Epidemiological impact of vaccination on the dynamics of two childhood diseases in rural Senegal

Measles and pertussis are ubiquitous vaccine-preventable diseases, which remain an important public health problem in developing countries. Hence, developing a deep understanding of their transmission dynamics remains imperative. To achieve this, we compared the impact of vaccination at both individual and population levels in a Senegalese rural community. This study represents the first such comparative study in tropical conditions and constitutes a point of comparison with other studies of disease dynamics in developed countries. Changes in the transmission rates of infections are reflected in their mean ages at infection and basic reproductive ratio calculated before and after vaccination. We explored persistence of both infections in relation to population size in each village and found the inter-epidemic period for the whole area using wavelets analysis. As predicted by epidemiological theory, we observed an increase in the mean age at infection and a decrease in the reproductive ratio of both diseases. We showed for both the pre- vaccination and vaccine eras that persistence depends on population size. After vaccination, persistence decreased and the inter-epidemic period increased. The observed changes suggest that vaccination against measles and pertussis induced a drop in their transmission. Similarities in disease dynamics to those of temperate regions such as England and Wales were also observed.     

A unifying framework for metapopulation dynamics

Many biologically important processes, such as genetic differentiation, the spread of disease, and population stability, are affected by the (natural or enforced) subdivision of populations into networks of smaller, partly isolated, subunits. Such "metapopulations" can have extremely complex dynamics. We present a new general model that uses only two functions to capture, at the metapopulation scale, the main behavior of metapopulations. We show how complex, structured metapopulation models can be translated into our generalized framework. The metapopulation dynamics arising from some important biological processes are illustrated: the rescue effect, the Allee effect, and what we term the "antirescue effect." The antirescue effect captures instances where high migration rates are deleterious to population persistence, a phenomenon that has been largely ignored in metapopulation conservation theory. Management regimes that ignore a significant antirescue effect will be inadequate and may actually increase extinction risk. Further, consequences of territoriality and conspecific attraction on metapopulation-level dynamics are investigated. The new, simplified framework can incorporate knowledge from epidemiology, genetics, and population biology in a phenomenological way. It opens up new possibilities to identify and analyze the factors that are important for the evolution and persistence of the many spatially subdivided species.     

Dispersal-induced desynchronization: from metapopulations to metacommunities

The conceptualization of fragmented populations in terms of metapopulation theory has become standard over the last three decades. It is well known that increases in between‐patch migration rates cause more synchronous population fluctuations and that this coherence increases the risk of global metapopulation extinction. Because species’ migration rates and the probability of individuals surviving migration events depend on the effective distance between patches, the benefit of improving conservation corridors or the matrix between habitat patches has been questioned. As populations occur in the context of larger communities, moving from a metapopulation to a metacommunity model framework is a natural extension to address the generality of these conclusions. We show how considering a metacommunity can modify the conclusion that decreasing the effective distance between habitat patches (via improving matrix quality or other measures) necessarily increases the degree of metapopulation synchrony. We show that decreases in effective between‐patch distance may deter population synchrony because of the simultaneous effect this change has on the migration patterns of other species. These results indicate that species interactions need to be considered when the effect of conservation measures on population synchrony, and ultimately persistence, is addressed.     

Seasonality and the persistence and invasion of measles

The critical community size (CCS) for measles, which separates persistent from extinction-prone populations, is arguably the best understood stochastic threshold in ecology. Using simple models, we explore a relatively neglected relationship of how the CCS scales with birth rate. A predominantly positive relationship of persistence with birth rate is complicated by the accompanying dynamical transitions of the underlying deterministic process. We show that these transitions imply a lower CCS for high birth rate less developed countries and contrary to the experience in lower birth rate, industrial countries, the CCS may increase after vaccination. We also consider the evolutionary implications of the CCS for the origin of measles; this analysis explores how the deterministic and stochastic thresholds for invasion and persistence set limits on the mechanism by which this highly infectious pathogen could have successfully colonized its human host.     

Dynamics of extinction in coupled populations of the flour beetle Tribolium castaneum.

