Modelling virus- and host-limitation in vectored plant disease epidemics

Reproduction number and sensitivity analysis of cassava mosaic disease spread for policy design

We develop a mathematical model for the dynamics of Cassava Mosaic Disease (CMD), which is driven by both planting of infected cuttings and whitefly transmission. We use the model to analyze the dynamics of a CMD outbreak and to identify the most cost-effective policy for controlling it. The model uses the reproduction number $ \mathscr{R}_0 $ as a threshold, calculated using the Next-Generation Method. A locally-asymptotically-stable disease-free equilibrium is established when $ \mathscr{R}_0 < 1 $, proved by the Routh-Hurwitz criterion. The globally-asymptotically-stable disease-free and endemic-equilibrium points are obtained using Lyapunov's method and LaSalle's invariance principle. Our results indicate that the disease-free equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 \leq 1 $, while the endemic-equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 > 1 $. Our sensitivity analysis shows that $ \mathscr{R}_0 $ is most sensitive to the density of whitefly. Numerical simulations confirmed the effectiveness of whitefly control for limiting an outbreak while minimizing costs.

The Epidemiology of Plant Virus Disease: Towards a New Synthesis

Epidemiology is the science of how disease develops in populations, with applications in human, animal and plant diseases. For plant diseases, epidemiology has developed as a quantitative science with the aims of describing, understanding and predicting epidemics, and intervening to mitigate their consequences in plant populations. Although the central focus of epidemiology is at the population level, it is often necessary to recognise the system hierarchies present by scaling down to the individual plant/cellular level and scaling up to the community/landscape level. This is particularly important for diseases caused by plant viruses, which in most cases are transmitted by arthropod vectors. This leads to range of virus-plant, virus-vector and vector-plant interactions giving a distinctive character to plant virus epidemiology (whilst recognising that some fungal, oomycete and bacterial pathogens are also vector-borne). These interactions have epidemiological, ecological and evolutionary consequences with implications for agronomic practices, pest and disease management, host resistance deployment, and the health of wild plant communities. Over the last two decades, there have been attempts to bring together these differing standpoints into a new synthesis, although this is more apparent for evolutionary and ecological approaches, perhaps reflecting the greater emphasis on shorter often annual time scales in epidemiological studies. It is argued here that incorporating an epidemiological perspective, specifically quantitative, into this developing synthesis will lead to new directions in plant virus research and disease management. This synthesis can serve to further consolidate and transform epidemiology as a key element in plant virus research.

When Viruses Play Team Sports: Mixed Infections in Plants

The pathological importance of mixed viral infections in plants might be underestimated except for a few well-characterized synergistic combinations in certain crops. Considering that the host ranges of many viruses often overlap and that most plant species can be infected by several unrelated viruses, it is not surprising to find more than one virus simultaneously in the same plant. Furthermore, dispersal of the majority of plant viruses relies on efficient transmission mechanisms mediated by vector organisms, mainly but not exclusively insects, which can contribute to the occurrence of multiple infections in the same plant. Recent work using different experimental approaches has shown that mixed viral infections can be remarkably frequent, up to the point that they could be considered the rule more than the exception. The purpose of this review is to describe the impact of multiple infections not only on the participating viruses themselves but also on their vectors and on the common host. From this standpoint, mixed infections arise as complex events that involve several cross-interacting players, and they consequently require a more general perspective than the analysis of single-virus/single-host approaches for a full understanding of their relevance.

Species interactions affect the spread of vector-borne plant pathogens independent of transmission mode

Within food webs, vectors of plant pathogens interact with individuals of other species across multiple trophic levels, including predators, competitors, and mutualists. These interactions may in turn affect vector-borne pathogens by altering vector fitness and behavior. Predators, for example, consume vectors and reduce their abundance, but often spur movement of vectors as they seek to avoid predation. However, a general framework to predict how species interactions affect vectors of plant pathogens, and the resulting spread of vector-borne pathogens, is lacking. Here we developed a mathematical model to assess whether interactions such as predation, competition, and mutualism affected the spread of vector-borne plant pathogens with nonpersistent or persistent transmission modes. We considered transmission mode because interactions affecting vector-host encounter rates were expected to most strongly affect nonpersistent pathogens that are transmitted with short feeding bouts; interactions that affect vector feeding duration were expected to most strongly affect persistent pathogens that require long feeding bouts for transmission. Our results show that interactions that affected vector behavior (feeding duration, vector-host encounter rates) substantially altered rates of spread for vector-borne plant pathogens, whereas those affecting vector fitness (births, deaths) had relatively small effects. These effects of species interactions were largely independent of transmission mode, except when interactions affected vector-host encounter rates, where effects were strongest for nonpersistent pathogens. Our results suggest that a better understanding of how vectors interact with other species within food webs could enhance our understanding of disease ecology.

Epidemics on plants: Modeling long-range dispersal on spatially embedded networks

Here we develop an epidemic model that accounts for long-range dispersal of pathogens between plants. This model generalizes the classical compartmental models-Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR)-to take into account those factors that are key to understand epidemics in real plant populations. These ingredients are the spatial characteristics of the plots and fields in which plants are embedded and the effect of long-range dispersal of pathogens. The spatial characteristics are included through the use of random rectangular graphs which allow to consider the effects of the elongation of plots and fields, while the long-range dispersal is implemented by considering transformations, such as the Mellin and Laplace transforms, of a generalization of the adjacency matrix of the geometric graph. Our results point out that long-range dispersal favors the propagation of pathogens while the elongation of plant plots increases the epidemic threshold and decreases dramatically the number of affected plants. Interestingly, our model is able of reproducing the existence of patchy regions of infected plants and the absence of a clear propagation front centered in the initial infected plants, as it is observed in real plant epidemics.

