Age-structured effects and disease interference in childhood infections

Recent studies have demonstrated that ecological interference among some childhood diseases may have important dynamic consequences. An interesting question is, when would we expect the interference effect to be pronounced? To address the issue, here we develop a seasonally forced two-disease age-structured model, using empirically derived age-specific force of infection (ASFOI) for numerous infections of childhood. Our comparative numerical analysis shows that when the ASFOIs for the two diseases largely overlap, the dynamics predicted by the two-disease model are generally different from those predicted by the analogous single-disease model, suggesting strong fingerprints of disease interference. When the ASFOIs overlap less, on the other hand, both diseases behave as predicted by the single-disease model, suggesting weak interference. We conclude that age structure is an important factor that should be taken into account in order to explore the underlying mechanisms of disease interference.     

Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission,extended feeding and tick aggregation

Lyme disease and Tick-Borne Encephalitis (TBE) are two emergent tick-borne diseases transmitted by the widely distributed European tick Ixodes ricinus. The life cycle of the vector and the number of hosts involved requires the development of complex models which consider different routes of pathogen transmission including those occurring between ticks that co-feed on the same host. Hence, we consider here a general model for tick-borne infections. We assumed ticks feed on two types of host species, one competent for viraemic transmission of infection, the second incompetent but included a third transmission route through non-viraemic transmission between ticks co-feeding on the same host. Since a blood meal lasts for several days these routes could lead to interesting nonlinearities in transmission rates, which may have important effects.We derive an explicit formula for the threshold for disease persistence in the case of viraemic transmission, also for the case of viraemic and non-viraemic transmission. From this formula, the effect of parameters on the persistence of infection can be determined. When only viraemic transmission occurs, we confirm that, while the density of the competent host has always a positive effect on infection persistence, the density of the incompetent host may have either a positive effect, by amplifying tick population, or a negative ("dilution") effect, by wasting tick bites on an incompetent host. With non-viraemic transmission, the "dilution" effect becomes less relevant. On the other hand, if the nonlinearity due to extended feeding is included, the dilution effect always occurs, but often at unrealistically high host densities. Finally, we incorporated the effects of tick aggregation on the hosts and correlation of tick stages and found that both had an important effect on infection persistence, if non-viraemic transmission occurred.     

Constraints on parasite fecundity and transmission in an insect-STD system

Parasites that are sexually transmitted (causing sexually transmitted diseases, or STDs) can have important effects on host population dynamics, but we know almost nothing for such parasites about constraints on fecundity and transmission. In this study, we have examined the effect of two potentially important constraints in one of the few empirically well-studied animal-STD systems, the ladybird, Adalia bipunctata , and its sexually transmitted mite, Coccipolipus hippodamiae . Using a factorial design, we manipulated: (i) within-host competition, by varying infection intensity; and (ii) host condition, by introducing dietary stress. Infection with C . hippodamiae significantly reduced ladybird survival whether or not diet was restricted, and restricting diet led to reduced survival regardless of infection status. Increased infection intensity and reduced host condition (dietary stress) both independently constrained per capita rates of parasite egg production and the development of infective larvae. Furthermore, when host condition was compromised, significantly fewer larvae were transmitted per adult mite during copulation. The effect of infection intensity on per mite transmission was more complex: there was no significant effect when hosts were fed normally, but when the ladybirds were nutritionally stressed higher infection intensity was associated with a slight increase in the numbers that were transmitted (despite the fact that mite fecundity was reduced under these conditions). These results indicate that host condition and within-host competition may both play an important role in shaping the epidemiology of the A . bipunctata – C . hippodamiae system, by influencing the parasite's basic reproductive ratio (R₀) and the rate of epidemic spread. Our data also extend general insights into STD ecology, by highlighting the importance of constraints on disease dynamics that are likely to be widespread.     

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.     

Kin selection and evolution of infectious disease resistance

Discoveries of mutations conferring resistance to infectious diseases have led to increased interest in the evolutionary dynamics of disease resistance. Several recent papers have estimated the historical strength of selection for mutations conferring disease resistance. These studies are based on simple population genetic models that do not take account of factors such as spatial and family structure. Such factors may have a substantial impact on the strength of natural selection through inclusive fitness effects. That is, people have a strong tendency to live with relatives and therefore have a high probability of transmitting infectious diseases to them. Thus, an allele that protects an individual against disease infection also protects that individual's family members. Because some of these family members are likely to also be carrying the allele, selection for that allele is magnified by family structure. In this paper, I use mathematical modeling techniques to explore the impact of such kin selection on the strength of selection for infectious disease resistance alleles. I show that if the resistance allele has the same proportional effect on both within- and between-family transmission, then the impact of kin selection is relatively minor. Selection coefficients are increased by 5-35%, with a greater benefit for weaker alleles. The reason is that an individual with a strong resistance allele does not need much protection from infection by family members and thus does not benefit much from their alleles. The effect of kin selection can be dramatic, however, if the resistance allele has a larger effect on between-family transmission than within-family transmission (which can occur if between-family infection rates are much smaller than within-family rates), increasing selection coefficients by as much as two- to threefold. These results show conditions when it is important to consider family structure in estimates of the strength of selection for infectious disease resistance alleles.     

