Variable prey development time suppresses predator-prey cycles and enhances stability.

Although theoretical models have demonstrated that predator-prey population dynamics can depend critically on age (stage) structure and the duration and variability in development times of different life stages, experimental support for this theory is non-existent. We conducted an experiment with a host-parasitoid system to test the prediction that increased variability in the development time of the vulnerable host stage can promote interaction stability. Host-parasitoid microcosms were subjected to two treatments: Normal and High variance in the duration of the vulnerable host stage. In control and Normal-variance microcosms, hosts and parasitoids exhibited distinct population cycles. In contrast, insect abundances were 18-24% less variable in High- than Normal-variance microcosms. More significantly, periodicity in host-parasitoid population dynamics disappeared in the High-variance microcosms. Simulation models confirmed that stability in High-variance microcosms was sufficient to prevent extinction. We conclude that developmental variability is critical to predator-prey population dynamics and could be exploited in pest-management programs.

Estimation of the diffusion rate and crossing probability for biased edge movement between two different types of habitat.

One of the fundamental goals of ecology is to examine how dispersal affects the distribution and dynamics of insects across natural landscapes. These landscapes are frequently divided into patches of habitat embedded in a matrix of several non-habitat regions, and dispersal behavior could vary within each landscape element as well as the edges between elements. Reaction-diffusion models are a common way of modeling dispersal and species interactions in such landscapes, but to apply these models we also need methods of estimating the diffusion rate and any edge behavior parameters. In this paper, we present a method of estimating the diffusion rate using the mean occupancy time for a circular region. We also use mean occupancy time to estimate a parameter (the crossing probability) that governs one type of edge behavior often used in these models, a biased random walk. These new methods have some advantages over other methods of estimating these parameters, including reduced computational cost and ease of use in the field. They also provide a method of estimating the diffusion rate for a particular location in space, compared to existing methods that represent averages over large areas. We further examine the statistical properties of the new method through simulation, and discuss how mean occupancy time could be estimated in field experiments.

Interactions among virulence, coinfection and drug resistance in a complex life-cycle parasite.

Motivated by relatively recent empirical studies on Schistosoma mansoni, we use a mathematical model to investigate the impacts of drug treatment of the definitive human host and coinfection of the intermediate snail host by multiple parasite strains on the evolution of parasites' drug resistance. Through the examination of evolutionarily stable strategies (ESS) of parasites, our study suggests that higher levels of drug treatment rates (which usually tend to promote monomorphism as the evolutionary equilibrium) favor parasite strains that have a higher level of drug resistance. Our study also shows that whether coinfection of intermediate hosts affects the levels of drug resistance at ESS points and their stability depends on the assumptions on the cost of parasites paid for drug resistance, coinfection functions and parasites' reproduction within coinfected hosts. This calls for more empirical studies on the parasite.

Evolution of host resistance to parasite infection in the snail-schistosome-human system.

The evolutionary strategies that emerge within populations can be dictated by numerous factors, including interactions with other species. In this paper, we explore the consequences of such a scenario using a host-parasite system of human concern. By analyzing the dynamical behaviors of a mathematical model we investigate the evolutionary outcomes resulting from interactions between Schistosoma mansoni and its snail and human hosts. The model includes two types of snail hosts representing resident and mutant types. Using this approach, we focus on establishing evolutionary stable strategies under conditions where snail hosts express different life-histories and when drug treatment is applied to an age-structured population of human hosts. Results from this work demonstrate that the evolutionary trajectories of host-parasite interactions can be varied, and at times, counter-intuitive, based on parasite virulence, host resistance, and drug treatment.

Comparative Proteomics of Mulberry Leaves at Different Developmental Stages Identify Novel Proteins Function Related to Photosynthesis.

Mulberry leaves at different positions are different in photosynthetic rate, nutrient substance and feeding impact to silkworms. Here, we investigated the proteomic differences of the first (L1), sixth (L6), and twentieth (L20) mulberry leaves at different stem positions (from top to the base) using a label-free quantitative proteomics approach. L1 contained less developed photosynthetic apparatus but was more active in protein synthesis. L20 has more channel proteins and oxidoreductases relative to L6. Proteins that detected in all measured leaves were classified into three groups according to their expression patterns in L1, L6, and L20. The protein group that displayed the maximum amount in L6 has the highest possibility that function related to photosynthesis. Nine function unknown proteins belong to this group were further analyzed in the light responsive expression, evolutionary tree and sub-cellular localization analysis. Based on the results, five proteins were suggested to be involved in photosynthesis. Taken together, these results reveal the molecular details of different roles of mulberry leaves at different developmental stages and contribute to the identification of five proteins that might function related to photosynthesis.

Developmental variability and stability in continuous-time host-parasitoid models.

Insect host-parasitoid systems are often modeled using delay-differential equations, with a fixed development time for the juvenile host and parasitoid stages. We explore here the effects of distributed development on the stability of these systems, for a random parasitism model incorporating an invulnerable host stage, and a negative binomial model that displays generation cycles. A shifted gamma distribution was used to model the distribution of development time for both host and parasitoid stages, using the range of parameter values suggested by a literature survey. For the random parasitism model, the addition of biologically plausible levels of developmental variability could potentially double the area of stable parameter space beyond that generated by the invulnerable host stage. Only variability in host development time was stabilizing in this model. For the negative binomial model, development variability reduced the likelihood of generation cycles, and variability in host and parasitoid was equally stabilizing. One source of stability in these models may be aggregation of risk, because hosts with varying development times have different vulnerabilities. High levels of variability in development time occur in many insects and so could be a common source of stability in host-parasitoid systems.

Timely identification of optimal control strategies for emerging infectious diseases.

BACKGROUND: Health authorities must rely on quarantine, isolation, and other non-pharmaceutical interventions to contain outbreaks of newly emerging human diseases. METHODS: We modeled a generic disease caused by a pathogen apparently transmitted by close interpersonal contact, but about which little else is known. In our model, people may be infectious while incubating or during their prodrome or acute illness. We derived an expression for Re, the reproduction number, took its partial derivatives with respect to control parameters, and encoded these analytical results in a user-friendly Mathematica notebook. With biological parameters for SARS estimated from the initial case series in Hong Kong and infection rates from hospitalizations in Singapore, we determined Re's sensitivity to control parameters. RESULTS: Stage-specific infection rate estimates from cases hospitalized before quarantine began exceed those from the entire outbreak, but are qualitatively similar: infectiousness was negligible until symptom onset, and increased 10-fold from prodrome to acute illness. Given such information, authorities might instead have emphasized a strategy whose efficiency more than compensates for any possible reduction in efficacy. CONCLUSIONS: In future outbreaks of new human diseases transmitted via close interpersonal contact, it should be possible to identify the optimal intervention early enough to facilitate effective decision-making.

Analysis of a negative binomial host-parasitoid model with two maturation delays and impulsive resource input.

To study the interaction of parasitoids and their insect hosts in laboratory environment, we propose a mathematical model incorporating impulsive resource inputs, stage-structure, maturation times and negative binomial distribution of parasitoid attacks. According to the adaptability of the insect host to the environment, we obtain conditions under which the system is uniformly permanent in two cases, which guarantee that the host and its parasitoid can coexist. By applying fixed point theory, we show existence of the positive periodic solution where the host and its parasitoid can coexist, and also obtain the conditions that ensure the existence of the parasitoid-extinction periodic solution. Our numerical analysis confirms and extends our theoretical results. The simulations show that when the total amount of resource is fixed, a smaller amount of recourse inputs with a shorter period of impulsive delivery results in smaller oscillation amplitude in the insect host population. However, the development of parasitoid population is not affected by the resource management strategy. It is also demonstrated that larger maturation times, either the host's or the parasitoid's, lead to the decline of the parasitoid population. But larger parasitoid's maturation time does accelerate the host's population growth. These are helpful for us to acquire a deeper knowledge of the host-parasitoid interaction in laboratory environment.

A schistosomiasis model with mating structure and time delay.

A system of homogeneous equations with a time delay is used to model the population dynamics of schistosomes. The model includes the parasite's mating structure, multiple resistant schistosome strains, and biological complexity associated with the parasite's life cycle. Invasion criteria of resistant strains and coexistence threshold conditions are derived. These results are used to explore the impact of drug treatment on resistant strain survival. Numerical simulations indicate that the dynamical behaviors of the current model are not qualitatively different from those derived from an earlier model that ignores the impact of time delays associated with the multiple stages in parasite's life cycle. However, quantitatively the time delays make it more likely for drug-resistant strains to invade in a parasite population.

Media alert in an SIS epidemic model with logistic growth.

In general, media coverage would not be implemented unless the number of infected cases reaches some critical number. To reflect this feature, we incorporate the media effect and a critical number of infected cases into the disease transmission rate and consider an susceptible-infected-susceptible epidemic model with logistic growth. Our model analysis shows that early media alert and strong media effects are preferable to decrease the numbers of infected cases at endemic equilibria. Furthermore, we noticed that the model may have up to three endemic equilibria and bi-stability can occur in a threshold interval for the critical number. Note that the interval depends on parameters for the focal disease and the media effect. It is possible to roughly estimate the interval for re-emerging diseases in a given region. Therefore, the result could be useful to health policymakers. Global stability is also obtained when the model admits a unique endemic equilibrium.

Epidemiological models with non-exponentially distributed disease stages and applications to disease control.

SEIR epidemiological models with the inclusion of quarantine and isolation are used to study the control and intervention of infectious diseases. A simple ordinary differential equation (ODE) model that assumes exponential distribution for the latent and infectious stages is shown to be inadequate for assessing disease control strategies. By assuming arbitrarily distributed disease stages, a general integral equation model is developed, of which the simple ODE model is a special case. Analysis of the general model shows that the qualitative disease dynamics are determined by the reproductive number [Formula: see text], which is a function of control measures. The integral equation model is shown to reduce to an ODE model when the disease stages are assumed to have a gamma distribution, which is more realistic than the exponential distribution. Outcomes of these models are compared regarding the effectiveness of various intervention policies. Numerical simulations suggest that models that assume exponential and non-exponential stage distribution assumptions can produce inconsistent predictions.

Evolutionary implications for interactions between multiple strains of host and parasite.

The interaction between multiple parasite strains within different host types may influence the evolutionary trajectories of parasites. In this article, we formulate a deterministic model with two strains of parasites and two host types in order to investigate how heterogeneities in parasite virulence and host life-history may affect the persistence and spread of diseases in natural systems. We compute the reproductive number of strain i (R(i)) independently, as well as the (conditional) "invasion" reproductive number for strains i (R(i)(j), j not equal i) when strain j is at a positive equilibrium. We show that the disease-free equilibrium is locally asymptotically stable if R(i)<1 for both strains and is unstable if R(i)>1 for one stain. We establish the criterion R(i)(j)>1 for strain i to invade strain j. Subthreshold coexistence driven by coinfection is possible even when R(i) of one strain is below 1. We identify conditions that determine the evolution of parasite specialism or generalism based on the life-history strategies employed by hosts, and investigate how host strains may influence parasite persistence.

On the role of schistosome mating structure in the maintenance of drug-resistant strains.

The effects of drug treatment of human hosts on a population of schistosome parasites depends on a variety of factors. Previous models have shown that multiple strains of drug-resistant parasites are likely to be favored as the treatment rate increases. However, such models have neglected to account for the complex nature of schistosome mating biology. To more accurately account for the biology of these parasites, a simple mating structure is included in a multi-strain schistosome model, with parasites under the influence of drug treatment of their human hosts. Parasites are assumed to pay a cost for drug resistance in terms of reduced reproduction and transmission. The dynamics of the parasite population are described by a system of homogeneous differential equations, and the existence and stability of the exponential solutions for this system are used to infer the impact of drug treatment on the maintenance of schistosome genetic diversity.

A spatially structured metapopulation model with patch dynamics.

Metapopulation models that incorporate both spatial and temporal structure are studied in this paper. The existence and stability of equilibria are provided, and an extinction threshold condition is derived which depends on patch dynamics (patch destruction and creation) and metapopulation dynamics (patch colonization and extinction). These results refine threshold conditions given by previous metapopulation models. By comparing landscapes with different spatial heterogeneities with respect to weighted long-term patch occupancies, we conclude that the pattern of a landscape is of overwhelming importance in determining metapopulation persistence and patch occupancy. We show that the same conclusion holds when a rescue effect is considered. We also derive a stochastic differential equations (SDE) model of the Itô type based on our deterministic model. Our simulations reveal good agreement between the deterministic model and the SDE model.

On the role of schistosome mating structure in the maintenance of drug resistant strains.

The effects of drug treatment of human hosts upon a population of schistosome parasites depend upon a variety of factors. Previous models have shown that multiple strains of drug-resistant parasites are likely to be favored as the treatment rate increases. However, such models have neglected to account for the complex nature of schistosome mating biology. To more accurately account for the biology of these parasites, a simple mating structure is included in a multi-strain schistosome model, with parasites under the influence of drug treatment of their human hosts. Parasites are assumed to pay a cost for drug resistance in terms of reduced reproduction and transmission. The dynamics of the parasite population are described by a system of homogeneous differential equations, and the existence and stability of the exponential solutions for this system are used to infer the impact of drug treatment on the maintenance of schistosome genetic diversity.