Plant Virus Epidemiology: Applications and Prospects for Mathematical Modeling and Analysis to Improve Understanding and Disease Control

In recent years, mathematical modeling has increasingly been used to complement experimental and observational studies of biological phenomena across different levels of organization. In this article, we consider the contribution of mathematical models developed using a wide range of techniques and uses to the study of plant virus disease epidemics. Our emphasis is on the extent to which models have contributed to answering biological questions and indeed raised questions related to the epidemiology and ecology of plant viruses and the diseases caused. In some cases, models have led to direct applications in disease control, but arguably their impact is better judged through their influence in guiding research direction and improving understanding across the characteristic spatiotemporal scales of plant virus epidemics. We restrict this article to plant virus diseases for reasons of length and to maintain focus even though we recognize that modeling has played a major and perhaps greater part in the epidemiology of other plant pathogen taxa, including vector-borne bacteria and phytoplasmas.

The basic reproduction number of vector-borne plant virus epidemics

The basic reproduction number R₀ is a key parameter in plant disease epidemiology, which largely determines whether or not an epidemic will occur in a plant population. The next generation matrix approach to deriving and calculating the basic reproduction number of a plant virus epidemic is described. The approach is illustrated through a series of examples of increasing complexity, ranging from the simplest case of one vector transmitting one virus to a single host, to the case of multiple vectors, to combined horizontal (vector) and vertical (seed) transmission, and where vector control using insecticides is practised. The importance of parameters representing host and vector population dynamics and their interaction in the absence of disease is stressed, and the constraints these place on the calculation of the basic reproduction number. Finally, mention is made of further elaborations to the approach that could prove useful in plant virus epidemiology.

Mathematical model of plant-virus interactions mediated by RNA interference

Cross-protection, which refers to a process whereby artificially inoculating a plant with a mild strain provides protection against a more aggressive isolate of the virus, is known to be an effective tool of disease control in plants. In this paper we derive and analyse a new mathematical model of the interactions between two competing viruses with particular account for RNA interference. Our results show that co-infection of the host can either increase or decrease the potency of individual infections depending on the levels of cross-protection or cross-enhancement between different viruses. Analytical and numerical bifurcation analyses are employed to investigate the stability of all steady states of the model in order to identify parameter regions where the system exhibits synergistic or antagonistic behaviour between viral strains, as well as different types of host recovery. We show that not only viral attributes but also the propagating component of RNA-interference in plants can play an important role in determining the dynamics.

The effect of time delay in plant--pathogen interactions with host demography

Botanical epidemic models are very important tools to study invasion, persistence and control of diseases. It is well known that limitations arise from considering constant infection rates. We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic model for plant--pathogen interactions with host demography. Sufficient conditions for the global stability of the pathogen-free equilibrium and the permanence of the system are among the results obtained through qualitative analysis. We also show that the delay can cause stability switches of the coexistence equilibrium. In the undelayed case, we prove that the onset of oscillations may occur through Hopf bifurcation.

Evolution and emergence of plant viruses

Viruses are common agents of plant infectious diseases. During last decades, worldwide agriculture production has been compromised by a series of epidemics caused by new viruses that spilled over from reservoir species or by new variants of classic viruses that show new pathogenic and epidemiological properties. Virus emergence has been generally associated with ecological change or with intensive agronomical practices. However, the complete picture is much more complex since the viral populations constantly evolve and adapt to their new hosts and vectors. This chapter puts emergence of plant viruses into the framework of evolutionary ecology, genetics, and epidemiology. We will stress that viral emergence begins with the stochastic transmission of preexisting genetic variants from the reservoir to the new host, whose fate depends on their fitness on each hosts, followed by adaptation to new hosts or vectors, and finalizes with an efficient epidemiological spread.

A life history view of mutualistic viral symbioses: quantity or quality for cooperation?

Mutualistic symbioses between viruses and their hosts do not employ a straightforward rule by viral genome characteristics, transmission mechanisms or host genotypes. In this review we propose that reproduction rates and environmental carrying capacity of hosts may play a major role in maintaining the mutualism. Depending on how host life history shifts following establishment of the symbiosis, a symbiosis can be classified as quality-selected mutualism or quantity-selected mutualism. Quality-selected mutualism is described with modified Lotka-Volterra models. Both our models and previous empirical examples support the hypothesis that quality-selected mutualism can reach stable equilibrium under certain conditions. Quantity-selected mutualism is rare and is not supported by our model. With increasing attention to mutualistic viral ecology, we will have a better understanding of how viruses drive evolution.

The impact of hepatitis A virus infection on hepatitis C virus infection: a competitive exclusion hypothesis

We address the observation that, in some cases, patients infected with the hepatitis C virus (HCV) are cleared of HCV when super-infected with the hepatitis A virus (HAV). We hypothesise that this phenomenon can be explained by the competitive exclusion principle, including the action of the immune system, and show that the inclusion of the immune system explains both the elimination of one virus and the co-existence of both infections for a certain range of parameters. We discuss the potential clinical implications of our findings.