A semi-stochastic model for Salmonella infection in a multi-group herd

A multi-group semi-stochastic model is formulated to identify possible causes of why different strains of Salmonella develop so much variation in their infection dynamics in UK dairy herds. The model includes demography (managed populations) and various types of transmission: direct, pseudovertical and indirect (via free-living infectious units in the environment). The effects of herd size and epidemiological parameters on mean prevalence of infection and mean time until fade out are investigated. Numerical simulation shows that higher pathogen-induced mortality, shorter infectious period, more persistent immune response and more rapid removal of faeces result in a lower mean prevalence of infection, a shorter mean time until fade out, and a greater probability of fade out of infection within 600 days. Combining these results and those for the deterministic counterpart could explain differences in observed epidemiological patterns and help to identify the factors inducing the decline in reported cases of epidemic strains such as DT104 in cattle. We further investigate the effect of group structure on the probability of a major outbreak by using the stochastic threshold theory in homogeneous populations and that in heterogeneous populations. Numerical studies suggest that group structure makes major outbreaks less likely than would be the case in a homogeneous population with the same basic reproduction number. Moreover, some control strategies are suggested by investigating the effect of epidemiological parameters on the probability of an epidemic.     

Pair approximations and the inclusion of indirect transmission: theory and application to between farm transmission of Salmonella

The spatial-temporal dynamics of farm animal diseases depend both on disease specific processes and the underlying contact network between farms. Indirect transmission via free-living bacteria in the environment is an important transmission route and contributes significantly to the dynamics. The pair-wise model has been developed to include both direct transmission and indirect transmission via free stages. The model is compared with stochastic simulations of epidemics on contact networks. The network framework is applied to the investigation of the epidemiological dynamics of between-herd transmission of Salmonella spp. The main results help to explain differences in observed epidemiological patterns and to identify possible causes for different strains of Salmonella developing so much variation in their infection dynamics in UK dairy herds. Numerical results show that shorter infectious period, more persistent immune response and more rapid removal of faeces result in a lower prevalence of infection and a greater tendency for (damped) oscillation. A possible control strategy is consequently suggested. Furthermore, the effect of network structure on long-term dynamics is examined.     

Stochastic disease dynamics of a hospital infection model

A stochastic model for hospital infection incorporating both direct transmission and indirect transmission via free-living bacteria in the environment is investigated. We examine the long term behavior of the model by calculating a stationary distribution and normal approximation of the distribution. The quasi-stationary distribution of the model is studied to investigate the models’ behavior before extinction and the time to extinction. Numerical results show agreement between the calculated distributions and results of event-driven simulations. Hand hygiene of volunteers is more effective in terms of reducing the mean (or standard deviation) of the stationary distribution of colonized patients and the expected time to extinction compared to hand hygiene of health care workers (HCWs), on the basis of our parameter values. However, the indirect (or direct) transmission rate can lead to either increase or decrease in the standard deviation of the stationary distribution, but the impact of the indirect transmission is much greater than that of the direct transmission. The findings suggest that isolation of new admitted colonized patients is most effective in reducing both the mean and standard deviation of the stationary distribution and measures related to indirect transmission are secondary in their effects compared to other interventions.     

Transmission shifts underlie variability in population responses to Yersinia pestis infection

Host populations for the plague bacterium, Yersinia pestis, are highly variable in their response to plague ranging from near deterministic extinction (i.e., epizootic dynamics) to a low probability of extinction despite persistent infection (i.e., enzootic dynamics). Much of the work to understand this variability has focused on specific host characteristics, such as population size and resistance, and their role in determining plague dynamics. Here, however, we advance the idea that the relative importance of alternative transmission routes may vary causing shifts from epizootic to enzootic dynamics. We present a model that incorporates host and flea ecology with multiple transmission hypotheses to study how transmission shifts determine population responses to plague. Our results suggest enzootic persistence relies on infection of an off-host flea reservoir and epizootics rely on transiently maintained flea infection loads through repeated infectious feeds by fleas. In either case, early-phase transmission by fleas (i.e., transmission immediately following an infected blood meal) has been observed in laboratory studies, and we show that it is capable of driving plague dynamics at the population level. Sensitivity analysis of model parameters revealed that host characteristics (e.g., population size and resistance) vary in importance depending on transmission dynamics, suggesting that host ecology may scale differently through different transmission routes enabling prediction of population responses in a more robust way than using either host characteristics or transmission shifts alone.     

Toxoplasma gondii, Source to Sea: Higher Contribution of Domestic Felids to Terrestrial Parasite Loading Despite Lower Infection Prevalence

Environmental transmission of Toxoplasma gondii, a global zoonotic parasite, adversely impacts human and animal health. Toxoplasma is a significant cause of mortality in threatened Southern sea otters, which serve as sentinels for disease threats to people and animals in coastal environments. As wild and domestic felids are the only recognized hosts capable of shedding Toxoplasma oocysts into the environment, otter infection suggests land-to-sea pathogen transmission. To assess relative contributions to terrestrial parasite loading, we evaluated infection and shedding among managed and unmanaged feral domestic cats, mountain lions, and bobcats in coastal California, USA. Infection prevalence differed among sympatric felids, with a significantly lower prevalence for managed feral cats (17%) than mountain lions, bobcats, or unmanaged feral cats subsisting on wild prey (73–81%). A geographic hotspot of infection in felids was identified near Monterey Bay, bordering a high-risk site for otter infection. Increased odds of oocyst shedding were detected in bobcats and unmanaged feral cats. Due to their large populations, pet and feral domestic cats likely contribute more oocysts to lands bordering the sea otter range than native wild felids. Continued coastal development may influence felid numbers and distribution, increase terrestrial pathogens in freshwater runoff, and alter disease dynamics at the human–animal–environment interface.     

Effects of tick population dynamics and host densities on the persistence of tick-borne infections

The transmission and the persistence of tick-borne infections are strongly influenced by the densities and the structure of host populations. By extending previous models and analysis, in this paper we analyse how the persistence of ticks and pathogens, is affected by the dynamics of tick populations, and by their host densities. The effect of host densities on infection persistence is explored through the analysis and simulation of a series of models that include different assumptions on tick-host dynamics and consider different routes of infection transmission. Ticks are assumed to feed on two types of host species which vary in their reservoir competence. Too low densities of competent hosts (i.e., hosts where transmission can occur) do not sustain the infection cycle, while too high densities of incompetent hosts may dilute the competent hosts so much to make infection persistence impossible. A dilution effect may occur also for competent hosts as a consequence of reduced tick to host ratio; this is possible only if the regulation of tick populations is such that tick density does not increase linearly with host densities.     

Population viability analysis of the butterfly Lopinga achine in a changing landscape in Sweden

Metapopulation theory has generally focused only on the stochastic turn-over rate among populations and assumed that the number and location of suitable habitat patches will remain constant through time. This study combines in a PVA both the deterministic landscape dynamics and the stochastic colonisations and extinctions of populations for the butterfly Lopinga achine in Sweden. With data on occupancy pattern and the rate of habitat change, we built a simulation model and examined five different scenarios with different assumptions of landscape changes for L. achine . If no landscape changes would be expected, around 80 populations are predicted to persist during the next 100 yr. Adding the knowledge that many of the sites are unmanaged and that the host plant will slowly deteriorate as canopies close over, and adding environmental variation and synchrony, showed that the number of populations will decrease to around of 4.3 and 2.8 respectively, with an extinction risk of 34% – quite different from the first scenario based only on the metapopulation model. This study has shown the importance of incorporating both deterministic and stochastic events when making a reliable population viability analysis. Even though one can not expect that the long-term predictions of either occupied patches or extinction risks will be accurate quantitatively, the qualitative implications are correct. The extinction risk will be high if grazing is not applied to more patches than is the case today. The simulations indicate that an absolute minimum of 10–30 top-ranked patches needs to be managed for the persistence of the metapopulation of L. achine in the long term. The same problem of abandoned and overgrowing habitats affects many other threatened species in the European landscape and a similar approach could also be applied to them.     

Horizontal and vertical transmission of viruses in the honey bee, Apis mellifera

The most crucial stage in the dynamics of virus infections is the mode of virus transmission. In general, transmission of viruses can occur through two pathways: horizontal and vertical transmission. In horizontal transmission, viruses are transmitted among individuals of the same generation, while vertical transmission occurs from mothers to their offspring. Because of its highly organized social structure and crowded population density, the honey bee colony represents a risky environment for the spread of disease infection. Like other plant and animal viruses, bee viruses use different survival strategies, including utilization of both horizontal and vertical routes, to transmit and maintain levels in a host population. In this review, we explore the current knowledge about the honey bee viruses and transmission routes of bee viruses. In addition, different transmission strategies on the persistence and dynamics of host-pathogen interactions are also discussed.     

Modeling routes of chronic wasting disease transmission: environmental prion persistence promotes deer population decline and extinction

Chronic wasting disease (CWD) is a fatal disease of deer, elk, and moose transmitted through direct, animal-to-animal contact, and indirectly, via environmental contamination. Considerable attention has been paid to modeling direct transmission, but despite the fact that CWD prions can remain infectious in the environment for years, relatively little information exists about the potential effects of indirect transmission on CWD dynamics. In the present study, we use simulation models to demonstrate how indirect transmission and the duration of environmental prion persistence may affect epidemics of CWD and populations of North American deer. Existing data from Colorado, Wyoming, and Wisconsin's CWD epidemics were used to define plausible short-term outcomes and associated parameter spaces. Resulting long-term outcomes range from relatively low disease prevalence and limited host-population decline to host-population collapse and extinction. Our models suggest that disease prevalence and the severity of population decline is driven by the duration that prions remain infectious in the environment. Despite relatively low epidemic growth rates, the basic reproductive number, R(0), may be much larger than expected under the direct-transmission paradigm because the infectious period can vastly exceed the host's life span. High prion persistence is expected to lead to an increasing environmental pool of prions during the early phases (i.e. approximately during the first 50 years) of the epidemic. As a consequence, over this period of time, disease dynamics will become more heavily influenced by indirect transmission, which may explain some of the observed regional differences in age and sex-specific disease patterns. This suggests management interventions, such as culling or vaccination, will become increasingly less effective as CWD epidemics progress.     

Transmission dynamics of the amphibian ranavirus Ambystoma tigrinum virus

Transmission is central to pathogen fitness and strongly influences the impact of pathogens on host populations. Particularly important to transmission dynamics is the distinction between direct transmission requiring close physical contact (e.g. bumping, fighting, or coughing) and indirect transmission from environmental sources such as contaminated substrates. We present data from 4 experiments addressing the form, routes, and timing of transmission of Ambystoma tigrinum virus (ATV) among tiger salamanders Ambystoma tigrinum nebulosum. Our data suggest that ATV is efficiently transmitted by direct interactions between live animals (bumping, biting and cannibalism) as well as by necrophagy and indirectly via water and fomites. Determining which form of transmission is most important in nature is essential for understanding transmission at the population level. Our experiments also revealed an important temporal aspect of infectiousness: larval salamanders become infectious soon after exposure to ATV and their propensity to infect others increases with time. These results begin to clarify the mechanisms and dynamics of ATV transmission and lead to key questions that need to be addressed in future research.     

On the evolutionary dynamics of pathogens with direct and environmental transmission

A number of ecologically and economically important pathogens exhibit a complex transmission dynamics that involves distinct transmission modes. In this paper, we study the evolutionary dynamics of pathogens for which transmission includes direct host-to-host as well as indirect environmental transmission. Different routes of infection spread require specific adaptations of the parasite, which may result in conflicting selection pressures. Using the framework of Adaptive dynamics, we investigate how these conflicting selection pressures are resolved in the course of evolution and determine the conditions for evolutionary diversification of pathogen strains. We show that evolutionary branching and subsequent evolution of specialist strains occurs in wide parameter regions but evolutionary bistability and evolution of generalist pathogens are possible as well. Our analysis reveals that the relative contributions of direct and environmental transmission, as well as the underlying ecological dynamics, play a crucial role in shaping the course of pathogen evolution. Our findings may explain the coexistence of high and low virulence strains observed in several pathogenic organisms using different transmission modes (e.g., influenza viruses) and highlight the importance of considering ecological dynamics in virulence management.     

