Population dynamics of botanical epidemics involving primary and secondary infection

In this paper we study the dynamical properties of models for botanical epidemics, especially for soil-borne fungal infection. The models develop several new concepts, involving dual sources of infection, host and inoculum dynamics. Epidemics are modelled with respect to the infection status of whole plants and plant organs (the G model) or to lesion density and size (the SW model). The infection can originate in two sources, either from the initial inoculum (primary infection) or by a direct transmission between plant tissue (secondary infection). The first term corresponds to the transmission through the free-living stages of macroparasites or an external source of infection in certain medical models, whereas the second term is equivalent to direct transmission between the hosts in microparasitic infections. The models allow for dynamics of host growth and inoculum decay. We show that the two models for root and lesion dynamics can be derived as special cases of a single generic model. Analytical and numerical methods are used to analyse the behaviour of the models for static, unlimited (exponential) and asymptotically limited host growth with and without secondary infection, and with and without decay of initial inoculum. The models are shown to exhibit a range of epidemic behaviour within single seasons that extends from simple monotonic increase with saturation of the host population, through temporary plateaux as the system switches from primary to secondary infection, to effective elimination of the pathogen by the host outgrowing the fungal infection. For certain conditions, the equilibrium values are shown to depend on initial conditions. These results have important consequences for the control of plant disease. They can be applied beyond soil-borne plant pathogens to mycorrhizal fungi and aerial pathogens while the principles of primary and secondary infection with host and inoculum dynamics may be used to link classical models for both microparasitic and macroparasitic infections.     

Transient dynamics and early diagnostics in infectious disease

To date, mathematical models of the dynamics of infectious disease have consistently focused on understanding the long-term behavior of the interacting components, where the steady state solutions are paramount. However for most acute infections, the long-term behavior of the pathogen population is of little importance to the host and population health. We introduce the notion of transient pathology, where the short-term dynamics of interaction between the immune system and pathogens is the principal focus. We identify the amplifying effect of the absence of a fully operative immune system on the pathogenesis of the initial inoculum, and its implication for the acute severity of the infection. We then formalize the underlying dynamics, and derive two measures of transient pathogenicity: the peak of infection (maximum pathogenic load) and the time to peak of infection, both crucial to understanding the early dynamics of infection and its consequences for early intervention. Received: 25 January 2000 / Revised version: 30 November 2000 / Published online: 12 October 2001     

A baseline model for the co-evolution of hosts and pathogens

The basic reproduction ratio (R (0)) is the expected number of secondary cases per primary in a totally susceptible population. In a baseline model, faced with an individual host strain pathogen virulence evolves to maximise R (0) which yields monomorphism. The basic depression ratio (D (0)) is the amount by which the total population is decreased, per infected individual, due to the presence of infection. Again, in a baseline model, faced with an individual pathogen strain host resistance evolves to minimise D (0) which yields monomorphism. With this in mind we analyse the community dynamics of the interaction between R (0) and D (0) and show that multi-strain co-existence (polymorphism) is possible and we discuss the possibility of stable cycles occuring within the co-existence states. We show for co-existence, the number of host and pathogen strains present need to be identical in order to achieve stable equilibria. For polymorphic states we observe contingencies (outcome dependent on initial conditions) between both point equilibrium and sustained oscillations. Invasion criteria for host and pathogen strains are identified.     

Mixed infections and insect–pathogen interactions

Abstract Most studies of insect–pathogen interactions consider the direct interaction between one disease agent and one species of host. However, given that hosts are subject to challenge from many pathogen/parasite species, mixed infections are probably common. In this study, using the desert locust and two species of fungal entomopathogen, we show how mixed infection with a largely avirulent pathogen can alter the virulence and reproduction of a second, highly virulent pathogen. We find that two strains of the avirulent pathogen vary in their interaction with the virulent pathogen, depending on the order of infection and environmental conditions. We propose that avirulent pathogens, which have largely been overlooked to date, could play a significant role in host–pathogen dynamics, with implications for biological control and evolution of virulence.     

