Structured models of infectious disease: inference with discrete data

Evaluating the potential impact of rubella-containing vaccine introduction on congenital rubella syndrome in Afghanistan, Dem. Republic of Congo, Ethiopia, Nigeria, and Pakistan: A mathematical modeling study

We assessed the potential impact of introducing rubella-containing vaccine (RCV) on congenital rubella syndrome (CRS) incidence in Afghanistan (AFG), Democratic Republic of Congo (COD), Ethiopia (ETH), Nigeria (NGA), and Pakistan (PAK). We simulated several RCV introduction scenarios over 30 years using a validated mathematical model. Our findings indicate that RCV introduction could avert between 86,000 and 535,000 CRS births, preventing 2.5 to 15.8 million disability-adjusted life years. AFG and PAK could reduce about 90% of CRS births by introducing RCV with current measles routine coverage and executing supplemental immunization activities (SIAs). However, COD, NGA, and ETH must increase their current routine vaccination coverage to reduce CRS incidence significantly. This study showcases the potential benefits of RCV introduction and reinforces the need for global action to strengthen immunization programs.

Pathogens stabilize or destabilize depending on host stage structure

A common assumption is that pathogens more readily destabilize their host populations, leading to an elevated risk of driving both the host and pathogen to extinction. This logic underlies many strategies in conservation biology and pest and disease management. Yet, the interplay between pathogens and population stability likely varies across contexts, depending on the environment and traits of both the hosts and pathogens. This context-dependence may be particularly important in natural consumer-host populations where size- and stage-structured competition for resources strongly modulates population stability. Few studies, however, have examined how the interplay between size and stage structure and infectious disease shapes the stability of host populations. Here, we extend previously developed size-dependent theory for consumer-resource interactions to examine how pathogens influence the stability of host populations across a range of contexts. Specifically, we integrate a size- and stage-structured consumer-resource model and a standard epidemiological model of a directly transmitted pathogen. The model reveals surprisingly rich dynamics, including sustained oscillations, multiple steady states, biomass overcompensation, and hydra effects. Moreover, these results highlight how the stage structure and density of host populations interact to either enhance or constrain disease outbreaks. Our results suggest that accounting for these cross-scale and bidirectional feedbacks can provide key insight into the structuring role of pathogens in natural ecosystems while also improving our ability to understand how interventions targeting one may impact the other.

Feasibility of measles and rubella vaccination programmes for disease elimination: a modelling study

Background

Marked reductions in the incidence of measles and rubella have been observed since the widespread use of the measles and rubella vaccines. Although no global goal for measles eradication has been established, all six WHO regions have set measles elimination targets. However, a gap remains between current control levels and elimination targets, as shown by large measles outbreaks between 2017 and 2019. We aimed to model the potential for measles and rubella elimination globally to inform a WHO report to the 73rd World Health Assembly on the feasibility of measles and rubella eradication.

Methods

In this study, we modelled the probability of measles and rubella elimination between 2020 and 2100 under different vaccination scenarios in 93 countries of interest. We evaluated measles and rubella burden and elimination across two national transmission models each (Dynamic Measles Immunisation Calculation Engine [DynaMICE], Pennsylvania State University [PSU], Johns Hopkins University, and Public Health England models), and one subnational measles transmission model (Institute for Disease Modeling model). The vaccination scenarios included a so-called business as usual approach, which continues present vaccination coverage, and an intensified investment approach, which increases coverage into the future. The annual numbers of infections projected by each model, country, and vaccination scenario were used to explore if, when, and for how long the infections would be below a threshold for elimination.

Findings

The intensified investment scenario led to large reductions in measles and rubella incidence and burden. Rubella elimination is likely to be achievable in all countries and measles elimination is likely in some countries, but not all. The PSU and DynaMICE national measles models estimated that by 2050, the probability of elimination would exceed 75% in 14 (16%) and 36 (39%) of 93 modelled countries, respectively. The subnational model of measles transmission highlighted inequity in routine coverage as a likely driver of the continuance of endemic measles transmission in a subset of countries.

Interpretation

To reach regional elimination goals, it will be necessary to innovate vaccination strategies and technologies that increase spatial equity of routine vaccination, in addition to investing in existing surveillance and outbreak response programmes.

Funding

WHO, Gavi, the Vaccine Alliance, US Centers for Disease Control and Prevention, and the Bill & Melinda Gates Foundation.

