Persistence in epidemic metapopulations: quantifying the rescue effects for measles, mumps, rubella and whooping cough

Spatial modeling of vaccine deserts as barriers to controlling SARS-CoV-2

Background

COVID-19 vaccine distribution is at risk of further propagating the inequities of COVID-19, which in the United States (US) has disproportionately impacted the elderly, people of color, and the medically vulnerable. We sought to measure if the disparities seen in the geographic distribution of other COVID-19 healthcare resources were also present during the initial rollout of the COVID-19 vaccine.

Methods

Using a comprehensive COVID-19 vaccine database (VaccineFinder), we built an empirically parameterized spatial model of access to essential resources that incorporated vaccine supply, time-willing-to-travel for vaccination, and previous vaccination across the US. We then identified vaccine deserts—US Census tracts with localized, geographic barriers to vaccine-associated herd immunity. We link our model results with Census data and two high-resolution surveys to understand the distribution and determinates of spatially accessibility to the COVID-19 vaccine.

Results

We find that in early 2021, vaccine deserts were home to over 30 million people, >10% of the US population. Vaccine deserts were concentrated in rural locations and communities with a higher percentage of medically vulnerable populations. We also find that in locations of similar urbanicity, early vaccination distribution disadvantaged neighborhoods with more people of color and older aged residents.

Conclusion

Given sufficient vaccine supply, data-driven vaccine distribution to vaccine deserts may improve immunization rates and help control COVID-19.

From outbreaks to endemic disease

Relief from the effects of epidemics may signal the start of low-level disease persistence.

Stochasticity-induced persistence in coupled social-ecological systems

Stochasticity is often associated with negative consequences for population dynamics since a population may die out due to random chance during periods when population size is very low (stochastic fade-out). Here we develop a coupled social-ecological model based on stochastic differential equations that includes natural expansion and harvesting of a forest ecosystem, and dynamics of conservation opinions, social norms and social learning in a human population. Our objective was to identify mechanisms that influence long-term persistence of the forest ecosystem in the presence of noise. We found that most of the model parameters had a significant influence on the time to extinction of the forest ecosystem. Increasing the social learning rate and the net benefits of conservation significantly increased the time to extinction, for instance. Most interestingly, we found a parameter regime where an increase in the amount of system stochasticity caused an increase in the mean time to extinction, instead of causing stochastic fade-out. This effect occurs for a subset of realizations, but the effect is large enough to increase the mean time to extinction across all realizations. Such "stochasticity-induced persistence" occurs when stochastic dynamics in the social system generates benefits in the forest system at crucial points in its temporal dynamics. We conclude that studying relatively simple social-ecological models has the benefit of facilitating characterization of dynamical states and thereby enabling us to formulate new hypothesis about mechanisms that could be operating in empirical social-ecological systems.

Economic evaluation of disease elimination: An extension to the net-benefit framework and application to human African trypanosomiasis

The global health community has earmarked a number of diseases for elimination or eradication, and these goals have often been praised on the premise of long-run cost savings. However, decision makers must contend with a multitude of demands on health budgets in the short or medium term, and costs per case often rise as the burden of a disease falls, rendering such efforts beyond the cost-effective use of scarce resources. In addition, these decisions must be made in the presence of substantial uncertainty regarding the feasibility and costs of elimination or eradication efforts. Therefore, analytical frameworks are necessary to consider the additional effort for reaching global goals, like elimination or eradication, that are beyond the cost-effective use of country resources. We propose a modification to the net-benefit framework to consider the implications of switching from an optimal strategy, in terms of cost-per-burden averted, to a strategy with a higher likelihood of meeting the global target of elimination or eradication. We illustrate the properties of our framework by considering the economic case of efforts to eliminate the transmission of gambiense human African trypanosomiasis (gHAT), a vector-borne, parasitic disease in West and Central Africa, by 2030.