Vector-Borne Pathogen and Host Evolution in a Structured Immuno-Epidemiological System

Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host’s immune system influences the pathogen’s transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence–transmission trade-offs and evolution in vector-borne pathogen–host systems. Here, we consider an immuno-epidemiological model that links the within-host dynamics to between-host circulation of a vector-borne disease. On the immunological scale, the model mimics antibody-pathogen dynamics for arbovirus diseases, such as Rift Valley fever and West Nile virus. The within-host dynamics govern transmission and host mortality and recovery in an age-since-infection structured host-vector-borne pathogen epidemic model. By considering multiple pathogen strains and multiple competing host populations differing in their within-host replication rate and immune response parameters, respectively, we derive evolutionary optimization principles for both pathogen and host. Invasion analysis shows that the \({\mathcal {R}}_0\) maximization principle holds for the vector-borne pathogen. For the host, we prove that evolution favors minimizing case fatality ratio (CFR). These results are utilized to compute host and pathogen evolutionary trajectories and to determine how model parameters affect evolution outcomes. We find that increasing the vector inoculum size increases the pathogen \({\mathcal {R}}_0\), but can either increase or decrease the pathogen virulence (the host CFR), suggesting that vector inoculum size can contribute to virulence of vector-borne diseases in distinct ways.     

Effect of repeated exposure to Plasmodium relictum (lineage SGS1) on infection dynamics in domestic canaries

Parasites are known to exert strong selection pressures on their hosts and, as such, favour the evolution of defence mechanisms. The negative impact of parasites on their host can have substantial consequences in terms of population persistence and the epidemiology of the infection. In natural populations, however, it is difficult to assess the cost of infection while controlling for other potentially confounding factors. For instance, individuals are repeatedly exposed to a variety of parasite strains, some of which can elicit immunological memory, further protecting the host from subsequent infections. Cost of infection is, therefore, expected to be particularly strong for primary infections and to decrease for individuals surviving the first infectious episode that are re-exposed to the pathogen. We tested this hypothesis experimentally using avian malaria parasites (Plasmodium relictum-lineage SGS1) and domestic canaries (Serinus canaria) as a model. Hosts were infected with a controlled dose of P. relictum as a primary infection and control birds were injected with non-infected blood. The changes in haematocrit and body mass were monitored during a 20 day period. A protein of the acute phase response (haptoglobin) was assessed as a marker of the inflammatory response mounted in response to the infection. Parasite intensity was also monitored. Surviving birds were then re-infected 37 days post primary infection. In agreement with the predictions, we found that primary infected birds paid a substantially higher cost in terms of infection-induced reduction in haematocrit compared with re-exposed birds. After the secondary infection, re-exposed hosts were also able to clear the infection at a faster rate than after the primary infection. These results have potential consequences for the epidemiology of avian malaria, since birds re-exposed to the pathogen can maintain parasitemia with low fitness costs, allowing the persistence of the pathogen within the host population.     

Costs and benefits of sublethal Drosophila C virus infection

Viruses are major evolutionary drivers of insect immune systems. Much of our knowledge of insect immune responses derives from experimental infections using the fruit fly Drosophila melanogaster. Most experiments, however, employ lethal pathogen doses through septic injury, frequently overwhelming host physiology. While this approach has revealed several immune mechanisms, it is less informative about the fitness costs hosts may experience during infection in the wild. Using both systemic and oral infection routes, we find that even apparently benign, sublethal infections with the horizontally transmitted Drosophila C virus (DCV) can cause significant physiological and behavioural morbidity that is relevant for host fitness. We describe DCV‐induced effects on fly reproductive output, digestive health and locomotor activity, and we find that viral morbidity varies according to the concentration of pathogen inoculum, host genetic background and sex. Notably, sublethal DCV infection resulted in a significant increase in fly reproduction, but this effect depended on host genotype. We discuss the relevance of sublethal morbidity for Drosophila ecology and evolution, and more broadly, we remark on the implications of deleterious and beneficial infections for the evolution of insect immunity.     