Infectious disease in an era of global change

The twenty-first century has witnessed a wave of severe infectious disease outbreaks, not least the COVID-19 pandemic, which has had a devastating impact on lives and livelihoods around the globe. The 2003 severe acute respiratory syndrome coronavirus outbreak, the 2009 swine flu pandemic, the 2012 Middle East respiratory syndrome coronavirus outbreak, the 2013-2016 Ebola virus disease epidemic in West Africa and the 2015 Zika virus disease epidemic all resulted in substantial morbidity and mortality while spreading across borders to infect people in multiple countries. At the same time, the past few decades have ushered in an unprecedented era of technological, demographic and climatic change: airline flights have doubled since 2000, since 2007 more people live in urban areas than rural areas, population numbers continue to climb and climate change presents an escalating threat to society. In this Review, we consider the extent to which these recent global changes have increased the risk of infectious disease outbreaks, even as improved sanitation and access to health care have resulted in considerable progress worldwide.

Examination of scenarios introducing rubella vaccine in the Democratic Republic of the Congo

•

Serosurvey data suggest R₀ values for rubella in the DRC on the range 3 to 8.

•

Supplementary immunization activities provide multi-decade reduction in burden.

•

Post-vaccine introduction, burden will likely be concentrated in outbreaks.

Background

Rubella vaccine has yet to be introduced into the national immunization schedule of the Democratic Republic of the Congo (DRC); the current burden of congenital rubella syndrome (CRS) is unknown and likely to be high. An important consideration prior to introducing rubella containing vaccine (RCV) is the potential inverse relationship between RCV coverage and CRS incidence. Increasing RCV coverage will also increase in the average age of infection. Cumulative infections across all age groups will decrease, but the number of infections in age groups vulnerable to CRS may increase.

Methods

Rubella transmission dynamics in the DRC were simulated using a stochastic agent-based model of transmission. Input parameter values for known properties, demographic variables, and interventions were fixed; infectivity was inferred from seropositivity profiles in survey data.

Results

Our simulations of RCV introduction for the DRC demonstrate that an increase in CRS burden is unlikely. Continued endemic transmission is only plausible when routine immunization coverage is less than 40% and follow-up supplemental immunization activities have poor coverage for decades.

Conclusion

Increased vaccination coverage tends to increase the annual variability of CRS burden. Simulations examining low vaccination coverage and high mean CRS burden are outbreak prone, with multiple years of reduced burden followed by acute outbreaks. These outcomes contrast simulations with no vaccination coverage and high mean CRS burden, which have more consistent burden from year to year.

Lives saved with vaccination for 10 pathogens across 112 countries in a pre-COVID-19 world

Background

Vaccination is one of the most effective public health interventions. We investigate the impact of vaccination activities for Haemophilus influenzae type b, hepatitis B, human papillomavirus, Japanese encephalitis, measles, Neisseria meningitidis serogroup A, rotavirus, rubella, Streptococcus pneumoniae, and yellow fever over the years 2000-2030 across 112 countries.

Methods

Twenty-one mathematical models estimated disease burden using standardised demographic and immunisation data. Impact was attributed to the year of vaccination through vaccine-activity-stratified impact ratios.

Results

We estimate 97 (95%CrI[80, 120]) million deaths would be averted due to vaccination activities over 2000-2030, with 50 (95%CrI[41, 62]) million deaths averted by activities between 2000 and 2019. For children under-5 born between 2000 and 2030, we estimate 52 (95%CrI[41, 69]) million more deaths would occur over their lifetimes without vaccination against these diseases.

Conclusions

This study represents the largest assessment of vaccine impact before COVID-19-related disruptions and provides motivation for sustaining and improving global vaccination coverage in the future.

Funding

VIMC is jointly funded by Gavi, the Vaccine Alliance, and the Bill and Melinda Gates Foundation (BMGF) (BMGF grant number: OPP1157270 / INV-009125). Funding from Gavi is channelled via VIMC to the Consortium's modelling groups (VIMC-funded institutions represented in this paper: Imperial College London, London School of Hygiene and Tropical Medicine, Oxford University Clinical Research Unit, Public Health England, Johns Hopkins University, The Pennsylvania State University, Center for Disease Analysis Foundation, Kaiser Permanente Washington, University of Cambridge, University of Notre Dame, Harvard University, Conservatoire National des Arts et Métiers, Emory University, National University of Singapore). Funding from BMGF was used for salaries of the Consortium secretariat (authors represented here: TBH, MJ, XL, SE-L, JT, KW, NMF, KAMG); and channelled via VIMC for travel and subsistence costs of all Consortium members (all authors). We also acknowledge funding from the UK Medical Research Council and Department for International Development, which supported aspects of VIMC's work (MRC grant number: MR/R015600/1).JHH acknowledges funding from National Science Foundation Graduate Research Fellowship; Richard and Peggy Notebaert Premier Fellowship from the University of Notre Dame. BAL acknowledges funding from NIH/NIGMS (grant number R01 GM124280) and NIH/NIAID (grant number R01 AI112970). The Lives Saved Tool (LiST) receives funding support from the Bill and Melinda Gates Foundation.This paper was compiled by all coauthors, including two coauthors from Gavi. Other funders had no role in study design, data collection, data analysis, data interpretation, or writing of the report. All authors had full access to all the data in the study and had final responsibility for the decision to submit for publication.