Determination of critical community size from an HIV/AIDS model

After an epidemic outbreak, the infection persists in a community long enough to engulf the entire susceptible population. Local extinction of the disease could be possible if the susceptible population gets depleted. In large communities, the tendency of eventual damp down of recurrent epidemics is balanced by random variability. But, in small communities, the infection would die out when the number of susceptible falls below a certain threshold. Critical community size (CCS) is considered to be the mentioned threshold, at which the infection is as likely as not to die out after a major epidemic for small communities unless reintroduced from outside. The determination of CCS could aid in devising systematic control strategies to eradicate the infectious disease from small communities. In this article, we have come up with a simplified computation based approach to deduce the CCS of HIV disease dynamics. We consider a deterministic HIV model proposed by Silva and Torres, and following Nåsell, introduce stochasticity in the model through time-varying population sizes of different compartments. Besides, Metcalf’s group observed that the relative risk of extinction of some infections on islands is almost double that in the mainlands i.e. infections cease to exist at a significantly higher rate in islands compared to the mainlands. They attributed this phenomenon to the greater recolonization in the mainlands. Interestingly, the application of our method on demographic facts and figures of countries in the AIDS belt of Africa led us to expect that existing control measures and isolated locations would assist in temporary eradication of HIV infection much faster. For example, our method suggests that through systematic control strategies, after 7.36 years HIV epidemics will temporarily be eradicated from different communes of island nation Madagascar, where the population size falls below its CCS value, unless the disease is reintroduced from outside.

The persistence of a SIR disease in a metapopulation: Hendra virus epidemics in Australian black flying foxes (Pteropus alecto)

Understanding how emerging viruses persist in bat populations is a fundamental step to understand the processes by which viruses are transmitted from reservoir hosts to spillover hosts. Hendra virus, which has caused fatal infections in horses and humans in eastern Australia since 1994, spills over from its natural reservoir hosts, Pteropus bats (colloquially known as flying foxes). It has been suggested that the Hendra virus maintenance mechanism in the bat populations might be implicated with their metapopulation structure. Here, we examine whether a metapopulation consisting of black flying fox (P. alecto) colonies that are smaller than the critical community size can maintain the Hendra virus. By using the Gillespie algorithm, stochastic mathematical models were used to simulate a cycle, in which viral extinction and recolonisation were repeated in a single colony within a metapopulation. Given estimated flying fox immigration rates, the simulation results showed that recolonisation occurred more frequently than extinction, which indicated that infection would not go extinct in the metapopulation. Consequently, this study suggests that a collection of transient epidemics of Hendra virus in numerous colonies of flying foxes in Australia can support the long-term persistence of the virus at the metapopulation level.

Local lockdowns outperform global lockdown on the far side of the COVID-19 epidemic curve

In the late stages of an epidemic, infections are often sporadic and geographically distributed. Spatially structured stochastic models can capture these important features of disease dynamics, thereby allowing a broader exploration of interventions. Here we develop a stochastic model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission among an interconnected group of population centers representing counties, municipalities, and districts (collectively, "counties"). The model is parameterized with demographic, epidemiological, testing, and travel data from Ontario, Canada. We explore the effects of different control strategies after the epidemic curve has been flattened. We compare a local strategy of reopening (and reclosing, as needed) schools and workplaces county by county, according to triggers for county-specific infection prevalence, to a global strategy of province-wide reopening and reclosing, according to triggers for province-wide infection prevalence. For trigger levels that result in the same number of COVID-19 cases between the two strategies, the local strategy causes significantly fewer person-days of closure, even under high intercounty travel scenarios. However, both cases and person-days lost to closure rise when county triggers are not coordinated and when testing rates vary among counties. Finally, we show that local strategies can also do better in the early epidemic stage, but only if testing rates are high and the trigger prevalence is low. Our results suggest that pandemic planning for the far side of the COVID-19 epidemic curve should consider local strategies for reopening and reclosing.

Long-term changes in endemic threshold populations for pertussis in England and Wales: A spatiotemporal analysis of Lancashire and South Wales, 1940-69

Metapopulation dynamics play a critical role in driving endemic persistence and transmission of childhood infections. The endemic threshold concept, also referred to as critical community size (CCS), is a key example and is defined as the minimum population size required to sustain a continuous chain of infection transmission. The concept is fundamental to the implementation of effective vaccine-based disease control programmes. Vaccination serves to increase endemic threshold population size, promoting disease fadeout and eventual elimination of infection. To date, empirical investigations of the relationship between vaccination and endemic threshold population size have tended to focus on isolated populations in island communities. Very few studies have examined endemic threshold dynamics in 'mainland' regional populations with complex hierarchical spatial structures and varying levels of connectivity between subpopulations. The present paper provides the first spatially explicit analysis of the temporal changes in endemic threshold populations for one vaccine-preventable childhood infection (pertussis) in two dynamic regions of England and Wales: Lancashire and South Wales. Drawing upon weekly disease records of the Registrar-General of England and Wales over a 30-year period (January 1940-December 1969) regression techniques were used to estimate the endemic threshold size for pertussis in the two study regions. Survival analyses were performed to compare disease fadeout duration and probability for both regions in the pre-vaccine and vaccine eras, respectively. Our findings reveal the introduction of mass vaccination led to a considerable increase in threshold size for both Lancashire (~387,333) and South Wales (~1,460,667). Significant growth in fadeout duration was observed in the vaccine era for pertussis non-hotspots in both regions, consistent with geographical synchronisation of epidemic activity. Regional differences in endemic threshold populations reflect significant regional variations in spatial connectivity, population dispersion and level of geographical isolation.