Population dynamics of plant-parasite interactions: thresholds for invasion

Thresholds are derived for the invasion of plant populations by parasites. The theory is developed for a generic model that takes into account two features characteristic of plant-parasite interactions: a dual source of inoculum (infection from primary or externally introduced inoculum and secondary infection from contact between susceptible and infected host tissue) and a host response to infection load. Each of the threshold criteria is shown to be the sum of the individual components for primary and secondary infection. This indicates that if parasite invasion is not possible through primary or secondary infection alone, when the two modes of transmission are combined, the parasite may be able to invade. The invasion criteria demonstrate that there is a threshold population of susceptible hosts below which the parasite is unable to invade. If there are nonlinearities in the population dynamics (arising through either the transmission process or the host response), there are also threshold densities for the infected hosts and parasite populations below which invasion does not occur. The implications of the results for the control of plant disease are discussed.     

Factors affecting host range in a generalist seed pathogen of semi-arid shrublands

Generalist pathogens can exhibit differential success on different hosts, resulting in complex host range patterns. Several factors operate to reduce realized host range relative to potential host range, particularly under field conditions. We explored factors influencing host range of the naturally occurring generalist ascomycete grass seed pathogen Pyrenophora semeniperda. We measured potential host range in laboratory experiments at high inoculum loads with 26 grass species, including the primary host Bromus tectorum, and developed models to predict susceptibility and tolerance based on host traits, including germination speed, seed hardness, seed size, and phylogenetic relations. We also examined pathogen and host density effects on infection and mortality. All species tested were at least somewhat susceptible to the pathogen at high inoculum loads, but both infection and mortality varied widely. Species more closely related to the original host (B. tectorum) were more susceptible to infection, whereas species with slower germination were less tolerant and therefore more likely to suffer mortality. Infection and mortality were sharply reduced as inoculum load was reduced. Intermediate loads had major negative impacts on dormant B. tectorum seeds but generally minimal effects on native species. In addition, field seed bank studies determined that P. semeniperda rarely exploits native grass species as hosts. This marked reduction in realized host range relative to potential host range indicates that laboratory host range studies are potentially a poor predictor of either the current or possible future realized host range for wildland plant pathogens.     

Condition-dependent alteration of cellular immunity by secondary symbionts in the pea aphid,Acyrthosiphon pisum

Endosymbionts can fundamentally alter host physiology. Whether such changes are beneficial or detrimental to one or both partners may depend on the dynamics of the symbiotic relationship. Here we investigate the relationship between facultative symbionts and host immune responses. The pea aphid, Acyrthosiphon pisum, maintains an obligate primary symbiont, but may also harbour one or more facultative, secondary symbionts. Given their more transient nature and relatively recent adoption of a symbiotic lifestyle compared to primary symbionts, secondary symbionts may present a challenge for the host immune system. We assessed the response of several key components of the cellular immune system (phenoloxidase activity, encapsulation, immune cell counts) in the presence of alternative secondary symbionts, investigating the role of host and secondary symbiont genotype in specific responses. There was no effect of secondary symbiont presence on the phenoloxidase response, but we found variation in the encapsulation response and in immune cell counts based largely on the secondary symbiont. Host genotype was less influential in determining immunity outcomes. Our results highlight the importance of secondary symbionts in shaping host immunity. Understanding the complex physiological responses that can be propagated by host-symbiont associations has important consequences for host ecology, including symbiont and pathogen transmission dynamics.     

Host genetics and pathogen species modulate infection-induced changes in social aggregation behaviour

Identifying how infection modifies host behaviours that determine social contact networks is important for understanding heterogeneity in infectious disease dynamics. Here, we investigate whether group social behaviour is modified during bacterial infection in fruit flies (Drosophila melanogaster) according to pathogen species, infectious dose, host genetic background and sex. In one experiment, we find that systemic infection with four different bacterial species results in a reduction in the mean pairwise distance within infected female flies, and that the extent of this change depends on pathogen species. However, susceptible flies did not show any evidence of avoidance in the presence of infected flies. In a separate experiment, we observed genetic- and sex-based variation in social aggregation within infected, same-sex groups, with infected female flies aggregating more closely than infected males. In general, our results confirm that bacterial infection induces changes in fruit fly behaviour across a range of pathogen species, but also highlight that these effects vary between fly genetic backgrounds and can be sex-specific. We discuss possible explanations for sex differences in social aggregation and their consequences for individual variation in pathogen transmission.     