Preclinical transmission of prions by blood transfusion is influenced by donor genotype and route of infection

Variant Creutzfeldt-Jakob disease (vCJD) is a human prion disease resulting from zoonotic transmission of bovine spongiform encephalopathy (BSE). Documented cases of vCJD transmission by blood transfusion necessitate on-going risk reduction measures to protect blood supplies, such as leucodepletion (removal of white blood cells, WBCs). This study set out to determine the risks of prion transmission by transfusion of labile blood components (red blood cells, platelets, plasma) commonly used in human medicine, and the effectiveness of leucodepletion in preventing infection, using BSE-infected sheep as a model. All components were capable of transmitting prion disease when donors were in the preclinical phase of infection, with the highest rates of infection in recipients of whole blood and buffy coat, and the lowest in recipients of plasma. Leucodepletion of components (<10⁶ WBCs/unit) resulted in significantly lower transmission rates, but did not completely prevent transmission by any component. Donor PRNP genotype at codon 141, which is associated with variation in incubation period, also had a significant effect on transfusion transmission rates. A sensitive protein misfolding cyclic amplification (PMCA) assay, applied to longitudinal series of blood samples, identified infected sheep from 4 months post infection. However, in donor sheep (orally infected), the onset of detection of PrP^Sc in blood was much more variable, and generally later, compared to recipients (intravenous infection). This shows that the route and method of infection may profoundly affect the period during which an individual is infectious, and the test sensitivity required for reliable preclinical diagnosis, both of which have important implications for disease control. Our results emphasize that blood transfusion can be a highly efficient route of transmission for prion diseases. Given current uncertainties over the prevalence of asymptomatic vCJD carriers, this argues for the maintenance and improvement of current measures to reduce the risk of transmission by blood products.     

Interacting Epidemics and Coinfection on Contact Networks

The spread of certain diseases can be promoted, in some cases substantially, by prior infection with another disease. One example is that of HIV, whose immunosuppressant effects significantly increase the chances of infection with other pathogens. Such coinfection processes, when combined with nontrivial structure in the contact networks over which diseases spread, can lead to complex patterns of epidemiological behavior. Here we consider a mathematical model of two diseases spreading through a single population, where infection with one disease is dependent on prior infection with the other. We solve exactly for the sizes of the outbreaks of both diseases in the limit of large population size, along with the complete phase diagram of the system. Among other things, we use our model to demonstrate how diseases can be controlled not only by reducing the rate of their spread, but also by reducing the spread of other infections upon which they depend.     

Disease Interventions Can Interfere with One Another through Disease-Behaviour Interactions

Theoretical models of disease dynamics on networks can aid our understanding of how infectious diseases spread through a population. Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccination choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. However, these two interventions are usually modelled separately. Here, we construct a simulation model of influenza transmission through a contact network, where individuals can choose whether to become vaccinated and/or practice NPIs. These decisions are based on previous experience with the disease, the current state of infection amongst one''s contacts, and the personal and social impacts of the choices they make. We find that the interventions interfere with one another: because of negative feedback between intervention uptake and infection prevalence, it is difficult to simultaneously increase uptake of all interventions by changing utilities or perceived risks. However, on account of vaccine efficacy being higher than NPI efficacy, measures to expand NPI practice have only a small net impact on influenza incidence due to strongly mitigating feedback from vaccinating behaviour, whereas expanding vaccine uptake causes a significant net reduction in influenza incidence, despite the reduction of NPI practice in response. As a result, measures that support expansion of only vaccination (such as reducing vaccine cost), or measures that simultaneously support vaccination and NPIs (such as emphasizing harms of influenza infection, or satisfaction from preventing infection in others through both interventions) can significantly reduce influenza incidence, whereas measures that only support expansion of NPI practice (such as making hand sanitizers more available) have little net impact on influenza incidence. (However, measures that improve NPI efficacy may fare better.) We conclude that the impact of interference on programs relying on multiple interventions should be more carefully studied, for both influenza and other infectious diseases.     