Stochastic simulations of a multi-group compartmental model for Johne's disease on US dairy herds with test-based culling intervention

Infection elimination may be an important goal of control programs. Only in stochastic infection models can true infection elimination be observed as a fadeout. The phenomena of fadeout and variable prevalence are important in understanding the transmission dynamics of infectious diseases and these phenomena are essential to evaluate the effectiveness of control measures. To investigate the stochastic dynamics of Mycobacterium avium subsp. paratuberculosis (MAP) infection on US dairy herds with test-based culling intervention, we developed a multi-group stochastic compartmental model (a continuous time Markov chain model) with both horizontal and vertical transmission. The stochastic model predicted fadeout and within-herd prevalence to have a large variance. Although test-based culling intervention generally decreased prevalence over time, it took longer than desired by producers to eliminate the endemic MAP infection from a herd. Uncertainty analysis showed that, using annual culture test and culling of only high shedders or culling of both low and high shedders with a 12-month delay in culling of low shedders, MAP infection persisted in many herds beyond 20 years. While using semi-annual culture test and culling of low and high shedders with a 6-month delay in culling of low shedders, MAP infection in many herds would be extinct within 20 years. Sensitivity analysis of the cumulative density function of fadeout suggested that combining test-based culling intervention and reduction of transmission rates through improved management between susceptible calves and shedding animals may be more effective than either alone in eliminating endemic MAP infection. We also discussed the effects of other factors such as herd size, heifer replacement, and adult cow infection on the probability of fadeout.     

Persistence of Pathogens with Short Infectious Periods in Seasonal Tick Populations: The Relative Importance of Three Transmission Routes

Background

The flaviviruses causing tick-borne encephalitis (TBE) persist at low but consistent levels in tick populations, despite short infectious periods in their mammalian hosts and transmission periods constrained by distinctly seasonal tick life cycles. In addition to systemic and vertical transmission, cofeeding transmission has been proposed as an important route for the persistence of TBE-causing viruses. Because cofeeding transmission requires ticks to feed simultaneously, the timing of tick activity may be critical to pathogen persistence. Existing models of tick-borne diseases do not incorporate all transmission routes and tick seasonality. Our aim is to evaluate the influence of seasonality on the relative importance of different transmission routes by using a comprehensive mathematical model.

Methodology/Principal Findings

We developed a stage-structured population model that includes tick seasonality and evaluated the relative importance of the transmission routes for pathogens with short infectious periods, in particular Powassan virus (POWV) and the related “deer tick virus,” emergent encephalitis-causing flaviviruses in North America. We used the next generation matrix method to calculate the basic reproductive ratio and performed elasticity analyses. We confirmed that cofeeding transmission is critically important for such pathogens to persist in seasonal tick populations over the reasonable range of parameter values. At higher but still plausible rates of vertical transmission, our model suggests that vertical transmission can strongly enhance pathogen prevalence when it operates in combination with cofeeding transmission.

Conclusions/Significance

Our results demonstrate that the consistent prevalence of POWV observed in tick populations could be maintained by a combination of low vertical, intermediate cofeeding and high systemic transmission rates. When vertical transmission is weak, nymphal ticks support integral parts of the transmission cycle that are critical for maintaining the pathogen. We also extended the model to pathogens that cause chronic infections in hosts and found that cofeeding transmission could contribute to elevating prevalence even in these systems. Therefore, the common assumption that cofeeding transmission is not relevant in models of chronic host infection, such as Lyme disease, could lead to underestimating pathogen prevalence.     

The evolution of covert,silent infection as a parasite strategy

Many parasites and pathogens cause silent/covert infections in addition to the more obvious infectious disease-causing pathology. Here, we consider how assumptions concerning superinfection, protection and seasonal host birth and transmission rates affect the evolution of such covert infections as a parasite strategy. Regardless of whether there is vertical infection or effects on sterility, overt infection is always disadvantageous in relatively constant host populations unless it provides protection from superinfection. If covert infections are protective, all individuals will enter the covert stage if there is enough vertical transmission, and revert to overt infections after a ‘latent’ period (susceptible, exposed, infected epidemiology). Seasonal variation in transmission rates selects for non-protective covert infections in relatively long-lived hosts with low birth rates typical of many mammals. Variable host population density caused by seasonal birth rates may also select for covert transmission, but in this case it is most likely in short-lived fecund hosts. The covert infections of some insects may therefore be explained by their outbreak population dynamics. However, our models consistently predict proportions of covert infection, which are lower than some of those observed in nature. Higher proportions of covert infection may occur if there is a direct link between covert infection and overt transmission success, the covert infection is protective or the covert state is the result of suppression by the host. Relatively low proportions of covert transmission may, however, be explained as a parasite strategy when transmission opportunities vary.     

