Complex Dynamical Behaviour in an Epidemic Model with Control.

We analyse the dynamical behaviour of a simple, widely used model that integrates epidemiological dynamics with disease control and economic constraint on the control resources. We consider both the deterministic model and its stochastic counterpart. Despite its simplicity, the model exhibits mathematically rich dynamics, including multiple stable fixed points and stable limit cycles arising from global bifurcations. We show that the existence of the limit cycles in the deterministic model has important consequences in modelling the range of potential effects the control can have. The stochastic effects further interact with the deterministic dynamical structure by facilitating transitions between different attractors of the system. The interaction is important for the predictive power of the model and in using the model to optimize allocation when resources for control are limited. We conclude that when studying models with constrained control, special care should be given to the dynamical behaviour of the system and its interplay with stochastic effects.This is the final version of the article. It first appeared from Elsevier via https://doi.org/10.1007/s11538-016-0217-

Applications of percolation theory to fungal spread with synergy

There is increasing interest in the use of the percolation paradigm to analyze and predict the progress of disease spreading in spatially-structured populations of animals and plants. The wider utility of the approach has been limited, however, by several restrictive assumptions, foremost of which is a strict requirement for simple nearest-neighbour transmission, in which the disease history of an individual is in uenced only by that of its neighbours. In a recent paper the percolation paradigm has been generalised to incorporate synergistic interactions in host infectivity and susceptibility and the impact of these interactions on the invasive dynamics of an epidemic has been demonstrated. In the current paper we elicit evidence that such synergistic interactions may underlie transmission dynamics in real-world systems by rst formulating a model for the spread of a ubiquitous parasitic and saprotrophic fungus through replicated populations of nutrient sites and subsequently tting and testing the model using data from experimental microcosms. Using Bayesian computational methods for model tting, we demonstrate that synergistic interactions are necessary to explain the dynamics observed in the replicate experiments. The broader implications of this work in identifying disease control strategies that de ect epidemics from invasive to non-invasive regimes are discussed

What is pathogen-mediated insect superabundance?

When increasing abundance of insect vectors is manifest across multiple fields of a crop at the landscape scale, the phenomenon is sometimes referred to as insect superabundance. The phenomenon may reflect environmental factors (i.e. environmentally mediated insect superabundance, EMiS), including climatic change. A number of pathogens, however, are also known to modify the quality of infected plants as a resource for their insect vectors. In this paper, we term increasing vector abundance when associated with pathogen modification of plants as pathogen-mediated insect superabundance (henceforth PMiS). We investigate PMiS using a new epidemiological framework. We formalize a definition of PMiS and indicate the epidemiological mechanism by which it is most likely to arise. This study is motivated by the occurrence of a particularly destructive cassava virus epidemic that has been associated with superabundant whitefly populations in sub-Saharan Africa. Our results have implications for how PMiS can be distinguished from EMiS in field data. Above all, they represent a timely foundation for further investigations into the association between insect superabundance and plant pathogens.Bill and Melinda Gates Foundatio

Resource Allocation for Epidemic Control in Metapopulations

Deployment of limited resources is an issue of major importance for decision-making in crisis events. This is especially true for large-scale outbreaks of infectious diseases. Little is known when it comes to identifying the most efficient way of deploying scarce resources for control when disease outbreaks occur in different but interconnected regions. The policy maker is frequently faced with the challenge of optimizing efficiency (e.g. minimizing the burden of infection) while accounting for social equity (e.g. equal opportunity for infected individuals to access treatment). For a large range of diseases described by a simple SIRS model, we consider strategies that should be used to minimize the discounted number of infected individuals during the course of an epidemic. We show that when faced with the dilemma of choosing between socially equitable and purely efficient strategies, the choice of the control strategy should be informed by key measurable epidemiological factors such as the basic reproductive number and the efficiency of the treatment measure. Our model provides new insights for policy makers in the optimal deployment of limited resources for control in the event of epidemic outbreaks at the landscape scale

Pathogenic modification of plants enhances long-distance dispersal of non-persistently transmitted viruses to new hosts.

Aphids spread the majority of plant viruses through ‘non-persistent’ transmission (NPT) whereby virus particles attach transiently to these insects’ probing mouthparts. Virus acquisition from infected plants and inoculation to healthy host plants is favored when aphids briefly probe plant epidermal cells. It is well established that NPT virus infection can alter plant-vector interactions, and moreover such pathogen modifications are found in a range of plant and animal systems. In particular, viruses can make plants more attractive to aphids but inhibit aphid settling on infected plants. It is hypothesized that this viral ‘reprogramming’ of plants promotes virus acquisition and encourages dispersal of virus-bearing aphids to fresh hosts. In contrast, it is hypothesized that virus-induced biochemical changes encouraging prolonged feeding on infected hosts inhibit NPT. To understand how these virus-induced modifications affect epidemics, we developed a modeling framework accounting for important but often neglected factors, including: feeding behaviors (probing or prolonged feeding) and distinct spatial scales of transmission (as conditioned by wingless or winged aphids). Analysis of our models confirmed that when viruses inhibit aphid settling on infected plants this initially promotes virus transmission. However, initially enhanced transmission is self-limiting because it decreases vector density. Another important finding is that virus-induced changes encouraging settling will stimulate birth of winged aphids, which promotes epidemics of NPT viruses over greater distances. Thus our results illustrate how plant virus modifications influence epidemics by altering vector distribution, density, and even vector form. Our insights are important for understanding how pathogens in general propagate through natural plant communities and crops

Estimating epidemiological parameters from experiments in vector access to host plants, the method of matching gradients.

