Impact of the Infection Period Distribution on the Epidemic Spread in a Metapopulation Model

Epidemic models usually rely on the assumption of exponentially distributed sojourn times in infectious states. This is sometimes an acceptable approximation, but it is generally not realistic and it may influence the epidemic dynamics as it has already been shown in one population. Here, we explore the consequences of choosing constant or gamma-distributed infectious periods in a metapopulation context. For two coupled populations, we show that the probability of generating no secondary infections is the largest for most parameter values if the infectious period follows an exponential distribution, and we identify special cases where, inversely, the infection is more prone to extinction in early phases for constant infection durations. The impact of the infection duration distribution on the epidemic dynamics of many connected populations is studied by simulation and sensitivity analysis, taking into account the potential interactions with other factors. The analysis based on the average nonextinct epidemic trajectories shows that their sensitivity to the assumption on the infectious period distribution mostly depends on , the mean infection duration and the network structure. This study shows that the effect of assuming exponential distribution for infection periods instead of more realistic distributions varies with respect to the output of interest and to other factors. Ultimately it highlights the risk of misleading recommendations based on modelling results when models including exponential infection durations are used for practical purposes.     

Improving efficiency of inference in clinical trials with external control data

Suppose we are interested in the effect of a treatment in a clinical trial. The efficiency of inference may be limited due to small sample size. However, external control data are often available from historical studies. Motivated by an application to Helicobacter pylori infection, we show how to borrow strength from such data to improve efficiency of inference in the clinical trial. Under an exchangeability assumption about the potential outcome mean, we show that the semiparametric efficiency bound for estimating the average treatment effect can be reduced by incorporating both the clinical trial data and external controls. We then derive a doubly robust and locally efficient estimator. The improvement in efficiency is prominent especially when the external control data set has a large sample size and small variability. Our method allows for a relaxed overlap assumption, and we illustrate with the case where the clinical trial only contains a treated group. We also develop doubly robust and locally efficient approaches that extrapolate the causal effect in the clinical trial to the external population and the overall population. Our results also offer a meaningful implication for trial design and data collection. We evaluate the finite-sample performance of the proposed estimators via simulation. In the Helicobacter pylori infection application, our approach shows that the combination treatment has potential efficacy advantages over the triple therapy.     

The Distribution of Ocular Chlamydia Prevalence across Tanzanian Communities Where Trachoma Is Declining

BackgroundMathematical models predict an exponential distribution of infection prevalence across communities where a disease is disappearing. Trachoma control programs offer an opportunity to test this hypothesis, as the World Health Organization has targeted trachoma for elimination as a public health concern by the year 2020. Local programs may benefit if a single survey could reveal whether infection was headed towards elimination. Using data from a previously-published 2009 survey, we test the hypothesis that Chlamydia trachomatis prevalence across 75 Tanzanian communities where trachoma had been documented to be disappearing is exponentially distributed.Methods/FindingsWe fit multiple continuous distributions to the Tanzanian data and found the exponential gave the best approximation. Model selection by Akaike Information Criteria (AIC_c) suggested the exponential distribution had the most parsimonious fit to the data. Those distributions which do not include the exponential as a special or limiting case had much lower likelihoods of fitting the observed data. 95% confidence intervals for shape parameter estimates of those distributions which do include the exponential as a special or limiting case were consistent with the exponential. Lastly, goodness-of-fit testing was unable to reject the hypothesis that the prevalence data came from an exponential distribution.ConclusionsModels correctly predict that infection prevalence across communities where a disease is disappearing is best described by an exponential distribution. In Tanzanian communities where local control efforts had reduced the clinical signs of trachoma by 80% over 10 years, an exponential distribution gave the best fit to prevalence data. An exponential distribution has a relatively heavy tail, thus occasional high-prevalence communities are to be expected even when infection is disappearing. A single cross-sectional survey may be able to reveal whether elimination efforts are on-track.     

Operon dynamics with state dependent transcription and/or translation delays

This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a susceptible individual is proportional to the number of infected individuals in a disc around it. The main focus of the paper is a model where points are also subject to some random motion. Conservation equations for moment measures are leveraged to analyze the stationary regime of the point processes of infected and susceptible individuals. A heuristic factorization of the third moment measure is then proposed to obtain simple polynomial equations allowing one to derive closed form approximations for the fraction of infected individuals in the steady state. These polynomial equations also lead to a phase diagram which tentatively delineates the regions of the space of parameters (population density, infection radius, infection and recovery rate, and motion rate) where the epidemic survives and those where there is extinction. A key take-away from this phase diagram is that the extinction of the epidemic is not always aided by a decrease in the motion rate. These results are substantiated by simulations on large two dimensional tori. These simulations show that the polynomial equations accurately predict the fraction of infected individuals when the epidemic survives. The simulations also show that the proposed phase diagram accurately predicts the parameter regions where the mean survival time of the epidemic increases (resp. decreases) with motion rate.

     

Effects of deterministic and random refuge in a prey-predator model with parasite infection

Most natural ecosystem populations suffer from various infectious diseases and the resulting host-pathogen dynamics is dependent on host's characteristics. On the other hand, empirical evidences show that for most host pathogen systems, a part of the host population always forms a refuge. To study the role of refuge on the host-pathogen interaction, we study a predator-prey-pathogen model where the susceptible and the infected prey can undergo refugia of constant size to evade predator attack. The stability aspects of the model system is investigated from a local and global perspective. The study reveals that the refuge sizes for the susceptible and the infected prey are the key parameters that control possible predator extinction as well as species co-existence. Next we perform a global study of the model system using Lyapunov functions and show the existence of a global attractor. Finally we perform a stochastic extension of the basic model to study the phenomenon of random refuge arising from various intrinsic, habitat-related and environmental factors. The stochastic model is analyzed for exponential mean square stability. Numerical study of the stochastic model shows that increasing the refuge rates has a stabilizing effect on the stochastic dynamics.     

Extinction and fixation times with dominance and inbreeding

The effect of partial inbreeding on extinction and fixation times of a selected allele with partial dominance is studied using a diffusion model. Asymptotic approximations are obtained for large populations and the accuracy of the approximations was found to increase with inbreeding level. They show that inbreeding reduces extinction and fixation times compared to random mating at least by a factor 1+F, where F is Wright’s fixation index. The reduction of extinction and fixation times due to inbreeding is stronger for strong selection and if alleles are either highly recessive or highly dominant. This bears implications for the effect of inbreeding on the signature of selective sweeps. These findings extend previous results obtained for random mating populations and help clarifying previous simulation and numerical results on the effect of inbreeding on the dynamics of selected alleles.     

Endogenous IFN-gamma is required for resistance to acute Trypanosoma cruzi infection in mice

In order to study the role of endogenous IFN-gamma in Trypanosoma cruzi infection in mice, a potent murine IFN-gamma-specific mAb was injected i.p. on days -1, 7, and 14, relative to infection. Irrespective of the parasite inocula (100 or 25,000), groups of antibody-treated mice had significantly greater cumulative mortality rates than did appropriate controls. In antibody-treated mice, mean survival times were also significantly shorter, and maximum mean parasitemia levels were significantly higher, than in controls. Moreover, the number of amastigote nests in tissues was higher than in control mice and attained a maximum at the same time as parasitemia. As evident from kinetic studies of neutralizing activity, injected mAb were rapidly consumed in infected, but not in noninfected, mice, which is suggestive of massive IFN-gamma production during the early parasitemic phase of the disease. Nevertheless, IFN-gamma remained undetectable in the sera of infected but untreated mice. Unexpectedly, however, a peak of IFN-like antiviral activity, characterizable as a mixture of IFN-gamma and IFN-beta, appeared in mAb-treated mice that survived to infection at a time when neutralizing activity of injected mAb had drastically decreased in the circulation. We hypothesize that this high level of artificially induced endogenous IFN-gamma, not neutralized by the amounts of injected mAb, was due to the more intense parasite multiplication occurring in mAb-treated mice, which in turn may have induced an increased amount of various cytokines. TNF-alpha was not found in the serum of our mice. The humoral immune response entered its exponential phase at a time point later than that when protection by endogenous IFN-gamma was evident. Treatment with IFN-gamma-specific antibody, as applied in our study, failed to affect the level of different Ig isotypes or of T. cruzi-specific antibodies. Our study clearly indicates that IFN-gamma is produced early in acute T. cruzi infection and exerts a protective effect that is probably independent from the humoral immune response.     

Reinfection induced disease in a spatial SIRI model

Spatial models are widely used in epidemiology to investigate persistence and extinction of disease as well as their spatial patterns. One of the most important issues in studying epidemic models is the role of infection on the persistence and extinction of the disease. In this paper, we investigate a spatial susceptible–infected–recovered–infected model using cellular automata. We show that, in the regime where disease disappears in the susceptible–infected–recovered–susceptible model, spiral and target waves will emerge in the two-dimensional space due to the reinfection. The obtained results may point out that reinfection has great influence on the epidemic spreading, which enriches the findings of spatiotemporal dynamics in epidemic models.     

On the interpretation and application of mean times to extinction

As a metric of population viability, conservation biologists routinely predict the mean time to extinction (MTE). Interpretation of MTE depends on the underlying distribution of times to extinction (DTE). Despite claims to the contrary, all information regarding extinction risk can be obtained from this single statistic, the MTE, provided the DTE is exponential. We discuss the proper interpretation of MTE and illustrate how to calculate any population viability statistic when only the MTE is known and the DTE is assumed to be exponential. We also discuss the restrictive assumptions underlying the exponential DTE and the conditions under which alternative models for the DTE are preferable to the conventional (exponential) model. Despite superficial similarities between the exponential and alternative DTEs, several key differences can lead to substantially different interpretations of the MTE.     

Climate‐driven extinctions shape the phylogenetic structure of temperate tree floras

When taxa go extinct, unique evolutionary history is lost. If extinction is selective, and the intrinsic vulnerabilities of taxa show phylogenetic signal, more evolutionary history may be lost than expected under random extinction. Under what conditions this occurs is insufficiently known. We show that late Cenozoic climate change induced phylogenetically selective regional extinction of northern temperate trees because of phylogenetic signal in cold tolerance, leading to significantly and substantially larger than random losses of phylogenetic diversity (PD). The surviving floras in regions that experienced stronger extinction are phylogenetically more clustered, indicating that non‐random losses of PD are of increasing concern with increasing extinction severity. Using simulations, we show that a simple threshold model of survival given a physiological trait with phylogenetic signal reproduces our findings. Our results send a strong warning that we may expect future assemblages to be phylogenetically and possibly functionally depauperate if anthropogenic climate change affects taxa similarly.     

Testing a key assumption of host‐pathogen theory: density and disease transmission

Conventional disease theory suggests that extinction with density‐dependent transmission is unlikely as the threshold host density (KT) is greater than zero. Extinction may result if transmission is frequency dependent or the pathogen has an environmental reservoir. Given the importance of understanding how pathogens affect species richness and diversity there are few empirical tests of these conclusions. We used an Ambystoma tigrinum–Ambystoma tigrinum virus (ATV) model system in the laboratory to examine disease transmission dynamics. Susceptible A. tigrinum larvae were exposed to three different densities and proportions of infected larvae for 24 h. We then housed susceptible hosts individually for 28 days and monitored them for infection. The density of infected hosts to which susceptible hosts were exposed was the best predictor of infection (p=0.037). There was no effect of host clutch on the probability of becoming infected (p=0.67). Larvae in the highest density treatments died sooner than larvae in lower density treatments (p<0.001). Asymptomatic but infected hosts shed sufficient virus into the water in a 24‐h period to infect susceptible hosts without any direct contact between individuals. ATV transmission was best described by a power function, leading to the prediction that extinction of A. tigrinum as a result of this pathogen is unlikely. Indeed, field observations show that larval salamander populations that experience ATV‐driven epidemics may decrease, but not to extinction, and then recover. Disease is proposed as a possible explanation for the global decline of amphibians. Ranaviruses infect many amphibian populations, but based on our results may not be a general cause of declines to extinction. In contrast, frequency dependent transmission, environmental reservoirs and alternative hosts may be the most likely explanation for the enigmatic decline, at times to extinction, of some amphibian populations as a result of emerging infectious diseases, like the chytrid fungus Batrachochytrium dendrobatidis.     