Haemoplasmas in wild rodents: Routes of transmission and infection dynamics

The way that some parasites and pathogens persist in the hostile environment of their host for long periods remains to be resolved. Here, longitudinal field surveys were combined with laboratory experiments to investigate the routes of transmission and infection dynamics of such a pathogen—a wild rodent haemotropic bacterium, specifically a Mycoplasma haemomuris‐like bacterium. Fleaborne transmission, direct rodent‐to‐rodent transmission and vertical transmission from fleas or rodents to their offspring were experimentally quantified, and indications were found that the main route of bacterial transmission is direct, although its rate of successful transmission is low (~20%). The bacterium's temporal dynamics was then compared in the field to that observed under a controlled infection experiment in field‐infected and laboratory‐infected rodents, and indications were found, under all conditions, that the bacterium reached its peak infection level after 25–45 days and then decreased to low bacterial loads, which persist for the rodent's lifetime. These findings suggest that the bacterium relies on persistency with low bacterial loads for long‐term coexistence with its rodent host, having both conceptual and applied implications.     

Understanding the dynamics of Salmonella infections in dairy herds: a modelling approach

There is evidence of variation in the infection dynamics of different Salmonella serotypes in cattle--ranging from transient epidemics to long term persistence and recurrence. We seek to identify possible causes of these differences. In this study we present mathematical models which describe both managed population dynamics and epidemiology and use these to investigate the effects of demographic and epidemiological factors on epidemic behaviour and threshold for invasion. In particular, when the system is perturbed by higher culling or pathogen-induced mortality we incorporate mechanisms to constrain the lactating herd size to remain constant in the absence of pathogen or to lie within a fairly small interval in the presence of pathogen. A combination of numerical and analytical techniques is used to analyse the models. We find that the epidemiologically dominating management group can change from the dry/lactating cycle to the weaned group with increasing culling rate. Pseudovertical transmission is found to have little effect on the invasion criteria, while indirect transmission has significant influence. Pathogen-induced mortality, recovery, immune response and pathogen removal are found to be factors inducing damped oscillations; variation in these factors between Salmonella serotypes may be responsible for some of the observed differences in within herd dynamics. Specifically, higher pathogen-induced mortality, shorter infectious period, more persistent immune response and more rapid removal of faeces result in a lower number of infectives and smaller epidemics but a greater tendency for damped oscillations.     

Comparison of deterministic and stochastic SIS and SIR models in discrete time

The dynamics of deterministic and stochastic discrete-time epidemic models are analyzed and compared. The discrete-time stochastic models are Markov chains, approximations to the continuous-time models. Models of SIS and SIR type with constant population size and general force of infection are analyzed, then a more general SIS model with variable population size is analyzed. In the deterministic models, the value of the basic reproductive number R0 determines persistence or extinction of the disease. If R0 < 1, the disease is eliminated, whereas if R0 > 1, the disease persists in the population. Since all stochastic models considered in this paper have finite state spaces with at least one absorbing state, ultimate disease extinction is certain regardless of the value of R0. However, in some cases, the time until disease extinction may be very long. In these cases, if the probability distribution is conditioned on non-extinction, then when R0 > 1, there exists a quasi-stationary probability distribution whose mean agrees with deterministic endemic equilibrium. The expected duration of the epidemic is investigated numerically.     

Language dynamics in finite populations

Any mechanism of language acquisition can only learn a restricted set of grammars. The human brain contains a mechanism for language acquisition which can learn a restricted set of grammars. The theory of this restricted set is universal grammar (UG). UG has to be sufficiently specific to induce linguistic coherence in a population. This phenomenon is known as "coherence threshold". Previously, we have calculated the coherence threshold for deterministic dynamics and infinitely large populations. Here, we extend the framework to stochastic processes and finite populations. If there is selection for communicative function (selective language dynamics), then the analytic results for infinite populations are excellent approximations for finite populations; as expected, finite populations need a slightly higher accuracy of language acquisition to maintain coherence. If there is no selection for communicative function (neutral language dynamics), then linguistic coherence is only possible for finite populations.