Crayfish population size under different routes of pathogen transmission

We present an epidemiological model for the crayfish plague, a disease caused by an invasive oomycete Aphanomyces astaci, and its general susceptible freshwater crayfish host. The pathogen shows high virulence with resulting high mortality rates in freshwater crayfishes native to Europe, Asia, Australia, and South America. The crayfish plague occurrence shows complicated dynamics due to the several types of possible infection routes, which include cannibalism and necrophagy. We explore this complexity by addressing the roles of host cannibalism and the multiple routes of transmission through (1) environment, (2) contact, (3) cannibalism, and (4) scavenging of infected carcasses. We describe a compartment model having six classes of crayfish and a pool of crayfish plague spores from a single nonevolving strain. We show that environmental transmission is the decisive factor in the development of epidemics. Compared with a pathogen-free crayfish population, the presence of the pathogen with a low environmental transmission rate, regardless of the contact transmission rate, decreases the crayfish population size with a low risk of extinction. Conversely, a high transmission rate could drive both the crayfish and pathogen populations to extinction. High contact transmission rate with a low but nonzero environmental transmission rate can have mixed outcomes from extinction to large healthy population, depending on the initial values. Scavenging and cannibalism have a relevant role only when the environmental transmission rate is low, but scavenging can destabilize the system by transmitting the pathogen from a dead to a susceptible host. To the contrary, cannibalism stabilizes the dynamics by decreasing the proportion of infected population. Our model provides a simple tool for further analysis of complex host parasite dynamics and for the general understanding of crayfish disease dynamics in the wild.     

Early events in hepatitis B infection: the role of inoculum dose

The relationship between the inoculum dose and the ability of the pathogen to invade the host is poorly understood. Experimental studies in non-human primates infected with different inoculum doses of hepatitis B virus have shown a non-monotonic relationship between dose magnitude and infection outcome, with high and low doses leading to 100% liver infection and intermediate doses leading to less than 0.1% liver infection, corresponding to CD4 T-cell priming. Since hepatitis B clearance is CD8 T-cell mediated, the question of whether the inoculum dose influences CD8 T-cell dynamics arises. To help answer this question, we developed a mathematical model of virus–host interaction following hepatitis B virus infection. Our model explains the experimental data well, and predicts that the inoculum dose affects both the timing of the CD8 T-cell expansion and the quality of its response, especially the non-cytotoxic function. We find that a low-dose challenge leads to slow CD8 T-cell expansion, weak non-cytotoxic functions, and virus persistence; high- and medium-dose challenges lead to fast CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance; while a super-low-dose challenge leads to delayed CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance. These results are useful for designing immune cell-based interventions.     

Studying and approximating spatio-temporal models for epidemic spread and control

A class of simple spatio-temporal stochastic models for the spread and control of plant disease is investigated. We consider a lattice-based susceptible-infected model in which the infection of a host occurs through two distinct processes: a background infective challenge representing primary infection from external sources, and a short-range interaction representing the secondary infection of susceptibles by infectives within the population. Recent data-modelling studies have suggested that the above model may describe the spread of aphid-borne virus diseases in orchards. In addition, we extend the model to represent the effects of different control strategies involving replantation (or recovery). The Contact Process is a particular case of this model. The behaviour of the model has been studied using Cellular-Automata simulations. An alternative approach is to formulate a set of deterministic differential equations that captures the essential dynamics of the stochastic system. Approximate solutions to this set of equations, describing the time evolution over the whole parameter range, have been obtained using the pairwise approximation (PA) as well as the most commonly used mean-field approximation (MF). Comparison with simulation results shows that PA is significantly superior to MF, predicting accurately both transient and long-run, stationary behaviour over relevant parts of the parameter space. The conditions for the validity of the approximations to the present model and extensions thereof are discussed.     