In this study we analyzed the effect of migration on the persistence time of coupled local populations of Tribolium in different environments. Four treatments were set up to compare different levels of environmental heterogeneity. We established high, low, moderate, and no heterogeneity. These levels were estimated by the different amounts of food offered to each population. To investigate how risk spreading works, a stochastic model for two subpopulations was employed. The high heterogeneity treatment resulted in the longest persistence, even though survival analysis revealed no significant difference among treatments. The magnitude of differences in growth rates among subpopulations is probably associated with persistence.     

The effects of human movement on the persistence of vector-borne diseases

With the recent resurgence of vector-borne diseases due to urbanization and development there is an urgent need to understand the dynamics of vector-borne diseases in rapidly changing urban environments. For example, many empirical studies have produced the disturbing finding that diseases continue to persist in modern city centers with zero or low rates of transmission. We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain disease persistence in patches with zero transmission. We construct two classes of models using different approaches: (i) Lagrangian models that mimic human commuting behavior and (ii) Eulerian models that mimic human migration. We determine the basic reproduction number R₀ for both modeling approaches. We show that for both approaches that if the disease-free equilibrium is stable (R₀<1) then it is globally stable and if the disease-free equilibrium is unstable (R₀>1) then there exists a unique positive (endemic) equilibrium that is globally stable among positive solutions. Finally, we prove in general that Lagrangian and Eulerian modeling approaches are not equivalent. The modeling approaches presented provide a framework to explore spatial vector-borne disease dynamics and control in heterogeneous environments. As an example, we consider two patches in which the disease dies out in both patches when there is no movement between them. Numerical simulations demonstrate that the disease becomes endemic in both patches when humans move between the two patches.     

Deciphering the relative weights of demographic transition and vaccination in the decrease of measles incidence in Italy

In Italy, during the course of the past century to the present-day, measles incidence underwent a remarkable decreasing trend that started well before the introduction of the national immunization programme. In this work, we aim at examining to what extent both the demographic transition, characterized by declining mortality and fertility rates over time, and the vaccination programme are responsible for the observed epidemiological pattern. Making use of a non-stationary, age-structured disease transmission model, we show that in the pre-vaccination era, from 1901 to 1982, the decline in birth rates has resulted in a drastic decrease in the effective transmission rate, which in turn has determined a declining trend of measles incidence (from 25.2 to 10.3 infections per 1000 individuals). However, since 1983, vaccination appears to have become the major contributing factor in the decrease of measles incidence, which otherwise would have remained stable as a consequence of the nearly constant birth rates. This led to a remarkable decrease in the effective transmission rate, to a level well below the critical threshold for disease persistence. These findings call for the adoption of epidemiological models, which deviate the age structure from stationary equilibrium solutions, to better understand the biology of infectious diseases and evaluate immunization programmes.     

Local actin dynamics couple speed and persistence in a cellular Potts model of cell migration

Cell migration is astoundingly diverse. Molecular signatures, cell-cell interactions, and environmental structures each play their part in shaping cell motion, yielding numerous morphologies and migration modes. Nevertheless, in recent years, a simple unifying law was found to describe cell migration across many different cell types and contexts: faster cells turn less frequently. This universal coupling between speed and persistence (UCSP) was explained by retrograde actin flow from front to back, but it remains unclear how this mechanism generalizes to cells with complex shapes and cells migrating in structured environments, which may not have a well-defined front-to-back orientation. Here, we present an in-depth characterization of an existing cellular Potts model, in which cells polarize dynamically from a combination of local actin dynamics (stimulating protrusions) and global membrane tension along the perimeter (inhibiting protrusions). We first show that the UCSP emerges spontaneously in this model through a cross talk of intracellular mechanisms, cell shape, and environmental constraints, resembling the dynamic nature of cell migration in vivo. Importantly, we find that local protrusion dynamics suffice to reproduce the UCSP—even in cases in which no clear global, front-to-back polarity exists. We then harness the spatial nature of the cellular Potts model to show how cell shape dynamics limit both the speed and persistence a cell can reach and how a rigid environment such as the skin can restrict cell motility even further. Our results broaden the range of potential mechanisms underlying the speed-persistence coupling that has emerged as a fundamental property of migrating cells.     

