Joanne Turner

A clarification of transmission terms in host-microparasite models: numbers, densities and areas.

Transmission is the driving force in the dynamics of any infectious disease. A crucial element in understanding disease dynamics, therefore, is the transmission term describing the rate at which susceptible hosts are converted into infected hosts by their contact with infectious material. Recently, the conventional form of this term has been increasingly questioned, and new terminologies and conventions have been proposed. Here, therefore, we review the derivation of transmission terms, explain the basis of confusion, and provide clarification. The root of the problem has been a failure to include explicit consideration of the area occupied by a host population, alongside both the number of infectious hosts and their density within the population. We argue that the terms density-dependent transmission and frequency-dependent transmission remain valid and useful (though a fuller transmission term for the former is identified), but that the terms mass action, true mass action and pseudo mass action are all unhelpful and should be dropped. Also, contrary to what has often been assumed, the distinction between homogeneous and heterogeneous mixing in a host population is orthogonal to the distinction between density- and frequency-dependent transmission modes.

Frequency and Spatial Distribution of Environmental Campylobacter spp.

ABSTRACT Humans are exposed to Campylobacter spp. in a range of sources via both food and environmental pathways. For this study, we explored the frequency and distribution of thermophilic Campylobacter spp. in a 10- by 10-km square rural area of Cheshire, United Kingdom. The area contains approximately 70, mainly dairy, farms and is used extensively for outdoor recreational activities. Campylobacter spp. were isolated from a range of environmental samples by use of a systematic sampling grid. Livestock (mainly cattle) and wildlife feces and environmental water and soil samples were cultured, and isolates were presumptively identified by standard techniques. These isolates were further characterized by PCR. Campylobacter jejuni was the most prevalent species in all animal samples, ranging from 11% in samples from nonavian wildlife to 36% in cattle feces, and was isolated from 15% of water samples. Campylobacter coli was commonly found in water (17%) and sheep (21%) samples, but rarely in other samples. Campylobacter lari was recovered from all sample types, with the exception of sheep feces, and was found in moderate numbers in birds (7%) and water (5%). Campylobacter hyointestinalis was only recovered from cattle (7%) and birds (1%). The spatial distribution and determinants of C. jejuni in cattle feces were examined by the use of model-based spatial statistics. The distribution was consistent with very localized within-farm or within-field transmission and showed little evidence of any larger-scale spatial dependence. We concluded that there is a potentially high risk of human exposure to Campylobacter spp., particularly C. jejuni, in the environment of our study area. The prevalence and likely risk posed by C. jejuni-positive cattle feces in the environment diminished as the fecal material aged. After we took into account the age of the fecal material, the absence or presence of rain, and the presence of bird feces, there was evidence of significant variation in the prevalence of C. jejuni-positive cattle feces between grazing fields but no evidence of spatial clustering beyond this resolution. The spatial pattern of C. jejuni is therefore consistent with that for an organism that is ubiquitous in areas contaminated with cattle feces, with a short-scale variation in infection intensity that cannot be explained solely by variations in the age of the fecal material. The observed pattern is not consistent with large-scale transmission attributable to watercourses, wildlife territories, or other geographical features that transcend field and farm boundaries.

Prevalence and genetic diversity of Campylobacter spp. in environmental water samples from a 100-square-kilometer predominantly dairy farming area.

ABSTRACT Water samples were taken systematically from a 100-km2 area of mainly dairy farmland in northwestern England and examined for Campylobacter spp. Pulsed-field gel electrophoresis-restriction fragment length polymorphism (PFGE-RFLP) and flaA strain typing of Campylobacter jejuni and Campylobacter coli isolates were done. Data on the water source and the adjacent environment were recorded and examined as explanatory variables. Campylobacter spp. were isolated from 40.5% (n = 119) of the water samples tested. C. jejuni was isolated from 14.3%, C. coli was isolated from 18.5%, and Campylobacter lari was isolated from 4.2% of the samples. Campylobacter hyointestinalis was not isolated from any water source. The difference in prevalence between water types (trough, running, and standing) was significant (P = 0.001). C. jejuni was the species most commonly isolated from trough-water and running-water sources, while C. coli was the most frequently isolated from standing water (P < 0.001). No association was found between the presence of Escherichia coli and that of Campylobacter spp. The final multivariable logistic regression model for Campylobacter spp. included the following variables: water source, soil type, aspect, and amount of cattle fecal material in the environment (fecal pat count). Strain typing demonstrated a diverse population of C. jejuni and the presence of a common C. coli flaA type that was widely distributed throughout the area. Most of the isolates within the common flaA type were discriminated by PFGE-RFLP. These findings suggest a possible role for environmental water in the epidemiology of Campylobacter spp. in a farming environment.

Global risk model for vector-borne transmission of Zika virus reveals the role of El Niño 2015

Significance This study quantifies the impact of climate variability on Zika virus (ZIKV) transmission by two mosquito vectors with distinct characteristics: Aedes aegypti and Aedes albopictus. Observed climate data were used to dynamically drive a two vectors–one host R0 epidemiological model. Our modeling results indicate that temperature conditions related to the 2015 El Niño climate phenomenon were exceptionally conducive for mosquito-borne transmission of ZIKV over South America. The virus is believed to have entered the continent earlier in 2013. This finding implicates that such a large ZIKV outbreak occurred not solely because of the introduction of ZIKV in a naive population, but because the climatic conditions were optimal for mosquito-borne transmission of ZIKV over South America in 2015. Zika, a mosquito-borne viral disease that emerged in South America in 2015, was declared a Public Health Emergency of International Concern by the WHO in February of 2016. We developed a climate-driven R0 mathematical model for the transmission risk of Zika virus (ZIKV) that explicitly includes two key mosquito vector species: Aedes aegypti and Aedes albopictus. The model was parameterized and calibrated using the most up to date information from the available literature. It was then driven by observed gridded temperature and rainfall datasets for the period 1950–2015. We find that the transmission risk in South America in 2015 was the highest since 1950. This maximum is related to favoring temperature conditions that caused the simulated biting rates to be largest and mosquito mortality rates and extrinsic incubation periods to be smallest in 2015. This event followed the suspected introduction of ZIKV in Brazil in 2013. The ZIKV outbreak in Latin America has very likely been fueled by the 2015–2016 El Niño climate phenomenon affecting the region. The highest transmission risk globally is in South America and tropical countries where Ae. aegypti is abundant. Transmission risk is strongly seasonal in temperate regions where Ae. albopictus is present, with significant risk of ZIKV transmission in the southeastern states of the United States, in southern China, and to a lesser extent, over southern Europe during the boreal summer season.

A model appropriate to the transmission of a human food-borne pathogen in a multigroup managed herd.

We describe a model of microparasite transmission within a multigroup managed farming system. The model was formulated to represent transmission of Escherichia coli O157 within a typical UK dairy herd and was used to suggest possible on-farm control strategies. The model includes birth, death, maturation, the dry/lactating cycle and various types of transmission (i.e. direct, pseudovertical (representing direct faecal-oral transmission between dam and calf within the first 48 h) and indirect (via free-living infectious units in the environment)). A combination of numerical and analytical techniques was used to analyse the model. We found that pseudovertical transmission and indirect transmission via infectious units in the general environment can lead to more groups being affected, but otherwise have relatively little effect on the invasion criteria. To reduce infection within the herd, we suggest that efforts be directed at reducing the opportunity for group-specific indirect transmission-particularly within the weaned group.

Modelling pathogen transmission: the interrelationship between local and global approaches

We describe two spatial (cellular automaton) host–pathogen models with contrasting types of transmission, where the biologically realistic transmission mechanisms are based entirely on ‘local’ interactions. The two models, fixed contact area (FCA) and fixed contact number (FCN), may be viewed as local ‘equivalents’ of commonly used global density– (and frequency–) dependent models. Their outputs are compared with each other and with the patterns generated by these global terms. In the FCN model, unoccupied cells are bypassed, but in the FCA model these impede pathogen spread, extending the period of the epidemic and reducing the prevalence of infection when the pathogen persists. Crucially, generalized linear modelling reveals that the global transmission terms βSI and βSI/N are equally good at describing transmission in both the FCA and FCN models when infected individuals are homogeneously distributed and N is approximately constant, as at the quasi–equilibrium. However, when N varies, the global frequency–dependent term βSI/N is better than the density–dependent one, βSI, at describing transmission in both the FCA and FCN models. Our approach may be used more generally to compare different local contact structures and select the most appropriate global transmission term.

A network model of E. coli O157 transmission within a typical UK dairy herd: the effect of heterogeneity and clustering on the prevalence of infection.

Cattle are considered to be the main reservoir for Vero cytotoxin-producing Escherichia coli (VTEC) O157, a cause of food-poisoning (and even death) in humans. Here, the transmission of E. coli O157 within a typical UK dairy herd is modelled using a semi-stochastic network model. The model incorporates demographic as well as infection processes. Indirect transmission is modelled homogeneously, while direct transmission is modelled via a dynamic contact network. The aim was to investigate the effects of heterogeneity and clustering on the prevalence of infection within the herd and discover whether, particularly in terms of choosing an intervention strategy, it is necessary to include heterogeneity in direct contacts when modelling this sort of system. Results show that heterogeneity in direct contacts can make it more difficult for the pathogen to persist, particularly when the average number of contacts (per animal) in each group is small. They also show that the relationship between clustering and prevalence is not simple. For example, increasing the average number of contacts can increase clustering and prevalence. However, when the average number of contacts in each group is sufficiently high, higher clustering leads to lower prevalence. It would seem that clustering can aid the flow of infection under certain circumstances, but hinder it under others (probably by preventing wider dissemination). Further results show that indirect transmission (as it is modelled here) effectively removes the effect of heterogeneity in direct contacts. In terms of investigating proposed interventions, the results suggest that a network model would only be required if there was evidence to suggest that direct transmission was the major source of infection.

Modelling bluetongue virus transmission between farms using animal and vector movements

Bluetongue is a notifiable disease of ruminants which, in 2007, occurred for the first time in England. We present the first model for bluetongue that explicitly incorporates farm to farm movements of the two main hosts, as well as vector dispersal. The model also includes a seasonal vector to host ratio and dynamic restriction zones that evolve as infection is detected. Batch movements of sheep were included by modelling degree of mixing at markets. We investigate the transmission of bluetongue virus between farms in eastern England (the focus of the outbreak). Results indicate that most parameters affecting outbreak size relate to vectors and that the infection generally cannot be maintained without between-herd vector transmission. Movement restrictions are effective at reducing outbreak size, and a targeted approach would be as effective as a total movement ban. The model framework is flexible and can be adapted to other vector-borne diseases of livestock.

Inferences about the transmission of Schmallenberg virus within and between farms

In the summer of 2011 Schmallenberg virus (SBV), a Culicoides-borne orthobunyavirus, emerged in Germany and The Netherlands and subsequently spread across much of Europe. To draw inferences about the transmission of SBV we have developed two models to describe its spread within and between farms. The within-farm model was fitted to seroprevalence data for cattle and sheep farms in Belgium and The Netherlands, with parameters estimated using approximate Bayesian computation. Despite the short duration of viraemia in cattle and sheep (mean of 3–4 days) the within-farm seroprevalence can reach high levels (mean within-herd seroprevalence >80%), largely because the probability of transmission from host to vector is high (14%) and SBV is able to replicate quickly (0.03 per day-degree) and at relatively low temperatures (threshold for replication: 12.3 °C). Parameter estimates from the within-farm model were then used in a separate between-farm model to simulate the regional spread of SBV. This showed that the rapid spread of SBV at a regional level is primarily a consequence of the high probability of transmission from host to vector and the temperature requirements for virus replication. Our results, obtained for a region of the UK in a typical year with regard to animal movements, indicate that there is no need to invoke additional transmission mechanisms to explain the observed patterns of rapid spread of SBV in Europe. Moreover, the imposition of movement restrictions, even a total movement ban, has little effect on the spread of SBV at this scale.

Two-Host, Two-Vector Basic Reproduction Ratio (R0) for Bluetongue

Mathematical formulations for the basic reproduction ratio (R 0) exist for several vector-borne diseases. Generally, these are based on models of one-host, one-vector systems or two-host, one-vector systems. For many vector borne diseases, however, two or more vector species often co-occur and, therefore, there is a need for more complex formulations. Here we derive a two-host, two-vector formulation for the R 0 of bluetongue, a vector-borne infection of ruminants that can have serious economic consequences; since 1998 for example, it has led to the deaths of well over 1 million sheep in Europe alone. We illustrate our results by considering the situation in South Africa, where there are two major hosts (sheep, cattle) and two vector species with differing ecologies and competencies as vectors, for which good data exist. We investigate the effects on R 0 of differences in vector abundance, vector competence and vector host preference between vector species. Our results indicate that R 0 can be underestimated if we assume that there is only one vector transmitting the infection (when there are in fact two or more) and/or vector host preferences are overlooked (unless the preferred host is less beneficial or more abundant). The two-host, one-vector formula provides a good approximation when the level of cross-infection between vector species is very small. As this approaches the level of intraspecies infection, a combination of the two-host, one-vector R 0 for each vector species becomes a better estimate. Otherwise, particularly when the level of cross-infection is high, the two-host, two-vector formula is required for accurate estimation of R 0. Our results are equally relevant to Europe, where at least two vector species, which co-occur in parts of the south, have been implicated in the recent epizootic of bluetongue.