The ecological dynamics of the coronavirus epidemics during transmission from outside sources when R 0 is successfully managed below one

Since COVID-19 spread globally in early 2020 and was declared a pandemic by the World Health Organization (WHO) in March, many countries are managing the local epidemics effectively through intervention measures that limit transmission. The challenges of immigration of new infections into regions and asymptomatic infections remain. Standard deterministic compartmental models are inappropriate for sub- or peri-critical epidemics (reproductive number close to or less than one), so individual-based models are often used by simulating transmission from an infected person to others. However, to be realistic, these models require a large number of parameters, each with its own set of uncertainties and lack of analytic tractability. Here, we apply stochastic age-structured Leslie theory with a long history in ecological research to provide some new insights to epidemic dynamics fuelled by external imports. We model the dynamics of an epidemic when R ₀ is below one, representing COVID-19 transmission following the successful application of intervention measures, and the transmission dynamics expected when infections migrate into a region. The model framework allows more rapid prediction of the shape and size of an epidemic to improve scaling of the response. During an epidemic when the numbers of infected individuals are rapidly changing, this will help clarify the situation of the pandemic and guide faster and more effective intervention.

Feasibility assessment of measles and rubella eradication

This report addresses the epidemiological aspects and feasibility of measles and rubella eradication and the potential resource requirements in response to the request of the Director-General at the Seventieth World Health Assembly held on May 31, 2017. A guiding principle is that the path toward measles and rubella eradication should serve to strengthen primary health care, promote universal health coverage, and be a pathfinder for new vision and strategy for immunization over the next decade as laid out in the Immunization Agenda 2030. Specifically, this report: 1) highlights the importance of measles and rubella as global health priorities; 2) reviews the current global measles and rubella situation; 3) summarizes prior assessments of the feasibility of measles and rubella eradication; 4) assesses the progress and challenges in achieving regional measles and rubella elimination; 5) assesses additional considerations for measles and rubella eradication, including the results of modelling and economic analyses; 6) assesses the implications of establishing a measles and rubella eradication goal and the process for setting an eradication target date; 7) proposes a framework for determining preconditions for setting a target date for measles and rubella eradication and how these preconditions should be understood and used; and 8) concludes with recommendations endorsed by SAGE.

The Impact of Rubella Vaccine Introduction on Rubella Infection and Congenital Rubella Syndrome: A Systematic Review of Mathematical Modelling Studies

INTRODUCTION

Rubella vaccines have been used to prevent rubella and congenital rubella syndrome (CRS) in several World Health Organization (WHO) regions. Mathematical modelling studies have simulated introduction of rubella-containing vaccines (RCVs), and their results have been used to inform rubella introduction strategies in several countries. This systematic review aimed to synthesize the evidence from mathematical models regarding the impact of introducing RCVs.

METHODS

We registered the review in the international prospective register of systematic reviews (PROSPERO) with registration number CRD42020192638. Systematic review methods for classical epidemiological studies and reporting guidelines were followed as far as possible. A comprehensive search strategy was used to identify published and unpublished studies with no language restrictions. We included deterministic and stochastic models that simulated RCV introduction into the public sector vaccination schedule, with a time horizon of at least five years. Models focused only on estimating epidemiological parameters were excluded. Outcomes of interest were time to rubella and CRS elimination, trends in incidence of rubella and CRS, number of vaccinated individuals per CRS case averted, and cost-effectiveness of vaccine introduction strategies. The methodological quality of included studies was assessed using a modified risk of bias tool, and a qualitative narrative was provided, given that data synthesis was not feasible.

RESULTS

Seven studies were included from a total of 1393 records retrieved. The methodological quality was scored high for six studies and very high for one study. Quantitative data synthesis was not possible, because only one study reported point estimates and uncertainty intervals for the outcomes. All seven included studies presented trends in rubella incidence, six studies reported trends in CRS incidence, two studies reported the number vaccinated individuals per CRS case averted, and two studies reported an economic evaluation measure. Time to CRS elimination and time to rubella elimination were not reported by any of the included studies. Reported trends in CRS incidence showed elimination within five years of RCV introduction with scenarios involving mass vaccination of older children in addition to routine infant vaccination. CRS incidence was higher with RCV introduction than without RCV when public vaccine coverage was lower than 50% or only private sector vaccination was implemented. Although vaccination of children at a given age achieved slower declines in CRS incidence compared to mass campaigns targeting a wide age range, this approach resulted in the lowest number of vaccinated individuals per CRS case averted.