Estimating plant migration rates under habitat loss and fragmentation

Changes in the global environment are modifying the geographical locations of habitats suitable for plant growth. The capacity of plants to migrate to sites of suitable environmental quality will strongly influence future distributions of plant diversity. However, it is not well understood how rates of plant migration are influenced by the habitat loss and habitat fragmentation that characterise contemporary landscapes. In this study we develop a model that can predict migration rates in both intact landscapes (potential migration rate) and in fragmented landscapes (realised migration rates). Migration rates in fragmented landscapes might be slower for many reasons. In this study we focus on two, non‐exclusive reasons. First, the processes that move seeds may break down in fragmented landscapes causing seeds to be dispersed shorter distances. Second, in fragmented landscapes some proportion of seeds will not be deposited in habitats suitable for recruitment. We describe the breakdown of dispersal processes as a competing risk between the factors influencing dispersal in intact landscapes and the factors that may disrupt dispersal processes in fragmented landscapes. We show how the parameters that influence dispersal in fragmented landscapes can be estimated, and how these estimates can be used to forecast migration rates using an integrodifference equation (IDE). The forecasts of the IDE described the effects of reduced dispersal distances adequately. However, the IDE produced biased estimates of the effects of a reduction in plant habitat on migration rates. Model analyses showed that, although we can expect realised migration rates to be lower than potential migration rates, we can also expect the sensitivity of migration rate to habitat loss to vary. In addition, simulations showed that the qualitative nature of the responses of migration rate to habitat loss were variable – some model species responded non‐linearly to habitat loss, others responded linearly. While our method provides guidelines for empirical data collection and model parameterisation, we recognise that obtaining these data will be challenging.     

A Vaccination Model for a Multi-City System

A modelling approach is used for studying the effects of population vaccination on the epidemic dynamics of a set of n cities interconnected by a complex transportation network. The model is based on a sophisticated mover-stayer formulation of inter-city population migration, upon which is included the classical SIS dynamics of disease transmission which operates within each city. Our analysis studies the stability properties of the Disease-Free Equilibrium (DFE) of the full n-city system in terms of the reproductive number R (0). Should vaccination reduce R (0) below unity, the disease will be eradicated in all n-cities. We determine the precise conditions for which this occurs, and show that disease eradication by vaccination depend on the transportation structure of the migration network in a very direct manner. Several concrete examples are presented and discussed, and some counter-intuitive results found.     

An epidemiological framework for modelling fungicide dynamics and control

Defining appropriate policies for controlling the spread of fungal disease in agricultural landscapes requires appropriate theoretical models. Most existing models for the fungicidal control of plant diseases do not explicitly include the dynamics of the fungicide itself, nor do they consider the impact of infection occurring during the host growth phase. We introduce a modelling framework for fungicide application that allows us to consider how "explicit" modelling of fungicide dynamics affects the invasion and persistence of plant pathogens. Specifically, we show that "explicit" models exhibit bistability zones for values of the basic reproductive number ([Formula: see text]) less than one within which the invasion and persistence threshold depends on the initial infection levels. This is in contrast to classical models where invasion and persistence thresholds are solely dependent on [Formula: see text]. In addition if initial infection occurs during the growth phase then an additional "invasion zone" can exist for even smaller values of [Formula: see text]. Within this region the system will experience an epidemic that is not able to persist. We further show that ideal fungicides with high levels of effectiveness, low rates of application and low rates of decay lead to the existence of these bistability zones. The results are robust to the inclusion of demographic stochasticity.     

