Pattern of Tick Aggregation on Mice: Larger Than Expected Distribution Tail Enhances the Spread of Tick-Borne Pathogens

The spread of tick-borne pathogens represents an important threat to human and animal health in many parts of Eurasia. Here, we analysed a 9-year time series of Ixodes ricinus ticks feeding on Apodemus flavicollis mice (main reservoir-competent host for tick-borne encephalitis, TBE) sampled in Trentino (Northern Italy). The tail of the distribution of the number of ticks per host was fitted by three theoretical distributions: Negative Binomial (NB), Poisson-LogNormal (PoiLN), and Power-Law (PL). The fit with theoretical distributions indicated that the tail of the tick infestation pattern on mice is better described by the PL distribution. Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance. In order to investigate the effect of different tails of tick distribution on the invasion of a non-systemically transmitted pathogen, we simulated the transmission of a TBE-like virus between susceptible and infective ticks using a stochastic model. Model simulations indicated different outcomes of disease spreading when considering different distribution laws of ticks among hosts. Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution. Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.     

Contributions to the mathematical theory of epidemics—I

(1) A mathematical investigation has been made of the progress of an epidemic in a homogeneous population. It has been assumed that complete immunity is conferred by a single attack, and that an individual is not infective at the moment at which he receives infection. With these reservations the problem has been investigated in its most general aspects, and the following conclusions have been arrived at. (2) In general a threshold density of population is found to exist, which depends upon the infectivity, recovery and death rates peculiar to the epidemic. No epidemic can occur if the population density is below this threshold value. (3) Small increases of the infectivity rate may lead to large epidemics; also, if the population density slightly exceeds its threshold value the effect of an epidemic will be to reduce the density as far below the threshold value as initially it was above it. (4) An epidemic, in general, comes to an end, before the susceptible population has been exhausted. (5) Similar results are indicated for the case in which transmission is through an intermediate host.     

Novel moment closure approximations in stochastic epidemics

Moment closure approximations are used to provide analytic approximations to non-linear stochastic population models. They often provide insights into model behaviour and help validate simulation results. However, existing closure schemes typically fail in situations where the population distribution is highly skewed or extinctions occur. In this study we address these problems by introducing novel second-and third-order moment closure approximations which we apply to the stochastic SI and SIS epidemic models. In the case of the SI model, which has a highly skewed distribution of infection, we develop a second-order approximation based on the beta-binomial distribution. In addition, a closure approximation based on mixture distribution is developed in order to capture the behaviour of the stochastic SIS model around the threshold between persistence and extinction. This mixture approximation comprises a probability distribution designed to capture the quasi-equilibrium probabilities of the system and a probability mass at 0 which represents the probability of extinction. Two third-order versions of this mixture approximation are considered in which the log-normal and the beta-binomial are used to model the quasi-equilibrium distribution. Comparison with simulation results shows: (1) the beta-binomial approximation is flexible in shape and matches the skewness predicted by simulation as shown by the stochastic SI model and (2) mixture approximations are able to predict transient and extinction behaviour as shown by the stochastic SIS model, in marked contrast with existing approaches. We also apply our mixture approximation to approximate a likehood function and carry out point and interval parameter estimation.     

Modeling the spread of vector-borne diseases on bipartite networks

Background

Vector-borne diseases for which transmission occurs exclusively between vectors and hosts can be modeled as spreading on a bipartite network.

Methodology/Principal Findings

In such models the spreading of the disease strongly depends on the degree distribution of the two classes of nodes. It is sufficient for one of the classes to have a scale-free degree distribution with a slow enough decay for the network to have asymptotically vanishing epidemic threshold. Data on the distribution of Ixodes ricinus ticks on mice and lizards from two independent studies are well described by a scale-free distribution compatible with an asymptotically vanishing epidemic threshold. The commonly used negative binomial, instead, cannot describe the right tail of the empirical distribution.

Conclusions/Significance

The extreme aggregation of vectors on hosts, described by the power-law decay of the degree distribution, makes the epidemic threshold decrease with the size of the network and vanish asymptotically.     