A ratio-dependent food chain model and its applications to biological control

While biological controls have been successfully and frequently implemented by nature and human, plausible mathematical models are yet to be found to explain the often observed deterministic extinctions of both pest and control agent in such processes. In this paper we study a three trophic level food chain model with ratio-dependent Michaelis-Menten type functional responses. We shall show that this model is rich in boundary dynamics and is capable of generating such extinction dynamics. Two trophic level Michaelis-Menten type ratio-dependent predator-prey system was globally and systematically analyzed in details recently. A distinct and realistic feature of ratio-dependence is its capability of producing the extinction of prey species, and hence the collapse of the system. Another distinctive feature of this model is that its dynamical outcomes may depend on initial populations levels. Theses features, if preserved in a three trophic food chain model, make it appealing for modelling certain biological control processes (where prey is a plant species, middle predator as a pest, and top predator as a biological control agent) where the simultaneous extinctions of pest and control agent is the hallmark of their successes and are usually dependent on the amount of control agent. Our results indicate that this extinction dynamics and sensitivity to initial population levels are not only preserved, but also enriched in the three trophic level food chain model. Specifically, we provide partial answers to questions such as: under what scenarios a potential biological control may be successful, and when it may fail. We also study the questions such as what conditions ensure the coexistence of all the three species in the forms of a stable steady state and limit cycle, respectively. A multiple attractor scenario is found.     

The role of infectious diseases in biological conservation

Recent increases in the magnitude and rate of environmental change, including habitat loss, climate change and overexploitation, have been directly linked to the global loss of biodiversity. Wildlife extinction rates are estimated to be 100–1000 times greater than the historical norm, and up to 50% of higher taxonomic groups are critically endangered. While many types of environmental changes threaten the survival of species all over the planet, infectious disease has rarely been cited as the primary cause of global species extinctions. There is substantial evidence, however, that diseases can greatly impact local species populations by causing temporary or permanent declines in abundance. More importantly, pathogens can interact with other driving factors, such as habitat loss, climate change, overexploitation, invasive species and environmental pollution to contribute to local and global extinctions. Regrettably, our current lack of knowledge about the diversity and abundance of pathogens in natural systems has made it difficult to establish the relative importance of disease as a significant driver of species extinction, and the context when this is most likely to occur. Here, we review the role of infectious diseases in biological conservation. We summarize existing knowledge of disease-induced extinction at global and local scales and review the ecological and evolutionary forces that may facilitate disease-mediated extinction risk. We suggest that while disease alone may currently threaten few species, pathogens may be a significant threat to already-endangered species, especially when disease interacts with other drivers. We identify control strategies that may help reduce the negative effects of disease on wildlife and discuss the most critical challenges and future directions for the study of infectious diseases in the conservation sciences.     

Inferring speciation and extinction rates under different sampling schemes

The birth-death process is widely used in phylogenetics to model speciation and extinction. Recent studies have shown that the inferred rates are sensitive to assumptions about the sampling probability of lineages. Here, we examine the effect of the method used to sample lineages. Whereas previous studies have assumed random sampling (RS), we consider two extreme cases of biased sampling: "diversified sampling" (DS), where tips are selected to maximize diversity and "cluster sampling (CS)," where sample diversity is minimized. DS appears to be standard practice, for example, in analyses of higher taxa, whereas CS may occur under special circumstances, for example, in studies of geographically defined floras or faunas. Using both simulations and analyses of empirical data, we show that inferred rates may be heavily biased if the sampling strategy is not modeled correctly. In particular, when a diversified sample is treated as if it were a random or complete sample, the extinction rate is severely underestimated, often close to 0. Such dramatic errors may lead to serious consequences, for example, if estimated rates are used in assessing the vulnerability of threatened species to extinction. Using Bayesian model testing across 18 empirical data sets, we show that DS is commonly a better fit to the data than complete, random, or cluster sampling (CS). Inappropriate modeling of the sampling method may at least partly explain anomalous results that have previously been attributed to variation over time in birth and death rates.     