CONCLUSION AND RECOMMENDATIONS

We were unable to conduct data synthesis of included studies due to discrepancies in outcome reporting. However, qualitative assessment of results of individual studies suggests that vaccination of infants should be combined with vaccination of older children to achieve rapid elimination of CRS. Better outcomes are obtained when rubella vaccination is introduced into public vaccination schedules at coverage figures of 80%, as recommended by WHO, or higher. Guidelines for reporting of outcomes in mathematical modelling studies and the conduct of systematic reviews of mathematical modelling studies are required.

Rubella Vaccine Introduction in the South African Public Vaccination Schedule: Mathematical Modelling for Decision Making

Background: age structured mathematical models have been used to evaluate the impact of rubella-containing vaccine (RCV) introduction into existing measles vaccination programs in several countries. South Africa has a well-established measles vaccination program and is considering RCV introduction. This study aimed to provide a comparison of different scenarios and their relative costs within the context of congenital rubella syndrome (CRS) reduction or elimination. Methods: we used a previously published age-structured deterministic discrete time rubella transmission model. We obtained estimates of vaccine costs from the South African medicines price registry and the World Health Organization. We simulated RCV introduction and extracted estimates of rubella incidence, CRS incidence and effective reproductive number over 30 years. Results: compared to scenarios without mass campaigns, scenarios including mass campaigns resulted in more rapid elimination of rubella and congenital rubella syndrome (CRS). Routine vaccination at 12 months of age coupled with vaccination of nine-year-old children was associated with the lowest RCV cost per CRS case averted for a similar percentage CRS reduction. Conclusion: At 80% RCV coverage, all vaccine introduction scenarios would achieve rubella and CRS elimination in South Africa. Any RCV introduction strategy should consider a combination of routine vaccination in the primary immunization series and additional vaccination of older children.

Measles and the canonical path to elimination

All World Health Organization regions have set measles elimination goals. We find that as countries progress toward these goals, they undergo predictable changes in the size and frequency of measles outbreaks. A country’s position on this “canonical path” is driven by both measles control activities and demographic factors, which combine to change the effective size of the measles-susceptible population, thereby driving the country through theoretically established dynamic regimes. Further, position on the path to elimination provides critical information for guiding vaccination efforts, such as the age profile of susceptibility, that could only otherwise be obtained through costly field studies or sophisticated analysis. Equipped with this information, countries can gain insight into their current and future measles epidemiology and select appropriate strategies to more quickly achieve elimination goals.

Estimation and prediction for a mechanistic model of measles transmission using particle filtering and maximum likelihood estimation

Disease incidence reported directly within health systems frequently reflects a partial observation relative to the true incidence in the population. State‐space models present a general framework for inferring both the dynamics of infectious disease processes and the unobserved burden of disease in the population. Here, we present a state‐space model of measles transmission and vaccine‐based interventions at the country‐level and a particle filter‐based estimation procedure. Our dynamic transmission model builds on previous work by incorporating population age‐structure to allow explicit representation of age‐targeted vaccine interventions. We illustrate the performance of estimators of model parameters and predictions of unobserved states on simulated data from two dynamic models: one on the annual time‐scale of observations and one on the biweekly time‐scale of the epidemiological dynamics. We show that our model results in approximately unbiased estimates of unobserved burden and the underreporting rate. We further illustrate the performance of the fitted model for prediction of future disease burden in the next one to 15 years.

Disentangling serology to elucidate henipa- and filovirus transmission in Madagascar fruit bats

Bats are reservoirs for emerging human pathogens, including Hendra and Nipah henipaviruses and Ebola and Marburg filoviruses. These viruses demonstrate predictable patterns in seasonality and age structure across multiple systems; previous work suggests that they may circulate in Madagascar's endemic fruit bats, which are widely consumed as human food. We aimed to (a) document the extent of henipa- and filovirus exposure among Malagasy fruit bats, (b) explore seasonality in seroprevalence and serostatus in these bat populations and (c) compare mechanistic hypotheses for possible transmission dynamics underlying these data. To this end, we amassed and analysed a unique dataset documenting longitudinal serological henipa- and filovirus dynamics in three Madagascar fruit bat species. We uncovered serological evidence of exposure to Hendra-/Nipah-related henipaviruses in Eidolon dupreanum, Pteropus rufus and Rousettus madagascariensis, to Cedar-related henipaviruses in E. dupreanum and R. madagascariensis and to Ebola-related filoviruses in P. rufus and R. madagascariensis. We demonstrated significant seasonality in population-level seroprevalence and individual serostatus for multiple viruses across these species, linked to the female reproductive calendar. An age-structured subset of the data highlighted evidence of waning maternal antibodies in neonates, increasing seroprevalence in young and decreasing seroprevalence late in life. Comparison of mechanistic epidemiological models fit to these data offered support for transmission hypotheses permitting waning antibodies but retained immunity in adult-age bats. Our findings suggest that bats may seasonally modulate mechanisms of pathogen control, with consequences for population-level transmission. Additionally, we narrow the field of candidate transmission hypotheses by which bats are presumed to host and transmit potentially zoonotic viruses globally.