A general model for stochastic SIR epidemics with two levels of mixing

This paper is concerned with a general stochastic model for susceptible→infective→removed epidemics, among a closed finite population, in which during its infectious period a typical infective makes both local and global contacts. Each local contact of a given infective is with an individual chosen independently according to a contact distribution ‘centred’ on that infective, and each global contact is with an individual chosen independently and uniformly from the whole population. The asymptotic situation in which the local contact distribution remains fixed as the population becomes large is considered. The concepts of local infectious clump and local susceptibility set are used to develop a unified approach to the threshold behaviour of this class of epidemic models. In particular, a threshold parameter R_* governing whether or not global epidemics can occur, the probability that a global epidemic occurs and the mean proportion of initial susceptibles ultimately infected by a global epidemic are all determined. The theory is specialised to (i) the households model, in which the population is partitioned into households and local contacts are chosen uniformly within an infective’s household; (ii) the overlapping groups model, in which the population is partitioned in several ways, with local uniform mixing within the elements of the partitions; and (iii) the great circle model, in which individuals are equally spaced on a circle and local contacts are nearest-neighbour.     

Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model

In this paper, we develop a new approach to deal with asymptotic behavior of the age-structured homogeneous epidemic systems and discuss its application to the MSEIR epidemic model. For the homogeneous system, there is no attracting nontrivial equilibrium, instead we have to examine existence and stability of persistent solutions. Assuming that the host population dynamics can be described by the stable population model, we rewrite the basic system into the system of ratio age distribution, which is the age profile divided by the stable age profile. If the host population has the stable age profile, the ratio age distribution system is reduced to the normalized system. Then we prove the stability principle that the local stability or instability of steady states of the normalized system implies that of the corresponding persistent solutions of the original homogeneous system. In the latter half of this paper, we prove the threshold and stability results for the normalized system of the age-structured MSEIR epidemic model.      

Stochastic two-group models with transmission dependent on host infectivity or susceptibility

ABSTRACT

Stochastic epidemic models with two groups are formulated and applied to emerging and re-emerging infectious diseases. In recent emerging diseases, disease spread has been attributed to superspreaders, highly infectious individuals that infect a large number of susceptible individuals. In some re-emerging infectious diseases, disease spread is attributed to waning immunity in susceptible hosts. We apply a continuous-time Markov chain (CTMC) model to study disease emergence or re-emergence from different groups, where the transmission rates depend on either the infectious host or the susceptible host. Multitype branching processes approximate the dynamics of the CTMC model near the disease-free equilibrium and are used to estimate the probability of a minor or a major epidemic. It is shown that the probability of a major epidemic is greater if initiated by an individual from the superspreader group or by an individual from the highly susceptible group. The models are applied to Severe Acute Respiratory Syndrome and measles.     

Using Extreme Value Theory Approaches to Forecast the Probability of Outbreak of Highly Pathogenic Influenza in Zhejiang,China

BackgroundInfluenza is a contagious disease with high transmissibility to spread around the world with considerable morbidity and mortality and presents an enormous burden on worldwide public health. Few mathematical models can be used because influenza incidence data are generally not normally distributed. We developed a mathematical model using Extreme Value Theory (EVT) to forecast the probability of outbreak of highly pathogenic influenza.MethodsThe incidence data of highly pathogenic influenza in Zhejiang province from April 2009 to November 2013 were retrieved from the website of Health and Family Planning Commission of Zhejiang Province. MATLAB “VIEM” toolbox was used to analyze data and modelling. In the present work, we used the Peak Over Threshold (POT) model, assuming the frequency as a Poisson process and the intensity to be Pareto distributed, to characterize the temporal variability of the long-term extreme incidence of highly pathogenic influenza in Zhejiang, China.ResultsThe skewness and kurtosis of the incidence of highly pathogenic influenza in Zhejiang between April 2009 and November 2013 were 4.49 and 21.12, which indicated a “fat tail” distribution. A QQ plot and a mean excess plot were used to further validate the features of the distribution. After determining the threshold, we modeled the extremes and estimated the shape parameter and scale parameter by the maximum likelihood method. The results showed that months in which the incidence of highly pathogenic influenza is about 4462/2286/1311/487 are predicted to occur once every five/three/two/one year, respectively.ConclusionsDespite the simplicity, the present study successfully offers the sound modeling strategy and a methodological avenue to implement forecasting of an epidemic in the midst of its course.     