Seasonal influences on population spread and persistence in streams: spreading speeds

The drift paradox asks how stream-dwelling organisms can persist, without being washed out, when they are continuously subject to the unidirectional stream flow. To date, mathematical analyses of the stream paradox have investigated the interplay of growth, drift and flow needed for species persistence under the assumption that the stream environment is temporally constant. However, in reality, streams are subject to major seasonal variations in environmental factors that govern population growth and dispersal. We consider the influence of such seasonal variations on the drift paradox, using a time-periodic integrodifferential equation model. We establish upstream and downstream spreading speeds under the assumption of periodically fluctuating environments, and also show the existence of periodic traveling waves. The sign of the upstream spreading speed then determines persistence. Fluctuating environments are characterized by seasonal correlations between the flow, transfer rates, diffusion and settling rates, and we investigate the effect of such correlations on the population spread and persistence. We also show how results in this paper can formally connect to those for autonomous integrodifferential equations, through the appropriate weighted averaging methods. Finally, for a specific dispersal function, we show that the upstream spreading speed is nonnegative if and only if the critical domain size exists in this temporally fluctuating environment.     

CONSUMER–RESOURCE INTERACTIONS AND THE EVOLUTION OF MIGRATION

Theoretical studies have demonstrated that selection will favor increased migration when fitnesses vary both temporally and spatially, but it is far from clear how pervasive those theoretical conditions are in nature. Although consumer–resource interactions are omnipresent in nature and can generate spatial and temporal variation, it is unknown even in theory whether these dynamics favor the evolution of migration. We develop a mathematical model to address whether and how migration evolves when variability in fitness is determined at least in part by consumer–resource coevolutionary interactions. Our analyses show that such interactions can drive the evolution of migration in the resource, consumer, or both species and thus supplies a general explanation for the pervasiveness of migration. Over short time scales, we show the direction of change in migration rate is determined primarily by the state of local adaptation of the species involved: rates increase when a species is locally maladapted and decrease when locally adapted. Our results reveal that long‐term evolutionary trends in migration rates can differ dramatically depending on the strength or weakness of interspecific interactions and suggest an explanation for the evolutionary divergence of migration rates among interacting species.     

Paradoxical effects of coupling infectious livestock populations and imposing transport restrictions

Spatial heterogeneity of a host population of mobile agents has been shown to be a crucial determinant of many aspects of disease dynamics, ranging from the proliferation of diseases to their persistence and to vaccination strategies. In addition, the importance of regional and structural differences grows in our modern world. Little is known, though, about the consequences when traits of a disease vary regionally. In this paper, we study the effect of a spatially varying per capita infection rate on the behaviour of livestock diseases. We show that the prevalence of an infectious livestock disease in a community of animals can paradoxically decrease owing to transport connections to other communities in which the risk of infection is higher. We study the consequences for the design of livestock transportation restriction measures and establish exact criteria to discriminate those connections that increase the level of infection in the community from those that decrease it.     

Maternal antibody persistence: a neglected life-history trait with implications from albatross conservation to comparative immunology

The evolution of different life-history strategies has been suggested as a major force constraining physiological mechanisms such as immunity. In some long-lived oviparous species, a prolonged persistence of maternal antibodies in offspring could thus be expected in order to protect them over their long growth period. Here, using an intergenerational vaccination design, we show that specific maternal antibodies can display an estimated half-life of 25 days post-hatching in the nestlings of a long-lived bird. This temporal persistence is much longer than previously known for birds and it suggests specific properties in the regulation of IgY immunoglobulin catabolism in such a species. We also show that maternal antibodies in the considered procellariiform species are functional as late as 20 days of age. Using a modelling approach, we highlight that the potential impact of such effects on population viability could be important, notably when using vaccination for conservation. These results have broad implications, from comparative immunology to evolutionary eco-epidemiology and conservation biology.     

ROLE OF SEX AND MIGRATION IN ADAPTATION TO SINK ENVIRONMENTS

Understanding the effects of sex and migration on adaptation to novel environments remains a key problem in evolutionary biology. Using a single‐cell alga Chlamydomonas reinhardtii, we investigated how sex and migration affected rates of evolutionary rescue in a sink environment, and subsequent changes in fitness following evolutionary rescue. We show that sex and migration affect both the rate of evolutionary rescue and subsequent adaptation. However, their combined effects change as the populations adapt to a sink habitat. Both sex and migration independently increased rates of evolutionary rescue, but the effect of sex on subsequent fitness improvements, following initial rescue, changed with migration, as sex was beneficial in the absence of migration but constraining adaptation when combined with migration. These results suggest that sex and migration are beneficial during the initial stages of adaptation, but can become detrimental as the population adapts to its environment.     