Age × stage-classified demographic analysis: a comprehensive approach

This paper presents a comprehensive theory for the demographic analysis of populations in which individuals are classified by both age and stage. The earliest demographic models were age classified. Ecologists adopted methods developed by human demographers and used life tables to quantify survivorship and fertility of cohorts and the growth rates and structures of populations. Later, motivated by studies of plants and insects, matrix population models structured by size or stage were developed. The theory of these models has been extended to cover all the aspects of age-classified demography and more. It is a natural development to consider populations classified by both age and stage. A steady trickle of results has appeared since the 1960s, analyzing one or another aspect of age × stage-classified populations, in both ecology and human demography. Here, we use the vec-permutation formulation of multistate matrix population models to incorporate age- and stage-specific vital rates into demographic analysis. We present cohort results for the life table functions (survivorship, mortality, and fertility), the dynamics of intra-cohort selection, the statistics of longevity, the joint distribution of age and stage at death, and the statistics of life disparity. Combining transitions and fertility yields a complete set of population dynamic results, including population growth rates and structures, net reproductive rate, the statistics of lifetime reproduction, and measures of generation time. We present a complete analysis of a hypothetical model species, inspired by poecilogonous marine invertebrates that produce two kinds of larval offspring. Given the joint effects of age and stage, many familiar demographic results become multidimensional, so calculations of marginal and mixture distributions are an important tool. From an age-classified point of view, stage structure is a form of unobserved heterogeneity. From a stage-classified point of view, age structure is unobserved heterogeneity. In an age × stage-classified model, variance in demographic outcomes can be partitioned into contributions from both sources. Because these models are formulated as matrices, they are amenable to a complete sensitivity analysis. As more detailed and longer longitudinal studies are developed, age × stage-classified demography will become more common and more important.

Epidemic dynamics, interactions and predictability of enteroviruses associated with hand, foot and mouth disease in Japan

Outbreaks of hand, foot and mouth disease have been documented in Japan since 1963. This disease is primarily caused by the two closely related serotypes of Enterovirus A71 (EV-A71) and Coxsackievirus A16 (CV-A16). Here, we analyse Japanese virologic and syndromic surveillance time-series data from 1982 to 2015. As in some other countries in the Asia Pacific region, EV-A71 in Japan has a 3 year cyclical component, whereas CV-A16 is predominantly annual. We observe empirical signatures of an inhibitory interaction between the serotypes; virologic lines of evidence suggest they may indeed interact immunologically. We fit the time series to mechanistic epidemiological models: as a first-order effect, we find the data consistent with single-serotype susceptible–infected–recovered dynamics. We then extend the modelling to incorporate an inhibitory interaction between serotypes. Our results suggest the existence of a transient cross-protection and possible asymmetry in its strength such that CV-A16 serves as a stronger forcing on EV-A71. Allowing for asymmetry yields accurate out-of-sample predictions and the directionality of this effect is consistent with the virologic literature. Confirmation of these hypothesized interactions would have important implications for understanding enterovirus epidemiology and informing vaccine development. Our results highlight the general implication that even subtle interactions could have qualitative impacts on epidemic dynamics and predictability.

Poverty dynamics, poverty thresholds and mortality: An age-stage Markovian model

Recent studies have examined the risk of poverty throughout the life course, but few have considered how transitioning in and out of poverty shape the dynamic heterogeneity and mortality disparities of a cohort at each age. Here we use state-by-age modeling to capture individual heterogeneity in crossing one of three different poverty thresholds (defined as 1×, 2× or 3× the “official” poverty threshold) at each age. We examine age-specific state structure, the remaining life expectancy, its variance, and cohort simulations for those above and below each threshold. Survival and transitioning probabilities are statistically estimated by regression analyses of data from the Health and Retirement Survey RAND data-set, and the National Longitudinal Survey of Youth. Using the results of these regression analyses, we parameterize discrete state, discrete age matrix models. We found that individuals above all three thresholds have higher annual survival than those in poverty, especially for mid-ages to about age 80. The advantage is greatest when we classify individuals based on 1× the “official” poverty threshold. The greatest discrepancy in average remaining life expectancy and its variance between those above and in poverty occurs at mid-ages for all three thresholds. And fewer individuals are in poverty between ages 40-60 for all three thresholds. Our findings are consistent with results based on other data sets, but also suggest that dynamic heterogeneity in poverty and the transience of the poverty state is associated with income-related mortality disparities (less transience, especially of those above poverty, more disparities). This paper applies the approach of age-by-stage matrix models to human demography and individual poverty dynamics. In so doing we extend the literature on individual poverty dynamics across the life course.