Body-size scaling in an SEI model of wildlife diseases

A number of wildlife pathogens are generalist and can affect different host species characterized by a wide range of body sizes. In this work we analyze the role of allometric scaling of host vital and epidemiological rates in a Susceptible-Exposed-Infected (SEI) model. Our analysis shows that the transmission coefficient threshold for the disease to establish in the population scales allometrically (exponent = 0.45) with host size as well as the threshold at which limit cycles occur. In contrast, the threshold of the basic reproduction number for sustained oscillations to occur is independent of the host size and is always greater than 5. In the case of rabies, we show that the oscillation periods predicted by the model match those observed in the field for a wide range of host sizes.The population dynamics of the SEI model is also analyzed in the case of pathogens affecting multiple coexisting hosts with different body sizes. Our analyses show that the basic reproduction number for limit cycles to occur depends on the ratio between host sizes, that the oscillation period in a multihost community is set by the smaller species dynamics, and that intermediate interspecific disease transmission can stabilize the epidemic occurrence in wildlife communities.     

Avian brood parasitism in a Mediterranean region: hosts and habitat preferences of Common Cuckoos Cuculus canorus

Capsule Cuckoos in Italy support the ‘host preference’ hypothesis.

Aims To identify the species parasitized in a Mediterranean area, in Italy; to quantify the frequency of parasitism on each host species; and to determine whether some species and/or habitat types are parasitized more than expected from a homogeneous distribution.

Methods Nest records dating from 1865 were compiled from literature, nest card programmes, and personal communication with ornithologists working in the region. Comparisons of parasitism frequencies were made among and within habitats for all cuckoo hosts.

Results The most frequently parasitized hosts were Great Reed Warbler, European Robin, Marsh Warbler, Redstart, and Reed Warbler. The highest number of parasitized species was in anthropic areas (15 host species), whereas wetlands supported the highest number of parasitized nests (471).

Conclusion Cuckoos select a different suite of hosts in Italy from those in continental Europe, but this was not always explained on the basis of different geographical distribution. Results support the ‘host preference’ hypothesis. We suggest further analyses to avoid over‐ or underestimates of parasitism on each host species when parasite preferences are examined.     

Temporal Duration and Event Size Distribution at the Epidemic Threshold

The epidemic event, seen as a nonequilibrium dynamic process, is studied through a simple stochastic system reminiscent of the classical SIR model. The system is described in terms of global and local variables and was mainly treated by means of Monte Carlo simulation; square lattices N×N, with N=23, 51, 100, 151, and 211 were used. Distinct extensive runs were performed and then classified as corresponding to epidemic or non-epidemic phase. They were examined with detail through the analysis of the event duration and event size; illustrations, such as density-like plots in the space of the model's parameters, are provided. The epidemic/non-epidemic phase presents smaller/larger relative fluctuations, whereas closer to the threshold the uncertainty reaches its highest values. Far enough from the threshold, the distribution (t) of the events time duration t shows a step-like appearance. However at the threshold line it shows an exponential behavior of the form (t) exp (-t); the same behavior is observed for the event size distribution. These results help to explain why the approach to epidemic threshold would be hard to anticipate with standard census data.     

Prediction of hot spot areas of hemorrhagic fever with renal syndrome in Hunan Province based on an information quantity model and logistical regression model

BackgroundChina’s “13^th 5-Year Plan” (2016–2020) for the prevention and control of sudden acute infectious diseases emphasizes that epidemic monitoring and epidemic focus surveys in key areas are crucial for strengthening national epidemic prevention and building control capacity. Establishing an epidemic hot spot areas and prediction model is an effective means of accurate epidemic monitoring and surveying. Objective: This study predicted hemorrhagic fever with renal syndrome (HFRS) epidemic hot spot areas, based on multi-source environmental variable factors. We calculated the contribution weight of each environmental factor to the morbidity risk, obtained the spatial probability distribution of HFRS risk areas within the study region, and detected and extracted epidemic hot spots, to guide accurate epidemic monitoring as well as prevention and control. Methods: We collected spatial HFRS data, as well as data on various types of natural and human social activity environments in Hunan Province from 2010 to 2014. Using the information quantity method and logistic regression modeling, we constructed a risk-area-prediction model reflecting the epidemic intensity and spatial distribution of HFRS. Results: The areas under the receiver operating characteristic curve of training samples and test samples were 0.840 and 0.816. From 2015 to 2019, HRFS case site verification showed that more than 82% of the cases occurred in high-risk areas.DiscussionThis research method could accurately predict HFRS hot spot areas and provided an evaluation model for Hunan Province. Therefore, this method could accurately detect HFRS epidemic high-risk areas, and effectively guide epidemic monitoring and surveyance.     