Wildlife disease elimination and density dependence

Disease control by managers is a crucial response to emerging wildlife epidemics, yet the means of control may be limited by the method of disease transmission. In particular, it is widely held that population reduction, while effective for controlling diseases that are subject to density-dependent (DD) transmission, is ineffective for controlling diseases that are subject to frequency-dependent (FD) transmission. We investigate control for horizontally transmitted diseases with FD transmission where the control is via culling or harvest that is non-selective with respect to infection and the population can compensate through DD recruitment or survival. Using a mathematical model, we show that culling or harvesting can eradicate the disease, even when transmission dynamics are FD. Eradication can be achieved under FD transmission when DD birth or recruitment induces compensatory growth of new, healthy individuals, which has the net effect of reducing disease prevalence by dilution. We also show that if harvest is used simultaneously with vaccination, and there is high enough transmission coefficient, application of both controls may be less efficient than vaccination alone. We illustrate the effects of these control approaches on disease prevalence for chronic wasting disease in deer where the disease is transmitted directly among deer and through the environment.     

Optimal link removal for epidemic mitigation: a two-way partitioning approach

The structure of the contact network through which a disease spreads may influence the optimal use of resources for epidemic control. In this work, we explore how to minimize the spread of infection via quarantining with limited resources. In particular, we examine which links should be removed from the contact network, given a constraint on the number of removable links, such that the number of nodes which are no longer at risk for infection is maximized. We show how this problem can be posed as a non-convex quadratically constrained quadratic program (QCQP), and we use this formulation to derive a link removal algorithm. The performance of our QCQP-based algorithm is validated on small Erd?s–Renyi and small-world random graphs, and then tested on larger, more realistic networks, including a real-world network of injection drug use. We show that our approach achieves near optimal performance and out-performs other intuitive link removal algorithms, such as removing links in order of edge centrality.     

Phylogenetically clustered extinction risks do not substantially prune the Tree of Life

Anthropogenic activities have increased the rate of biological extinction many-fold. Recent empirical studies suggest that projected extinction may lead to extensive loss to the Tree of Life, much more than if extinction were random. One suggested cause is that extinction risk is heritable (phylogenetically patterned), such that entire higher groups will be lost. We show here with simulation that phylogenetically clustered extinction risks are necessary but not sufficient for the extensive loss of phylogenetic diversity (PD) compared to random extinction. We simulated Yule trees and evolved extinction risks at various levels of heritability (measured using Pagel's λ). At most levels of heritability (λ in range of 0 to 10), mean values of extinction risk (range 0.25 to 0.75), tree sizes (64 to 128 tips), tree balance and temporal heterogeneity of diversification rates (Yule and coalescent trees), extinction risks do not substantially increase the loss of PD in these trees when compared to random extinction. The maximum loss of PD (20% above random) was only associated with the combination of extremely excessive values of phylogenetic signal, high mean species' extinction probabilities, and extreme (coalescent) tree shapes. Interestingly, we also observed a decline in the rate of increase in the loss of PD at high phylogenetic clustering (λ → 10) of extinction risks. Our results suggest that the interplay between various aspects of tree shape and a predisposition of higher extinction risks in species-poor clades is required to explain the substantial pruning of the Tree of Life.     

A note on generation times in epidemic models

The time between the infection of a primary case and one of its secondary cases is called a generation time. The distribution (and mean) of the generation times is derived for a rather general class of epidemic models. The relation to assumptions on distributions of latency times and infectious times or more generally on random time varying infectiousness, is investigated. Serial times, defined as the times between occurrence of observable events in the progress of an infectious disease (e.g., the onset of clinical symptoms), are also considered.     

High activity and Levy searches: jellyfish can search the water column like fish

Over-fishing may lead to a decrease in fish abundance and a proliferation of jellyfish. Active movements and prey search might be thought to provide a competitive advantage for fish, but here we use data-loggers to show that the frequently occurring coastal jellyfish (Rhizostoma octopus) does not simply passively drift to encounter prey. Jellyfish (327 days of data from 25 jellyfish with depth collected every 1 min) showed very dynamic vertical movements, with their integrated vertical movement averaging 619.2 m d(-1), more than 60 times the water depth where they were tagged. The majority of movement patterns were best approximated by exponential models describing normal random walks. However, jellyfish also showed switching behaviour from exponential patterns to patterns best fitted by a truncated Lévy distribution with exponents (mean μ=1.96, range 1.2-2.9) close to the theoretical optimum for searching for sparse prey (μopt≈2.0). Complex movements in these 'simple' animals may help jellyfish to compete effectively with fish for plankton prey, which may enhance their ability to increase in dominance in perturbed ocean systems.     

Selection, subdivision and extinction and recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.