Structure, space and size: competing drivers of variation in urban and rural measles transmission

A key concern in public health is whether disparities exist between urban and rural areas. One dimension of potential variation is the transmission of infectious diseases. In addition to potential differences between urban and rural local dynamics, the question of whether urban and rural areas participate equally in national dynamics remains unanswered. Specifically, urban and rural areas may diverge in local transmission as well as spatial connectivity, and thus risk for receiving imported cases. Finally, the potential confounding relationship of spatial proximity with size and urban/rural district type has not been addressed by previous research. It is rare to have sufficient data to explore these questions thoroughly. We use exhaustive weekly case reports of measles in 954 urban and 468 rural districts of the UK (1944–1965) to compare both local disease dynamics as well as regional transmission. We employ the time-series susceptible–infected–recovered model to estimate disease transmission, epidemic severity, seasonality and import dependence. Congruent with past results, we observe a clear dependence on population size for the majority of these measures. We use a matched-pair strategy to compare proximate urban and rural districts and control for possible spatial confounders. This analytical strategy reveals a modest difference between urban and rural areas. Rural areas tend to be characterized by more frequent, smaller outbreaks compared to urban counterparts. The magnitude of the difference is slight and the results primarily reinforce the importance of population size, both in terms of local and regional transmission. In sum, urban and rural areas demonstrate remarkable epidemiological similarity in this recent UK context.

Multi-scale dynamics of infectious diseases

To address the challenge of multiscale dynamics of infectious diseases, the Mathematical Biosciences Institute organized a workshop at The Ohio State University to bring together scientists from a variety of disciplines to share expertise gained through looking at infectious diseases across different scales. The researchers at the workshop, held in April 2018, were specifically looking at three model systems: foot-and-mouth disease, vector-borne diseases and enteric diseases. Although every multiscale model must be necessarily derived from a multiscale system, not every multiscale system has to lead to multiscale models. These three model systems seem to have produced a variety of both multiscale and integrated single-scale mechanistic models that have developed their own strengths and particular challenges. Here, we present papers from some of the workshop participants to show the breadth of the field.

Network analyses of transhumance movements and simulations of foot-and-mouth disease virus transmission among mobile livestock in Cameroon

Foot-and-mouth disease (FMD) affects cloven-hoofed livestock and agricultural economies worldwide. Analyses of the 2001 FMD outbreak in the United Kingdom informed how livestock movement contributed to disease spread. However, livestock reared in other locations use different production systems that might also influence disease dynamics. Here, we investigate a livestock production system known as transhumance, which is the practice of moving livestock between seasonal grazing areas. We built mechanistic models using livestock movement data from the Far North Region of Cameroon. We represented these data as a dynamic network over which we simulated disease transmission and examined three questions. First, we asked what were characteristics of simulated FMDV transmission across a transhumant pastoralist system. Second, we asked how simulated FMDV transmission across a transhumant pastoralist system differed from transmission across this same population held artificially stationary, thereby revealing the effect of movement on disease dynamics. Third, we asked if disease simulations on well-studied theoretical networks are similar to disease simulations on this empirical dynamic network. The results show that the empirical dynamic network was sparsely connected except for an eight-week period in September and October when pastoralists move from rainy season to dry season grazing areas. The mean epidemic size across all 3,744 simulations was 99.9% and the mean epidemic duration was 1.45 years. Disease simulations across the static network showed a smaller mean epidemic size (27.6%) and a similar epidemic duration (1.5 years). Epidemics simulated on theoretical networks showed similar final epidemic sizes (100%) and different mean durations. Our simulations indicate that transhumant livestock systems have the potential to host FMDV outbreaks that affect almost all livestock and last longer than a year. Furthermore, our comparison of empirical and theoretical networks underscores the importance of using empirical data to understand the role of mobility in the transmission of infectious diseases.