Parasite strain coexistence in a heterogeneous host population

Heterogeneity in host susceptibility and transmissibility to parasite attack allows a lower transmission rate to sustain an epidemic than is required in homogeneous host populations. However, this heterogeneity can leave some hosts with little susceptibility to disease, and at high transmission rates, epidemic size can be smaller than for diseases where the host population is homogeneous. In a heterogeneous host population, we model natural selection in a parasite population where host heterogeneity is exploited by different strains to varying degrees. This partitioning of the host population allows coexistence of competing parasite strains, with the heterogeneity-exploiting strains infecting the more susceptible hosts, in the absence of physiological tradeoffs and spatial heterogeneity, and even for markedly different transmission rates. In our model, intermediate-strategy parasites were selected against: should coexistence occur, an equilibrium is reached where strains occupied only the extreme ends of trait space, under appropriate conditions selecting for lower R₀.     

Re-assess Vector Indices Threshold as an Early Warning Tool for Predicting Dengue Epidemic in a Dengue Non-endemic Country

BackgroundDespite dengue dynamics being driven by complex interactions between human hosts, mosquito vectors and viruses that are influenced by climate factors, an operational model that will enable health authorities to anticipate the outbreak risk in a dengue non-endemic area has not been developed. The objectives of this study were to evaluate the temporal relationship between meteorological variables, entomological surveillance indices and confirmed dengue cases; and to establish the threshold for entomological surveillance indices including three mosquito larval indices [Breteau (BI), Container (CI) and House indices (HI)] and one adult index (AI) as an early warning tool for dengue epidemic.Conclusion/SignificanceThere was little evidence of quantifiable association among vector indices, meteorological factors and dengue transmission that could reliably be used for outbreak prediction. Our study here provided the proof-of-concept of how to search for the optimal model and determine the threshold for dengue epidemics. Since those factors used for prediction varied, depending on the ecology and herd immunity level under different geological areas, different thresholds may be developed for different countries using a similar structure of the two-stage model.     

SIR dynamics in random networks with heterogeneous connectivity

Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by showing how the SIR dynamics can be modeled with a system of three nonlinear ODE’s. The method makes use of the probability generating function (PGF) formalism for representing the degree distribution of a random network and makes use of network-centric quantities such as the number of edges in a well-defined category rather than node-centric quantities such as the number of infecteds or susceptibles. The PGF provides a simple means of translating between network and node-centric variables and determining the epidemic incidence at any time. The theory also provides a simple means of tracking the evolution of the degree distribution among susceptibles or infecteds. The equations are used to demonstrate the dramatic effects that the degree distribution plays on the final size of an epidemic as well as the speed with which it spreads through the population. Power law degree distributions are observed to generate an almost immediate expansion phase yet have a smaller final size compared to homogeneous degree distributions such as the Poisson. The equations are compared to stochastic simulations, which show good agreement with the theory. Finally, the dynamic equations provide an alternative way of determining the epidemic threshold where large-scale epidemics are expected to occur, and below which epidemic behavior is limited to finite-sized outbreaks.      

Intraspecific competition and density dependence in an Ephestia kuehniella–Venturia canescens laboratory system

A model host-parasitoid system of Ephestia kuehniella and Venturia canescens was used to examine the influence of host and parasitoid density on host and parasitoid life-history parameters via a two-way factorial experimental design (5 initial host densities×3 parasitoid densities). In the absence of parasitoids, E. kuehniella experienced scramble-type competition with reduced growth, diminished adult size and a subsequent fecundity trade-off for mortality. The mortality that did occur was confined to the late larval and pupal stages. In the presence of parasitoids attacking the late larval stage, competition changed from scramble for food to contest for enemy-free space, with hosts escaping parasitism being small with low fecundity and reduced egg size, and with parasitoid adult size inversely dependent on host density. Total insect emergence (host+parasitoid), a measure of the influence of host resource competition on survivorship, exhibited a threshold effect as a function of initial host density; the threshold value was increased to a higher initial host density in the presence of parasitoids. Models of host self-limitation were fitted to the data, with the generalized Beverton-Holt model that incorporates a threshold effect providing the best fit, and the Ricker model with no threshold providing a very poor fit to the data.     