Scaling and spatial dynamics in plant-pathogen systems: from individuals to populations

Components of transmission for primary infection from soil-borne inoculum and secondary (plant to plant) infection are estimated from experiments involving single plants. The results from these individual-based experiments are used in a probabilistic spatial contact process (cellular automaton) to predict the progress of an epidemic. The model accounts for spatial correlations between infected and susceptible plants due to inhomogeneous mixing caused by restricted movement of the pathogen in soil. It also integrates nonlinearities in infection, including small stochastic differences in primary infection that become amplified by secondary infection. The model predicts both the mean and the variance of the infection dynamics of R. solani when compared with replicated epidemics in populations of plants grown in microcosms. The broader consequences of the combination of experimental and modelling approaches for scaling-up from individual to population behaviour are discussed. <br>     

Modelling contact spread of infection in host-parasitoid systems: Vertical transmission of pathogens can cause chaos

All animals and plants are, to some extent, susceptible to disease caused by varying combinations of parasites, viruses and bacteria. In this paper, we develop a mathematical model of contact spread infection to investigate the effect of introducing a parasitoid-vectored infection into a one-host-two-parasitoid competition model. We use a system of ordinary differential equations to investigate the separate influences of horizontal and vertical pathogen transmission on a model system appropriate for a variety of competitive situations. Computational simulations and steady-state analysis show that the transient and long-term dynamics exhibited under contact spread infection are highly complex. Horizontal pathogen transmission has a stabilising effect on the system whilst vertical transmission can destabilise it to the point of chaotic fluctuations in population levels. This has implications when considering the introduction of host pathogens for the control of insect vectored diseases such as bovine tuberculosis or yellow fever.     

Scaling up tests on virulence of the cassava green mite fungal pathogen <Emphasis Type="Italic">Neozygites tanajoae</Emphasis> (Entomophthorales: Neozygitaceae) under controlled conditions: first observations at the population level

Virulence of entomopathogens is often measured at the individual level using a single host individual or a group of host individuals. To what extent these virulence assessments reflect the impact of an entomopathogen on their host in the field remains largely untested, however. A methodology was developed to induce epizootics of the cassava green mite fungal pathogen Neozygites tanajoae under controlled conditions to evaluate population-level virulence of two (one Beninese and one Brazilian) isolates of the entomopathogen—which had shown similar individual-level virulence but different field impacts. In unrepeated separate experiments we inoculated mite-infested potted cassava plants with either 50 or 25 live mites (high and low inoculum) previously exposed to spores of N. tanajoae and monitored the development of fungal infections for each isolate under the same conditions. Both isolates caused mite infections and an associated decline in host mite populations relative to the control (without fungus) in all experiments, but prevalence of the fungus varied with isolate and increased with inoculum density. Peak infection levels were 90% for the Beninese isolate and 36% for the Brazilian isolate at high inoculum density, and respectively 17% and 25% at low inoculum density. We also measured dispersal from inoculated plants and found that spore dispersal increased with host infection levels, independent of host densities, whereas mite dispersal varied between isolates. These results demonstrate that epizootiology of N. tanajoae can be studied under controlled conditions and suggest that virulence tests at the population level may help to better predict performance of fungal isolates than individual-level tests.     

Fluctuating temperatures alter environmental pathogen transmission in a Daphnia–pathogen system

Environmental conditions are rarely constant, but instead vary spatially and temporally. This variation influences ecological interactions and epidemiological dynamics, yet most experimental studies examine interactions under constant conditions. We examined the effects of variability in temperature on the host–pathogen relationship between an aquatic zooplankton host (Daphnia laevis) and an environmentally transmitted fungal pathogen (Metschnikowia bicuspidata). We manipulated temperature variability by exposing all populations to mean temperatures of 20°C for the length of the experiments, but introducing periods of 1, 2, and 4 hr each day where the populations were exposed to 28°C followed by periods of the same length (1, 2, and 4 hr, respectively) where the populations were exposed to 12°C. Three experiments were performed to assess the role of thermal variability on Daphnia–pathogen interactions, specifically with respect to: (1) host infection prevalence and intensity; (2) free‐living pathogen survival; and (3) host foraging ecology. We found that temperature variability affected host filtering rate, which is closely related to pathogen transmission in this system. Further, infection prevalence was reduced as a function of temperature variability, while infection intensity was not influenced, suggesting that pathogen transmission was influenced by temperature variability, but the growth of pathogen within infected hosts was not. Host survival was reduced by temperature variability, but environmental pathogen survival was unaffected, suggesting that zooplankton hosts were more sensitive than the fungal pathogen to variable temperatures. Together, these experiments suggest that temperature variability may influence host demography and host–pathogen interactions, providing a link between host foraging ecology and pathogen transmission.