Unequal contributions of species’ persistence and migration on plant communities’ response to climate warming throughout forests

Community reshuffling is lagging behind climate warming for many taxa, thereby generating a climatic debt. However, only few studies have attempted to assess the underlying factors that explain this debt. Here I examine how effects of species’ migration and persistence on the current climatic debt vary spatially in forest herbaceous communities throughout the French territory. I show that Mediterranean communities are responding to climate warming through both high species’ migration and persistence effects, while alpine forest is the only ecosystem where species’ migration overtakes species’ persistence mechanisms. Such an approach seems promising in assessing the underlying mechanisms of the biodiversity response to climate change locally, and it can be applied for conservation issues to assess biodiversity sensitivity and optimize its management.     

Migration highways and migration barriers created by host–parasite interactions

Co‐evolving parasites may play a key role in host migration and population structure. Using co‐evolving bacteria and viruses, we test general hypotheses as to how co‐evolving parasites affect the success of passive host migration between habitats that can support different intensities of host–parasite interactions. First, we show that parasites aid migration from areas of intense to weak co‐evolutionary interactions and impede migration in the opposite direction, as a result of intraspecific apparent competition mediated via parasites. Second, when habitats show qualitative difference such that some environments support parasite persistence while others do not, different population regulation forces (either parasitism or competitive exclusion) will reduce the success of migration in both directions. Our study shows that co‐evolution with parasites can predictably homogenises or isolates host populations, depending on heterogeneity of abiotic conditions, with the second scenario constituting a novel type of ‘isolation by adaptation’.     

Habitat persistence,habitat availability and the evolution of dispersal

Many organisms live in ephemeral habitats, making dispersal a vital element of life history. Here, we investigate how dispersal rate evolves in response to habitat persistence, mean habitat availability and landscape pattern. We show that dispersal rate is generally lowered by reduced habitat availability and by longer habitat persistence. However, for habitats that persist for an average of ten times the length of a generation, we show a clear non-monotonic relationship between habitat availability and dispersal rate. Some patterns of available habitat result in populations with dispersal polymorphisms. We explain these observations as a metapopulation effect, with the rate of evolution a function of both within-population and between-population selection pressures. Individuals in corridors evolve much lower dispersal rates than those in the mainland populations, especially within long, narrow corridors. We consider the implications of the results for conservation.     

Landscape attributes governing local transmission of an endemic zoonosis: Rabies virus in domestic dogs

Landscape heterogeneity plays an important role in disease spread and persistence, but quantifying landscape influences and their scale dependence is challenging. Studies have focused on how environmental features or global transport networks influence pathogen invasion and spread, but their influence on local transmission dynamics that underpin the persistence of endemic diseases remains unexplored. Bayesian phylogeographic frameworks that incorporate spatial heterogeneities are promising tools for analysing linked epidemiological, environmental and genetic data. Here, we extend these methodological approaches to decipher the relative contribution and scale‐dependent effects of landscape influences on the transmission of endemic rabies virus in Serengeti district, Tanzania (area ~4,900 km²). Utilizing detailed epidemiological data and 152 complete viral genomes collected between 2004 and 2013, we show that the localized presence of dogs but not their density is the most important determinant of diffusion, implying that culling will be ineffective for rabies control. Rivers and roads acted as barriers and facilitators to viral spread, respectively, and vaccination impeded diffusion despite variable annual coverage. Notably, we found that landscape effects were scale‐dependent: rivers were barriers and roads facilitators on larger scales, whereas the distribution of dogs was important for rabies dispersal across multiple scales. This nuanced understanding of the spatial processes that underpin rabies transmission can be exploited for targeted control at the scale where it will have the greatest impact. Moreover, this research demonstrates how current phylogeographic frameworks can be adapted to improve our understanding of endemic disease dynamics at different spatial scales.