility should lead to enhanced viral transmission. The increase in variance, however, widens the basis for selection imposed by unexplored natural forces, retaining the potential for reducing transmission overall.

Model-based inference from multiple dose, time course data reveals Wolbachia effects on infection profiles of type 1 dengue virus in Aedes aegypti.

Infection is a complex and dynamic process involving a population of invading microbes, the host and its responses, aimed at controlling the situation. Depending on the purpose and level of organization, infection at the organism level can be described by a process as simple as a coin toss, or as complex as a multi-factorial dynamic model; the former, for instance, may be adequate as a component of a population model, while the latter is necessary for a thorough description of the process beginning with a challenge with an infectious inoculum up to establishment or elimination of the pathogen. Experimental readouts in the laboratory are often static, snapshots of the process, assayed under some convenient experimental condition, and therefore cannot comprehensively describe the system. Different from the discrete treatment of infection in population models, or the descriptive summarized accounts of typical lab experiments, in this manuscript, infection is treated as a dynamic process dependent on the initial conditions of the infectious challenge, viral growth, and the host response along time. Here, experimental data is generated for multiple doses of type 1 dengue virus, and pathogen levels are recorded at different points in time for two populations of mosquitoes: either carrying endosymbiont bacteria Wolbachia or not. A dynamic microbe/host-response mathematical model is used to describe pathogen growth in the face of a host response like the immune system, and to infer model parameters for the two populations of insects, revealing a slight-but potentially important-protection conferred by the symbiont.

Vaccine Effects on Heterogeneity in Susceptibility and Implications for Population Health Management.

Heterogeneity in host susceptibility is a key determinant of infectious disease dynamics but is rarely accounted for in assessment of disease control measures. Understanding how susceptibility is distributed in populations, and how control measures change this distribution, is integral to predicting the course of epidemics with and without interventions. Using multiple experimental and modeling approaches, we show that rainbow trout have relatively homogeneous susceptibility to infection with infectious hematopoietic necrosis virus and that vaccination increases heterogeneity in susceptibility in a nearly all-or-nothing fashion. In a simple transmission model with an R0 of 2, the highly heterogeneous vaccine protection would cause a 35 percentage-point reduction in outbreak size over an intervention inducing homogenous protection at the same mean level. More broadly, these findings provide validation of methodology that can help to reduce biases in predictions of vaccine impact in natural settings and provide insight into how vaccination shapes population susceptibility.IMPORTANCE Differences among individuals influence transmission and spread of infectious diseases as well as the effectiveness of control measures. Control measures, such as vaccines, may provide leaky protection, protecting all hosts to an identical degree, or all-or-nothing protection, protecting some hosts completely while leaving others completely unprotected. This distinction can have a dramatic influence on disease dynamics, yet this distribution of protection is frequently unaccounted for in epidemiological models and estimates of vaccine efficacy. Here, we apply new methodology to experimentally examine host heterogeneity in susceptibility and mode of vaccine action as distinct components influencing disease outcome. Through multiple experiments and new modeling approaches, we show that the distribution of vaccine effects can be robustly estimated. These results offer new experimental and inferential methodology that can improve predictions of vaccine effectiveness and have broad applicability to human, wildlife, and ecosystem health.

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.

Expanding vaccine efficacy estimation with dynamic models fitted to cross-sectional prevalence data post-licensure.

The efficacy of vaccines is typically estimated prior to implementation, on the basis of randomized controlled trials. This does not preclude, however, subsequent assessment post-licensure, while mass-immunization and nonlinear transmission feedbacks are in place. In this paper we show how cross-sectional prevalence data post-vaccination can be interpreted in terms of pathogen transmission processes and vaccine parameters, using a dynamic epidemiological model. We advocate the use of such frameworks for model-based vaccine evaluation in the field, fitting trajectories of cross-sectional prevalence of pathogen strains before and after intervention. Using SI and SIS models, we illustrate how prevalence ratios in vaccinated and non-vaccinated hosts depend on true vaccine efficacy, the absolute and relative strength of competition between target and non-target strains, the time post follow-up, and transmission intensity. We argue that a mechanistic approach should be added to vaccine efficacy estimation against multi-type pathogens, because it naturally accounts for inter-strain competition and indirect effects, leading to a robust measure of individual protection per contact. Our study calls for systematic attention to epidemiological feedbacks when interpreting population level impact. At a broader level, our parameter estimation procedure provides a promising proof of principle for a generalizable framework to infer vaccine efficacy post-licensure.