Rabbitpox virus and vaccinia virus infection of rabbits as a model for human smallpox

The threat of smallpox release and use as a bioweapon has encouraged the search for new vaccines and antiviral drugs, as well as development of new small-animal models in which their efficacy can be determined. Here, we reinvestigate a rabbit model in which the intradermal infection of rabbits with very low doses of either rabbitpox virus (RPV) or vaccinia virus Western Reserve (VV-WR) recapitulates many of the clinical features of human smallpox. Following intradermal inoculation with RPV, rabbits develop systemic disease characterized by extensive viremia, numerous secondary lesions on the skin and mucocutaneous tissues, severe respiratory disease, death by 9 days postinfection, and, importantly, natural aerosol transmission between animals. Contrary to previous reports, intradermal infection with VV-WR also resulted in a very similar lethal systemic disease in rabbits, again with natural aerosol transmission between animals. When sentinel and index animals were cohoused, transmission rates approached 100% with either virus, with sentinel animals exhibiting a similar, severe disease. Lower rates of transmission were observed when index and sentinel animals were housed in separate cages. Sentinel animals infected with RPV with one exception succumbed to the disease. However, the majority of VV-WR-infected sentinel animals, while becoming seriously ill, survived. Finally, we tested the efficacy of the drug 1-O-hexadecyloxypropyl-cidofovir in the RPV/rabbit model and found that an oral dose of 5 mg/kg twice a day for 5 days beginning 1 day before infection was able to completely protect rabbits from lethal disease.     

Interference and the ideal free distribution: oviposition in a parasitoid wasp

The interference ideal free distribution (IFD) model of Sutherlandmakes a number of predictions that have yet to be tested andthat have implications for the validity of subsequent extensionsto the theory. We tested these predictions in a study usingdifferent densities of the parasitoid wasp, Venturia canescens,foraging on patches containing different densities of its host,Plodia interpunctella. Our results support a number of the interferenceIFD model's general predictions. Gain rate decreased becauseof increased interference at higher density. Although gain rateson the two patches differed slighdy, this would be expectedallowing for some sampling behavior and perceptual constraints.Early in each experiment when patch assessment is likely tooccur, wasp movement was higher and gain rates lower. However,the more specific prediction of Sutherland's model, that proportionalpatch use should be constant and independent of density, wasnot upheld. Contemporary IFD models use only one of severalequally valid potential relationships between gain rate, interference,and competitor density. The results of this study provide supportfor the additive model developed by Tregenza et al. (companionarticle).     

Models of infectious diseases in spatially heterogeneous environments

Most models of dynamics of infectious diseases have assumed homogeneous mixing in the host population. However, it is increasingly recognized that heterogeneity can arise through many processes. It is then important to consider the existence of subpopulations of hosts, and that the contact rate within subpopulations is different than that between subpopulations. We study models with hosts distributed in subpopulations as a consequence of spatial partitioning. Two types of models are considered. In the first one there is direct transmission. The second one is a model of dynamics of a mosquito-borne disease, with indirect transmission, and applicable to malaria. The contact between subpopulations is achieved through the visits of hosts. Two types of visit are considered: a first one in which the visit time is independent of the distance travelled, and a second one in which visit time decreases with distance. There are two types of spatial arrangement: one dimensional, and two dimensional. Conditions for the establishment of the disease are obtained. Results indicate that the disease becomes established with greater difficulty when the degree of spatial partition increases, and when visit time decreases. In addition, when visit time decreases with distance, the establishment of the disease is more difficult when the spatial arrangement is one dimensional than when it is two dimensional. The results indicate the importance of knowing the spatial distribution and mobility patterns to understand the dynamics of infectious diseases. The consequences of these results for the design of public health policies are discussed.     

Infectious disease modeling of social contagion in networks

Many behavioral phenomena have been found to spread interpersonally through social networks, in a manner similar to infectious diseases. An important difference between social contagion and traditional infectious diseases, however, is that behavioral phenomena can be acquired by non-social mechanisms as well as through social transmission. We introduce a novel theoretical framework for studying these phenomena (the SISa model) by adapting a classic disease model to include the possibility for 'automatic' (or 'spontaneous') non-social infection. We provide an example of the use of this framework by examining the spread of obesity in the Framingham Heart Study Network. The interaction assumptions of the model are validated using longitudinal network transmission data. We find that the current rate of becoming obese is 2 per year and increases by 0.5 percentage points for each obese social contact. The rate of recovering from obesity is 4 per year, and does not depend on the number of non-obese contacts. The model predicts a long-term obesity prevalence of approximately 42, and can be used to evaluate the effect of different interventions on steady-state obesity. Model predictions quantitatively reproduce the actual historical time course for the prevalence of obesity. We find that since the 1970s, the rate of recovery from obesity has remained relatively constant, while the rates of both spontaneous infection and transmission have steadily increased over time. This suggests that the obesity epidemic may be driven by increasing rates of becoming obese, both spontaneously and transmissively, rather than by decreasing rates of losing weight. A key feature of the SISa model is its ability to characterize the relative importance of social transmission by quantitatively comparing rates of spontaneous versus contagious infection. It provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviors, health states, ideas or diseases with reservoirs.     