Evidence of cryptic incidence in childhood diseases

Persistence and extinction are key processes in infectious disease dynamics that, owing to incomplete reporting, are seldom directly observable. For fully immunizing diseases, reporting probabilities can be readily estimated from demographic records and case reports. Yet reporting probabilities are not sufficient to unambiguously reconstruct disease incidence from case reports. Here, we focus on disease presence (i.e. marginal probability of non-zero incidence), which provides an upper bound on the marginal probability of disease extinction. We examine measles and pertussis in pre-vaccine era United States (US) cities, and describe a conserved scaling relationship between population size, reporting probability and observed presence (i.e. non-zero case reports). We use this relationship to estimate disease presence given perfect reporting, and define cryptic presence as the difference between estimated and observed presence. We estimate that, in early twentieth century US cities, pertussis presence was higher than measles presence across a range of population sizes, and that cryptic presence was common in small cities with imperfect reporting. While the methods employed here are specific to fully immunizing diseases, our results suggest that cryptic incidence deserves careful attention, particularly in diseases with low case counts, poor reporting and longer infectious periods.

Spatial clustering of measles vaccination coverage among children in sub-Saharan Africa

Background

During the past two decades, vaccination programs have greatly reduced global morbidity and mortality due to measles, but recently this progress has stalled. Even in countries that report high vaccination coverage rates, transmission has continued, particularly in spatially clustered subpopulations with low vaccination coverage.

Methods

We examined the spatial heterogeneity of measles vaccination coverage among children aged 12–23 months in ten Sub-Saharan African countries. We used the Anselin Local Moran’s I to estimate clustering of vaccination coverage based on data from Demographic and Health Surveys conducted between 2008 and 2013. We also examined the role of sociodemographic factors to explain clustering of low vaccination.

Results

We detected 477 spatial clusters with low vaccination coverage, many of which were located in countries with relatively high nationwide vaccination coverage rates such as Zambia and Malawi. We also found clusters in border areas with transient populations. Clustering of low vaccination coverage was related to low health education and limited access to healthcare.

Conclusions

Systematically monitoring clustered populations with low vaccination coverage can inform supplemental immunization activities and strengthen elimination programs. Metrics of spatial heterogeneity should be used routinely to determine the success of immunization programs and the risk of disease persistence.

Comparative epidemiology of poliovirus transmission

Understanding the determinants of polio transmission and its large-scale epidemiology remains a public health priority. Despite a 99% reduction in annual wild poliovirus (WPV) cases since 1988, tackling the last 1% has proven difficult. We identified key covariates of geographical variation in polio transmission patterns by relating country-specific annual disease incidence to demographic, socio-economic and environmental factors. We assessed the relative contributions of these variables to the performance of computer-generated models for predicting polio transmission. We also examined the effect of spatial coupling on the polio extinction frequency in islands relative to larger land masses. Access to sanitation, population density, forest cover and routine vaccination coverage were the strongest predictors of polio incidence, however their relative effect sizes were inconsistent geographically. The effect of climate variables on polio incidence was negligible, indicating that a climate effect is not identifiable at the annual scale, suggesting a role for climate in shaping the transmission seasonality rather than intensity. We found polio fadeout frequency to depend on both population size and demography, which should therefore be considered in policies aimed at extinction. Our comparative epidemiological approach highlights the heterogeneity among polio transmission determinants. Recognition of this variation is important for the maintenance of population immunity in a post-polio era.

A stochastic model for the probability of malaria extinction by mass drug administration

Background

Mass drug administration (MDA) has been proposed as an intervention to achieve local extinction of malaria. Although its effect on the reproduction number is short lived, extinction may subsequently occur in a small population due to stochastic fluctuations. This paper examines how the probability of stochastic extinction depends on population size, MDA coverage and the reproduction number under control, R_c. A simple compartmental model is developed which is used to compute the probability of extinction using probability generating functions. The expected time to extinction in small populations after MDA for various scenarios in this model is calculated analytically.

Results

The results indicate that mass drug administration (Firstly, R_c must be sustained at R_c < 1.2 to avoid the rapid re-establishment of infections in the population. Secondly, the MDA must produce effective cure rates of >95% to have a non-negligible probability of successful elimination. Stochastic fluctuations only significantly affect the probability of extinction in populations of about 1000 individuals or less. The expected time to extinction via stochastic fluctuation is less than 10 years only in populations less than about 150 individuals. Clustering of secondary infections and of MDA distribution both contribute positively to the potential probability of success, indicating that MDA would most effectively be administered at the household level.

Conclusions

There are very limited circumstances in which MDA will lead to local malaria elimination with a substantial probability.

Electronic supplementary material

The online version of this article (doi:10.1186/s12936-017-2010-x) contains supplementary material, which is available to authorized users.