Endemic infection reduces transmission potential of an epidemic parasite during co-infection

Endemic, low-virulence parasitic infections are common in nature. Such infections may deplete host resources, which in turn could affect the reproduction of other parasites during co-infection. We aimed to determine whether the reproduction, and therefore transmission potential, of an epidemic parasite was limited by energy costs imposed on the host by an endemic infection. Total lipids, triacylglycerols (TAG) and polar lipids were measured in cockroaches (Blattella germanica) that were fed ad libitum, starved or infected with an endemic parasite, Gregarina blattarum. Reproductive output of an epidemic parasite, Steinernema carpocapsae, was then assessed by counting the number of infective stages emerging from these three host groups. We found both starvation and gregarine infection reduced cockroach lipids, mainly through depletion of TAG. Further, both starvation and G. blattarum infection resulted in reduced emergence of nematode transmission stages. This is, to our knowledge, the first study to demonstrate directly that host resource depletion caused by endemic infection could affect epidemic disease transmission. In view of the ubiquity of endemic infections in nature, future studies of epidemic transmission should take greater account of endemic co-infections.     

Infestation by the mite Harpirhynchus nidulans in the Bearded Tit Panurus biarmicus

Capsule Mites sometimes induced voluminous subcutaneous cysts in featherless parts.

Aims To describe the first reported infestation by the skin-dweller mite Harpirhynchus nidulans in Bearded Tits Panurus biarmicus and for the Timaliidae family, to detect possible fitness costs for the host and to determine the distribution of the parasite within the distribution range of the host.

Methods Parasites were identified using a microscope. Wing-length and body mass were recorded on both uninfected and infected birds captured at different times during the year. We also considered historical data, and contact was made with 32 European ringing stations to identify the distribution range of the parasite.

Results Subcutaneous reproduction of the mite Harpirhynchus nidulans induced the development of voluminous dermal nodules in Panurus biarmicus. There were no differences in body mass or wing-length with respect to infestation. In the south of France, prevalence changed from 10.6% in spring to 4.7% in autumn. Both sexes are equally parasitized. Occurrence of dermal cysts is reported from several southern European populations of Bearded Tits, whereas it seems to be absent from northern latitudes.

Conclusion The occurrence of a Harpirhynchus mite in wild bird populations is reported for the first time. We consider aspects of its biology, host–parasite system, host-specificity, co-adaptation of the mite reproductive cycle to the social dynamics of its host and metapopulational host–parasite dynamics.     

How do toxicants affect epidemiological dynamics?

Populations are formed of their constituent interacting individuals, each with their own respective within‐host biological processes. Infection not only spreads within the host organism but also spreads between individuals. Here we propose and study a multilevel model which links the within‐host statuses of immunity and parasite density to population epidemiology under sublethal and lethal toxicant exposure. We analyse this nested model in order to better understand how toxicants impact the spread of disease within populations. We demonstrate that outbreak of infection within a population is completely determined by the level of toxicant exposure, and that it is maximised by intermediate toxicant dosage. We classify the population epidemiology into five phases of increasing toxicant exposure and calculate the conditions under which disease will spread, showing that there exists a threshold toxicant level under which epidemics will not occur. In general, higher toxicant load results in either extinction of the population or outbreak of infection. The within‐host statuses of the individual host also determine the outcome of the epidemic at the population level. We discuss applications of our model in the context of environmental epidemiology, predicting that increased exposure to toxicants could result in greater risk of epidemics within ecological systems. We predict that reducing sublethal toxicant exposure below our predicted safe threshold could contribute to controlling population level disease and infection.     

Control of emerging infectious diseases using responsive imperfect vaccination and isolation

This paper is concerned with a stochastic model for the spread of an SEIR (susceptible --> exposed (= latent) --> infective --> removed) epidemic among a population partitioned into households, featuring different rates of infection for within and between households. The model incorporates responsive vaccination and isolation policies, based upon the appearance of diagnosed cases in households. Different models for imperfect vaccine response are considered. A threshold parameter R*, which determines whether or not a major epidemic can occur, and the probability of a major epidemic are obtained for different infectious and latent period distributions. Simpler expressions for these quantities are obtained in the limiting case of infinite within-household infection rate. Numerical studies suggest that the choice of infectious period distribution and whether or not latent individuals are vaccine-sensitive have a material influence on the spread of the epidemic, while, for given vaccine efficacy, the choice of vaccine action model is less influential. They also suggest that an effective isolation policy has a more significant impact than vaccination. The results show that R* alone is not sufficient to summarise the potential for an epidemic.