Generation interval contraction and epidemic data analysis

The generation interval is the time between the infection time of an infected person and the infection time of his or her infector. Probability density functions for generation intervals have been an important input for epidemic models and epidemic data analysis. In this paper, we specify a general stochastic SIR epidemic model and prove that the mean generation interval decreases when susceptible persons are at risk of infectious contact from multiple sources. The intuition behind this is that when a susceptible person has multiple potential infectors, there is a "race" to infect him or her in which only the first infectious contact leads to infection. In an epidemic, the mean generation interval contracts as the prevalence of infection increases. We call this global competition among potential infectors. When there is rapid transmission within clusters of contacts, generation interval contraction can be caused by a high local prevalence of infection even when the global prevalence is low. We call this local competition among potential infectors. Using simulations, we illustrate both types of competition. Finally, we show that hazards of infectious contact can be used instead of generation intervals to estimate the time course of the effective reproductive number in an epidemic. This approach leads naturally to partial likelihoods for epidemic data that are very similar to those that arise in survival analysis, opening a promising avenue of methodological research in infectious disease epidemiology.     

Estimating a binary character's effect on speciation and extinction

Determining whether speciation and extinction rates depend on the state of a particular character has been of long-standing interest to evolutionary biologists. To assess the effect of a character on diversification rates using likelihood methods requires that we be able to calculate the probability that a group of extant species would have evolved as observed, given a particular model of the character's effect. Here we describe how to calculate this probability for a phylogenetic tree and a two-state (binary) character under a simple model of evolution (the "BiSSE" model, binary-state speciation and extinction). The model involves six parameters, specifying two speciation rates (rate when the lineage is in state 0; rate when in state 1), two extinction rates (when in state 0; when in state 1), and two rates of character state change (from 0 to 1, and from 1 to 0). Using these probability calculations, we can do maximum likelihood inference to estimate the model's parameters and perform hypothesis tests (e.g., is the rate of speciation elevated for one character state over the other?). We demonstrate the application of the method using simulated data with known parameter values.     

The basic reproduction number for complex disease systems: defining R(0) for tick-borne infections

Characterizing the basic reproduction number, R(0), for many wildlife disease systems can seem a complex problem because several species are involved, because there are different epidemiological reactions to the infectious agent at different life-history stages, or because there are multiple transmission routes. Tick-borne diseases are an important example where all these complexities are brought together as a result of the peculiarities of the tick life cycle and the multiple transmission routes that occur. We show here that one can overcome these complexities by separating the host population into epidemiologically different types of individuals and constructing a matrix of reproduction numbers, the so-called next-generation matrix. Each matrix element is an expected number of infectious individuals of one type produced by a single infectious individual of a second type. The largest eigenvalue of the matrix characterizes the initial exponential growth or decline in numbers of infected individuals. Values below 1 therefore imply that the infection cannot establish. The biological interpretation closely matches that of R(0) for disease systems with only one type of individual and where infection is directly transmitted. The parameters defining each matrix element have a clear biological meaning. We illustrate the usefulness and power of the approach with a detailed examination of tick-borne diseases, and we use field and experimental data to parameterize the next-generation matrix for Lyme disease and tick-borne encephalitis. Sensitivity and elasticity analyses of the matrices, at the element and individual parameter levels, allow direct comparison of the two etiological agents. This provides further support that transmission between cofeeding ticks is critically important for the establishment of tick-borne encephalitis.     

Population dynamic interference among childhood diseases.

Epidemiologists usually study the interaction between a host population and one parasitic infection. However, different parasite species effectively compete, in an ecological sense, for the same finite group of susceptible hosts, so there may be an indirect effect on the population dynamics of one disease due to epidemics of another. In human populations, recovery from any serious infection is normally preceded by a period of convalescence, during which infected individuals stay at home and are effectively shielded from exposure to other infectious diseases. We present a model for the dynamics of two infectious diseases, incorporating a temporary removal of susceptibles. We use this model to explore population-level consequences of a temporary insusceptibility in childhood diseases, the dynamics of which are partly driven by differences in contact rates in and out of school terms. Significant population dynamic interference is predicted and cannot be dismissed in the limited case-study data available for measles and whooping cough in England before the vaccination era.     

