Dashun Xu

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 parasites mating structure, multiple resistant schistosome strains, and biological complexity associated with the parasites 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 parasites life cycle. However, quantitatively the time delays make it more likely for drug-resistant strains to invade in a parasite population.

Bifurcations, chaos, and system collapse in a three node power system

A model of the three node power system proposed by Rajesh and Padiyar [Electr. Power Energy Syst. 21 (1999) 375] is studied. As the bifurcation parameter Pm (input power to the generator) is changed, the system including the effects of the non-linearity exhibits complex dynamics emerging from static and dynamic bifurcations which link with the system collapse. The analyses for the model exhibit dynamical bifurcations, including three Hopf bifurcations, cyclic fold bifurcations, torus bifurcations and period-doubling bifurcations, and complex dynamical behaviors, including periodic orbits, period-doubling orbits, quasi-periodic orbits, phase-locked phenomena and two chaotic regions between two Hopf bifurcations, i.e. in the ‘Hopf window’ and intermittency chaos. Moreover, one of the two chaotic regions results from period-doubling bifurcations, and another results from quasi-periodic orbits emerging from a torus bifurcation. Simulations are given to illustrate the various types of dynamic behaviors associated with the power system collapse for the model. In particular, we first shown that the oscillatory transient may play a role in the collapse, and there are different critical points for different dominated state variables. Besides, the hard-limits and increases of the damping factor widen the feasible operating region of the power system, and prevent the torus bifurcation to occur so that some complex dynamical phenomena can be inhibited. q 2003 Elsevier Science Ltd. All rights reserved.

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.

Timely identification of optimal control strategies for emerging infectious diseases.

Abstract 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 ℜ , 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 ℜ 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.

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.

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.

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.

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.

Identification of diffusion coefficient in nonhomogeneous landscapes

Diffusion models have been found in various applications in the study of spatial population dynamics for modeling the species dispersal process in natural environments. Diffusion coefficient is a critical parameter in diffusion equations. In this paper, a new method for estimating the diffusion coefficient of insects is presented in terms of occupancy time and the method can produce any desired accuracy. The study of modeling biological organism movement behaviors in a nonhomogeneous landscape is critical in investigating the interplay between environmental heterogeneity and organism movements. By constructing a set of eigenvalues, we can characterize the insect biased movement when insect crosses the intersection of two different type of landscape elements. Some numerical examples are provided to illustrate the theoretical outcomes obtained in the paper.