Force of infection of Helicobacter pylori in Mexico: evidence from a national survey using a hierarchical Bayesian model

Helicobacter pylori (H. pylori) is present in the stomach of half of the world's population. The force of infection describes the rate at which susceptibles acquire infection. In this article, we estimated the age-specific force of infection of H. pylori in Mexico. Data came from a national H. pylori seroepidemiology survey collected in Mexico in 1987-88. We modelled the number of individuals with H. pylori at a given age as a binomial random variable. We assumed that the cumulative risk of infection by a given age follows a modified exponential catalytic model, allowing some fraction of the population to remain uninfected. The cumulative risk of infection was modelled for each state in Mexico and were shrunk towards the overall national cumulative risk curve using Bayesian hierarchical models. The proportion of the population that can be infected (i.e. susceptible population) is 85.9% (95% credible interval (CR) 84.3%-87.5%). The constant rate of infection per year of age among the susceptible population is 0.092 (95% CR 0.084-0.100). The estimated force of infection was highest at birth 0.079 (95% CR 0.071-0.087) decreasing to zero as age increases. This Bayesian hierarchical model allows stable estimation of state-specific force of infection by pooling information between the states, resulting in more realistic estimates.

Rubella vaccination in India: identifying broad consequences of vaccine introduction and key knowledge gaps

Rubella virus infection typically presents as a mild illness in children; however, infection during pregnancy may cause the birth of an infant with congenital rubella syndrome (CRS). As of February 2017, India began introducing rubella-containing vaccine (RCV) into the public-sector childhood vaccination programme. Low-level RCV coverage among children over several years can result in an increase in CRS incidence by increasing the average age of infection without sufficiently reducing rubella incidence. We evaluated the impact of RCV introduction on CRS incidence across India's heterogeneous demographic and epidemiological contexts. We used a deterministic age-structured model that reflects Indian states’ rural and urban area-specific demography and vaccination coverage levels to simulate rubella dynamics and estimate CRS incidence with and without RCV introduction to the public sector. Our analysis suggests that current low-level private-sector vaccination has already slightly increased the burden of CRS in India. We additionally found that the effect of public-sector RCV introduction depends on the basic reproductive number, R₀, of rubella. If R₀ is five, a value empirically estimated from an array of settings, CRS incidence post-RCV introduction will likely decrease. However, if R₀ is seven or nine, some states may experience short-term or annual increases in CRS, even if a long-term total reduction in cases (30 years) is expected. Investment in population-based serological surveys and India's fever/rash surveillance system will be key to monitoring the success of the vaccination programme.

Demographics, epidemiology and the impact of vaccination campaigns in a measles-free world - Can elimination be maintained?

Introduction

All six WHO regions currently have goals for measles elimination by 2020. Measles vaccination is delivered via routine immunization programmes, which in most sub-Saharan African countries reach children around 9 months of age, and supplementary immunization activities (SIAs), which target a wider age range at multi-annual intervals. In the absence of endemic measles circulation, the proportion of individuals susceptible to measles will gradually increase through accumulation of new unvaccinated individuals in each birth cohort, increasing the risk of an epidemic. The impact of SIAs and the financial investment they require, depend on coverage and target age range.

Materials and methods

We evaluated the impact of target population age range for periodic SIAs, evaluating outcomes for two different levels of coverage, using a demographic and epidemiological model adapted to reflect populations in 4 sub-Saharan African countries.

Results

We found that a single SIA can maintain elimination over short time-scales, even with low routine coverage. However, maintaining elimination for more than a few years is difficult, even with large (high coverage/wide age range) recurrent SIAs, due to the build-up of susceptible individuals. Across the demographic and vaccination contexts investigated, expanding SIAs to target individuals over 10 years did not significantly reduce outbreak risk.

Conclusions

Elimination was not maintained in the contexts we evaluated without a second opportunity for vaccination. In the absence of an expanded routine program, SIAs provide a powerful option for providing this second dose. We show that a single high coverage SIA can deliver most key benefits in terms of maintaining elimination, with follow-up campaigns potentially requiring smaller investments. This makes post-campaign evaluation of coverage increasingly relevant to correctly assess future outbreak risk.

Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis

The devastation caused by periodic measles outbreaks motivated efforts over more than a century to mathematically model measles disease and transmission. Following the identification of rubella, which similarly presents with fever and rash and causes congenital rubella syndrome (CRS) in infants born to women first infected with rubella early in pregnancy, modelers also began to characterize rubella disease and transmission. Despite the relatively large literature, no comprehensive review to date provides an overview of dynamic transmission models for measles and rubella developed to support risk and policy analysis. This systematic review of the literature identifies quantitative measles and/or rubella dynamic transmission models and characterizes key insights relevant for prospective modeling efforts. Overall, measles and rubella represent some of the relatively simplest viruses to model due to their ability to impact only humans and the apparent life-long immunity that follows survival of infection and/or protection by vaccination, although complexities arise due to maternal antibodies and heterogeneity in mixing and some models considered potential waning immunity and reinfection. This review finds significant underreporting of measles and rubella infections and widespread recognition of the importance of achieving and maintaining high population immunity to stop and prevent measles and rubella transmission. The significantly lower transmissibility of rubella compared to measles implies that all countries could eliminate rubella and CRS by using combination of measles- and rubella-containing vaccines (MRCVs) as they strive to meet regional measles elimination goals, which leads to the recommendation of changing the formulation of national measles-containing vaccines from measles only to MRCV as the standard of care.

Introduction of rubella-containing-vaccine to Madagascar: implications for roll-out and local elimination

Few countries in Africa currently include rubella-containing vaccination (RCV) in their immunization schedule. The Global Alliance for Vaccines Initiative (GAVI) recently opened a funding window that has motivated more widespread roll-out of RCV. As countries plan RCV introductions, an understanding of the existing burden, spatial patterns of vaccine coverage, and the impact of patterns of local extinction and reintroduction for rubella will be critical to developing effective programmes. As one of the first countries proposing RCV introduction in part with GAVI funding, Madagascar provides a powerful and timely case study. We analyse serological data from measles surveillance systems to characterize the epidemiology of rubella in Madagascar. Combining these results with data on measles vaccination delivery, we develop an age-structured model to simulate rubella vaccination scenarios and evaluate the dynamics of rubella and the burden of congenital rubella syndrome (CRS) across Madagascar. We additionally evaluate the drivers of spatial heterogeneity in age of infection to identify focal locations where vaccine surveillance should be strengthened and where challenges to successful vaccination introduction are expected. Our analyses indicate that characteristics of rubella in Madagascar are in line with global observations, with an average age of infection near 7 years, and an impact of frequent local extinction with reintroductions causing localized epidemics. Modelling results indicate that introduction of RCV into the routine programme alone may initially decrease rubella incidence but then result in cumulative increases in the burden of CRS in some regions (and transient increases in this burden in many regions). Deployment of RCV with regular supplementary campaigns will mitigate these outcomes. Results suggest that introduction of RCV offers a potential for elimination of rubella in Madagascar, but also emphasize both that targeted vaccination is likely to be a lynchpin of this success, and the public health vigilance that this introduction will require.

Modeling Chagas Disease at Population Level to Explain Venezuela's Real Data

Objectives

In this paper we present an age-structured epidemiological model for Chagas disease. This model includes the interactions between human and vector populations that transmit Chagas disease.

Methods

The human population is divided into age groups since the proportion of infected individuals in this population changes with age as shown by real prevalence data. Moreover, the age-structured model allows more accurate information regarding the prevalence, which can help to design more specific control programs. We apply this proposed model to data from the country of Venezuela for two periods, 1961–1971, and 1961–1991 taking into account real demographic data for these periods.

Results

Numerical computer simulations are presented to show the suitability of the age-structured model to explain the real data regarding prevalence of Chagas disease in each of the age groups. In addition, a numerical simulation varying the death rate of the vector is done to illustrate prevention and control strategies against Chagas disease.

Conclusion

The proposed model can be used to determine the effect of control strategies in different age groups.

Bridging the gap between evidence and policy for infectious diseases: How models can aid public health decision-making

The dominant approach to decision-making in public health policy for infectious diseases relies heavily on expert opinion, which often applies empirical evidence to policy questions in a manner that is neither systematic nor transparent. Although systematic reviews are frequently commissioned to inform specific components of policy (such as efficacy), the same process is rarely applied to the full decision-making process. Mathematical models provide a mechanism through which empirical evidence can be methodically and transparently integrated to address such questions. However, such models are often considered difficult to interpret. In addition, models provide estimates that need to be iteratively reevaluated as new data or considerations arise. Using the case study of a novel diagnostic for tuberculosis, a framework for improved collaboration between public health decision-makers and mathematical modellers that could lead to more transparent and evidence-driven policy decisions for infectious diseases in the future is proposed. The framework proposes that policymakers should establish long-term collaborations with modellers to address key questions, and that modellers should strive to provide clear explanations of the uncertainty of model structure and outputs. Doing so will improve the applicability of models and clarify their limitations when used to inform real-world public health policy decisions.