Spatial Heterogeneity,Host Movement and Mosquito-Borne Disease Transmission

Mosquito-borne diseases are a global health priority disproportionately affecting low-income populations in tropical and sub-tropical countries. These pathogens live in mosquitoes and hosts that interact in spatially heterogeneous environments where hosts move between regions of varying transmission intensity. Although there is increasing interest in the implications of spatial processes for mosquito-borne disease dynamics, most of our understanding derives from models that assume spatially homogeneous transmission. Spatial variation in contact rates can influence transmission and the risk of epidemics, yet the interaction between spatial heterogeneity and movement of hosts remains relatively unexplored. Here we explore, analytically and through numerical simulations, how human mobility connects spatially heterogeneous mosquito populations, thereby influencing disease persistence (determined by the basic reproduction number R ₀), prevalence and their relationship. We show that, when local transmission rates are highly heterogeneous, R ₀ declines asymptotically as human mobility increases, but infection prevalence peaks at low to intermediate rates of movement and decreases asymptotically after this peak. Movement can reduce heterogeneity in exposure to mosquito biting. As a result, if biting intensity is high but uneven, infection prevalence increases with mobility despite reductions in R ₀. This increase in prevalence decreases with further increase in mobility because individuals do not spend enough time in high transmission patches, hence decreasing the number of new infections and overall prevalence. These results provide a better basis for understanding the interplay between spatial transmission heterogeneity and human mobility, and their combined influence on prevalence and R ₀.     

Covariation between the physiological and behavioral components of pathogen transmission: host heterogeneity determines epidemic outcomes

Although heterogeneity in contact rate, physiology, and behavioral response to infection have all been empirically demonstrated in host–pathogen systems, little is known about how interactions between individual variation in behavior and physiology scale‐up to affect pathogen transmission at a population level. The objective of this study is to evaluate how covariation between the behavioral and physiological components of transmission might affect epidemic outcomes in host populations. We tested the consequences of contact rate covarying with susceptibility, infectiousness, and infection status using an individual‐based, dynamic network model where individuals initiate and terminate contacts with conspecifics based on their behavioral predispositions and their infection status. Our results suggest that both heterogeneity in physiology and subsequent covariation of physiology with contact rate could powerfully influence epidemic dynamics. Overall, we found that 1) individual variability in susceptibility and infectiousness can reduce the expected maximum prevalence and increase epidemic variability; 2) when contact rate and susceptibility or infectiousness negatively covary, it takes substantially longer for epidemics to spread throughout the population, and rates of epidemic spread remained suppressed even for highly transmissible pathogens; and 3) reductions in contact rate resulting from infection‐induced behavioral changes can prevent the pathogen from reaching most of the population. These effects were strongest for theoretical pathogens with lower transmissibility and for populations where the observed variation in contact rate was higher, suggesting that such heterogeneity may be most important for less infectious, more chronic diseases in wildlife. Understanding when and how variability in pathogen transmission should be modelled is a crucial next step for disease ecology.     

Mixing in age-structured population models of infectious diseases

Infectious diseases are controlled by reducing pathogen replication within or transmission between hosts. Models can reliably evaluate alternative strategies for curtailing transmission, but only if interpersonal mixing is represented realistically. Compartmental modelers commonly use convex combinations of contacts within and among groups of similarly aged individuals, respectively termed preferential and proportionate mixing. Recently published face-to-face conversation and time-use studies suggest that parents and children and co-workers also mix preferentially. As indirect effects arise from the off-diagonal elements of mixing matrices, these observations are exceedingly important. Accordingly, we refined the formula published by Jacquez et al. [19] to account for these newly-observed patterns and estimated age-specific fractions of contacts with each preferred group. As the ages of contemporaries need not be identical nor those of parents and children to differ by exactly the generation time, we also estimated the variances of the Gaussian distributions with which we replaced the Kronecker delta commonly used in theoretical studies. Our formulae reproduce observed patterns and can be used, given contacts, to estimate probabilities of infection on contact, infection rates, and reproduction numbers. As examples, we illustrate these calculations for influenza based on "attack rates" from a prospective household study during the 1957 pandemic and for varicella based on cumulative incidence estimated from a cross-sectional serological survey conducted from 1988-94, together with contact rates from the several face-to-face conversation and time-use studies. Susceptibility to infection on contact generally declines with age, but may be elevated among adolescents and adults with young children.