Hand, Foot, and Mouth Disease in China: Critical Community Size and Spatial Vaccination Strategies

Hand Foot and Mouth Disease (HFMD) constitutes a considerable burden for health care systems across China. Yet this burden displays important geographic heterogeneity that directly affects the local persistence and the dynamics of the disease, and thus the ability to control it through vaccination campaigns. Here, we use detailed geographic surveillance data and epidemic models to estimate the critical community size (CCS) of HFMD associated enterovirus serotypes CV-A16 and EV-A71 and we explore what spatial vaccination strategies may best reduce the burden of HFMD. We found CCS ranging from 336,979 (±225,866) to 722,372 (±150,562) with the lowest estimates associated with EV-A71 in the southern region of China where multiple transmission seasons have previously been identified. Our results suggest the existence of a regional immigration-recolonization dynamic driven by urban centers. If EV-A71 vaccines doses are limited, these would be optimally deployed in highly populated urban centers and in high-prevalence areas. If HFMD vaccines are included in China's National Immunization Program in order to achieve high coverage rates (>85%), routine vaccination of newborns largely outperforms strategies in which the equivalent number of doses is equally divided between routine vaccination of newborns and pulse vaccination of the community at large.

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.

Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns

Epidemics of infectious diseases often occur in predictable limit cycles. Theory suggests these cycles can be disrupted by high amplitude seasonal fluctuations in transmission rates, resulting in deterministic chaos. However, persistent deterministic chaos has never been observed, in part because sufficiently large oscillations in transmission rates are uncommon. Where they do occur, the resulting deep epidemic troughs break the chain of transmission, leading to epidemic extinction, even in large cities. Here we demonstrate a new path to locally persistent chaotic epidemics via subtle shifts in seasonal patterns of transmission, rather than through high-amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era United States and United Kingdom. Unlike the regular limit cycles seen in the UK, measles cycles in US cities consistently exhibit spontaneous shifts in epidemic periodicity resulting in chaotic patterns. We show that these patterns were driven by small systematic differences between countries in the duration of the summer period of low transmission. This example demonstrates empirically that small perturbations in disease transmission patterns can fundamentally alter the regularity and spatiotemporal coherence of epidemics.

Differences in sensitivity to the fungal pathogen Batrachochytrium dendrobatidis among amphibian populations

Contributing to the worldwide biodiversity crisis are emerging infectious diseases, which can lead to extirpations and extinctions of hosts. For example, the infectious fungal pathogen Batrachochytrium dendrobatidis (Bd) is associated with worldwide amphibian population declines and extinctions. Sensitivity to Bd varies with species, season, and life stage. However, there is little information on whether sensitivity to Bd differs among populations, which is essential for understanding Bd-infection dynamics and for formulating conservation strategies. We experimentally investigated intraspecific differences in host sensitivity to Bd across 10 populations of wood frogs (Lithobates sylvaticus) raised from eggs to metamorphosis. We exposed the post-metamorphic wood frogs to Bd and monitored survival for 30 days under controlled laboratory conditions. Populations differed in overall survival and mortality rate. Infection load also differed among populations but was not correlated with population differences in risk of mortality. Such population-level variation in sensitivity to Bd may result in reservoir populations that may be a source for the transmission of Bd to other sensitive populations or species. Alternatively, remnant populations that are less sensitive to Bd could serve as sources for recolonization after epidemic events.

Conserved patterns of incomplete reporting in pre-vaccine era childhood diseases

Incomplete observation is an important yet often neglected feature of observational ecological timeseries. In particular, observational case report timeseries of childhood diseases have played an important role in the formulation of mechanistic dynamical models of populations and metapopulations. Yet to our knowledge, no comprehensive study of childhood disease reporting probabilities (commonly referred to as reporting rates) has been conducted to date. Here, we provide a detailed analysis of measles and whooping cough reporting probabilities in pre-vaccine United States cities and states, as well as measles in cities of England and Wales. Overall, we find the variability between locations and diseases greatly exceeds that between methods or time periods. We demonstrate a strong relationship within location between diseases and within disease between geographical areas. In addition, we find that demographic covariates such as ethnic composition and school attendance explain a non-trivial proportion of reporting probability variation. Overall, our findings show that disease reporting is both variable and non-random and that completeness of reporting is influenced by disease identity, geography and socioeconomic factors. We suggest that variations in incomplete observation can be accounted for and that doing so can reveal ecologically important features that are otherwise obscured.

Six challenges in the eradication of infectious diseases

Eradication and elimination are increasingly a part of the global health agenda. Once control measures have driven infection to low levels, the ecology of disease may change posing challenges for eradication efforts. These challenges vary from identifying pockets of susceptibles, improving monitoring during and after the endgame, to quantifying the economics of disease eradication versus sustained control, all of which are shaped and influenced by processes of loss of immunity, susceptible build-up, emergence of resistance, population heterogeneities and non-compliance with control measures. Here we discuss how modelling can be used to address these challenges.