Modeling infectious disease dynamics in the complex landscape of global health

Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational, and spatial scales, which span hours to months, cells to ecosystems, and local to global spread. Moreover, some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity and changeable human behavior, elevate prevention and control from matters of national policy to international challenge. In the face of this complexity, mathematical models offer valuable tools for synthesizing information to understand epidemiological patterns, and for developing quantitative evidence for decision-making in global health.

Balancing evidence and uncertainty when considering rubella vaccine introduction

BACKGROUND

Despite a safe and effective vaccine, rubella vaccination programs with inadequate coverage can raise the average age of rubella infection; thereby increasing rubella cases among pregnant women and the resulting congenital rubella syndrome (CRS) in their newborns. The vaccination coverage necessary to reduce CRS depends on the birthrate in a country and the reproductive number, R0, a measure of how efficiently a disease transmits. While the birthrate within a country can be known with some accuracy, R0 varies between settings and can be difficult to measure. Here we aim to provide guidance on the safe introduction of rubella vaccine into countries in the face of substantial uncertainty in R0.

METHODS

We estimated the distribution of R0 in African countries based on the age distribution of rubella infection using Bayesian hierarchical models. We developed an age specific model of rubella transmission to predict the level of R0 that would result in an increase in CRS burden for specific birth rates and coverage levels. Combining these results, we summarize the safety of introducing rubella vaccine across demographic and coverage contexts.

FINDINGS

The median R0 of rubella in the African region is 5.2, with 90% of countries expected to have an R0 between 4.0 and 6.7. Overall, we predict that countries maintaining routine vaccination coverage of 80% or higher are can be confident in seeing a reduction in CRS over a 30 year time horizon.

CONCLUSIONS

Under realistic assumptions about human contact, our results suggest that even in low birth rate settings high vaccine coverage must be maintained to avoid an increase in CRS. These results lend further support to the WHO recommendation that countries reach 80% coverage for measles vaccine before introducing rubella vaccination, and highlight the importance of maintaining high levels of vaccination coverage once the vaccine is introduced.

Implications of spatially heterogeneous vaccination coverage for the risk of congenital rubella syndrome in South Africa

Rubella is generally a mild childhood disease, but infection during early pregnancy may cause spontaneous abortion or congenital rubella syndrome (CRS), which may entail a variety of birth defects. Since vaccination at levels short of those necessary to achieve eradication may increase the average age of infection, and thus potentially the CRS burden, introduction of the vaccine has been limited to contexts where coverage is high. Recent work suggests that spatial heterogeneity in coverage should also be a focus of concern. Here, we use a detailed dataset from South Africa to explore the implications of heterogeneous vaccination for the burden of CRS, introducing realistic vaccination scenarios based on reported levels of measles vaccine coverage. Our results highlight the potential impact of country-wide reductions of incidence of rubella on the local CRS burdens in districts with small population sizes. However, simulations indicate that if rubella vaccination is introduced with coverage reflecting current estimates for measles coverage in South Africa, the burden of CRS is likely to be reduced overall over a 30 year time horizon by a factor of 3, despite the fact that this coverage is lower than the traditional 80 per cent rule of thumb for vaccine introduction, probably owing to a combination of relatively low birth and transmission rates. We conclude by discussing the likely impact of private-sector vaccination.

Impact of birth rate, seasonality and transmission rate on minimum levels of coverage needed for rubella vaccination

Childhood rubella infection in early pregnancy can lead to fetal death or congenital rubella syndrome (CRS) with multiple disabilities. Reduction of transmission via universal vaccination can prevent CRS, but inadequate coverage may increase CRS numbers by increasing the average age at infection. Consequently, many countries do not vaccinate against rubella. The World Health Organization recommends that for safe rubella vaccination, at least 80% coverage of each birth cohort should be sustained. The nonlinear relationship between CRS burden and infection dynamics has been much studied; however, how the complex interaction between epidemic and demographic dynamics affects minimum safe levels of coverage has not been quantitatively evaluated across scales necessary for a global assessment. We modelled 30-year CRS burdens across epidemiological and demographic settings, including the effect of local interruption of transmission via stochastic fadeout. Necessary minimum vaccination coverage increases markedly with birth and transmission rates, independent of amplitude of seasonal fluctuations in transmission. Susceptible build-up in older age groups following local stochastic extinction of rubella increased CRS burden, indicating that spatial context is important. In low birth-rate settings, 80% routine coverage is a conservative guideline, particularly if supplemented with campaigns and vaccination of women of childbearing age. Where birth and transmission rates are high, immunization coverage must be well above 80% and campaigns may be needed. Policy-makers should be aware of the potential negative effect of local extinction of rubella, since heterogeneity in vaccination coverage will shape extinction patterns, potentially increasing CRS burdens.