Estimation of pathogenic life-history values, for instance the duration a pathogen is retained in an insect vector (i.e., retention period) is of particular importance for understanding plant disease epidemiology. How can we extract values for these epidemiological parameters from conventional small-scale laboratory experiments in which transmission success is measured in relation to durations of vector access to host plants? We provide a solution to this problem by deriving formulae for the empirical curves that these experiments produce, called access period response curves (i.e., transmission success vs access period). We do this by writing simple equations for the fundamental life-cycle components of insect vectors in the laboratory. We then infer values of epidemiological parameters by matching the theoretical and empirical gradients of access period response curves. Using the example of Cassava brown streak virus (CBSV), which has emerged in sub-Saharan Africa and now threatens regional food security, we illustrate the method of matching gradients. We show how applying the method to published data produces a new understanding of CBSV through the inference of retention period, acquisition period and inoculation period parameters. We found that CBSV is retained for a far shorter duration in its insect vector (Bemisia tabaci whitefly) than had previously been assumed. Our results shed light on a number of critical factors that may be responsible for the transition of CBSV from sub- to super-threshold R0 in sub-Saharan Africa. The method is applicable to plant pathogens in general, to supply epidemiological parameter estimates that are crucial for practical management of epidemics and prediction of pandemic risk

Detecting Presymptomatic Infection Is Necessary to Forecast Major Epidemics in the Earliest Stages of Infectious Disease Outbreaks.

We assess how presymptomatic infection affects predictability of infectious disease epidemics. We focus on whether or not a major outbreak (i.e. an epidemic that will go on to infect a large number of individuals) can be predicted reliably soon after initial cases of disease have appeared within a population. For emerging epidemics, significant time and effort is spent recording symptomatic cases. Scientific attention has often focused on improving statistical methodologies to estimate disease transmission parameters from these data. Here we show that, even if symptomatic cases are recorded perfectly, and disease spread parameters are estimated exactly, it is impossible to estimate the probability of a major outbreak without ambiguity. Our results therefore provide an upper bound on the accuracy of forecasts of major outbreaks that are constructed using data on symptomatic cases alone. Accurate prediction of whether or not an epidemic will occur requires records of symptomatic individuals to be supplemented with data concerning the true infection status of apparently uninfected individuals. To forecast likely future behavior in the earliest stages of an emerging outbreak, it is therefore vital to develop and deploy accurate diagnostic tests that can determine whether asymptomatic individuals are actually uninfected, or instead are infected but just do not yet show detectable symptoms.This is the final version of the article. It first appeared from PLOS via http://dx.doi.org/10.1371/journal.pcbi.100483

When Does Spatial Diversification Usefully Maximize the Durability of Crop Disease Resistance?

Maximizing the durability of crop disease resistance genes in the face of pathogen evolution is a major challenge in modern agricultural epidemiology. Spatial diversification in the deployment of resistance genes, where susceptible and resistant fields are more closely intermixed, is predicted to drive lower epidemic intensities over evolutionary timescales. This is due to an increase in the strength of dilution effects, caused by pathogen inoculum challenging host tissue to which it is not well-specialized. The factors that interact with and determine the magnitude of this spatial suppressive effect are not currently well understood, however, leading to uncertainty over the pathosystems where such a strategy is most likely to be cost-effective. We model the effect on landscape scale disease dynamics of spatial heterogeneity in the arrangement of fields planted with either susceptible or resistant cultivars, and the way in which this effect depends on the parameters governing the pathosystem of interest. Our multiseason semidiscrete epidemiological model tracks spatial spread of wild-type and resistance-breaking pathogen strains, and incorporates a localized reservoir of inoculum, as well as the effects of within and between field transmission. The pathogen dispersal characteristics, any fitness cost(s) of the resistance-breaking trait, the efficacy of host resistance, and the length of the timeframe of interest all influence the strength of the spatial diversification effect. A key result is that spatial diversification has the strongest beneficial effect at intermediate fitness costs of the resistance-breaking trait, an effect driven by a complex set of nonlinear interactions. On the other hand, however, if the resistance-breaking strain is not fit enough to invade the landscape, then a partially effective resistance gene can result in spatial diversification actually worsening the epidemic. These results allow us to make general predictions of the types of system for which spatial diversification is most likely to be cost-effective, paving the way for potential economic modeling and pathosystem specific evaluation. These results highlight the importance of studying the effect of genetics on landscape scale spatial dynamics within host-pathogen disease systems.[Formula: see text] Copyright © 2020 The Author(s). This is an open access article distributed under the CC BY 4.0 International license

Prominent effect of soil network heterogeneity on microbial invasion

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil