Global stability and Hopf bifurcation of a host–parasite system

2017 ◽  
Vol 10 (04) ◽  
pp. 1750047
Author(s):  
Xuerui Wei ◽  
Zhipeng Qiu
Keyword(s):  
Hopf Bifurcation ◽  
Time Scale ◽  
Sufficient Conditions ◽  
Host Population ◽  
Complete Analysis ◽  
Logistic Growth ◽  
Free Living ◽  
Dynamical Mechanism ◽  
Host Parasite Interactions ◽  
Host Parasite

Understanding the dynamical mechanism of the host–parasite interactions is one of important issues on host–parasite association. In this paper, we formulate a three-dimensional host–macroparasite system to describe the host–parasite interactions, which includes the logistic growth rate of host population, the important free-living stage and the host fecundity reduction due to parasite infection. The purpose of the paper is to investigate the asymptotical behavior of the system. By using the properties of the solution to non-autonomous linear system, the basic production number [Formula: see text] is proved to be a threshold which determines the outcome of the parasites. If [Formula: see text], the parasite will eventually die out, and if [Formula: see text] the parasite will be uniformly persistent. Hopf bifurcation of the system is further studied, and sufficient conditions for the Hopf bifurcation are obtained. By using the singular perturbation techniques, the system is separated into two time scales with a faster time scale for the free-living infective particles and a slower time scale for the population dynamics of host and parasite, and then a complete analysis of the dynamics on the slow manifold is conducted. The theoretical results show that the level of aggregation of parasites within host may influence the persistence and stability of the system.

scholarly journals To delay once or twice: the effect of hypobiosis and free-living stages on the stability of host–parasite interactions

2008 ◽  
Vol 5 (25) ◽  
pp. 919-928 ◽  
Author(s):  
Sabrina Gaba ◽  
Sébastien Gourbière
Keyword(s):  
Population Dynamics ◽  
Life Cycle ◽  
Time Delay ◽  
Host Population ◽  
Previous Attempt ◽  
Maximal Effect ◽  
Parasite Life Cycle ◽  
Free Living ◽  
Host Parasite Interactions ◽  
Host Parasite

The life cycle of many endoparasites can be delayed by free-living infective stages and a developmental arrestment in the host referred to as hypobiosis. We investigated the effects of hypobiosis and its interaction with delay in the free-living stages on host–parasite population dynamics by expanding a previous attempt by Dobson & Hudson. When the parasite life cycle does not include free-living stages, hypobiosis destabilizes the host–parasite interactions, irrespective of the assumptions about the regulation of the host population dynamics. Interestingly, the destabilizing effect varies in a nonlinear way with the duration of hypobiosis, the maximal effect being expected for three to five months delay. When the parasite life cycle involves free-living stages, hypobiosis of short or intermediate duration increases the destabilizing effect of the first time delay. However, hypobiosis of a duration of five months or more can stabilize interactions, irrespective of the regulation of the host population dynamics. Overall, we confirmed that hypobiosis is an unusual time delay as it can stabilize a two-way interaction. Contrary to the previous conclusions, such an atypical effect does not require self-regulation of the host population, but instead depends on the existence of free-living stages.

scholarly journals Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Caijuan Yan ◽  
Jianwen Jia
Keyword(s):  
Hopf Bifurcation ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Sir Epidemic Model ◽  
Medical Resources ◽  
Reproduction Ratio ◽  
Disease Free ◽  
Information Variable

We consider SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratioℛ0<1, we discuss the global asymptotical stability of the disease-free equilibrium by constructing a Lyapunov functional. Ifℛ0>1, we obtain sufficient conditions under which the endemic equilibriumE*of system is locally asymptotically stable. And we also have discussed the stability and direction of Hopf bifurcations. Numerical simulations are carried out to explain the mathematical conclusions.

scholarly journals Hidden paths to endless forms most wonderful: Parasite-blind diversification of host quality

2020 ◽  
Author(s):  
Lisa Freund ◽  
Marie Vasse ◽  
Gregory J. Velicer
Keyword(s):  
Growth Suppression ◽  
Host Population ◽  
Host Quality ◽  
Evolution Theory ◽  
Evolutionary Diversification ◽  
Adaptive Landscapes ◽  
Host Parasite Interactions ◽  
Parasite Evolution ◽  
Host Parasite ◽  
Selective Environment

Evolutionary diversification can occur in allopatry or sympatry, can be unselected or driven by selection, and can be phenotypically manifested immediately or remain phenotypically latent until later manifestation in a newly encountered environment. Diversification of host-parasite interactions is frequently studied in the context of intrinsically selective coevolution, but the potential for host-parasite interaction phenotypes to diversify latently during parasite-blind evolution is rarely considered. Here we use a social bacterium experimentally adapted to several environments in the absence of phage to analyse allopatric diversification of latent host quality - the degree to which a host population supports a viral epidemic. Phage-blind evolution reduced host quality overall, with some bacteria becoming completely resistant to growth suppression by phage. Selective-environment differences generated only mild divergence in host-quality. However, selective environments nonetheless played a major role in shaping evolution by determining the degree of stochastic diversification among replicate populations within treatments. Ancestral motility genotype was also found to strongly shape patterns of latent hostquality evolution and diversification. These outcomes show that adaptive landscapes can differ in how they constrain stochastic diversification of a latent phenotype and that major effects of selection on biological diversification can be missed by focusing on trait means. Collectively, our findings suggest that latent-phenotype evolution (LPE) should inform host-parasite evolution theory and that diversification should be conceived broadly to include latent phenotypes.

Effect of environmental variables and their interaction on gordiid hairworm larvae (Nematomorpha)

2021 ◽  
Vol 95 ◽  
Author(s):  
C.L. Achiorno ◽  
G. Minardi ◽  
L. Ferrari
Keyword(s):  
Freshwater Ecosystems ◽  
Effect Of Temperature ◽  
Extreme Temperatures ◽  
Free Living ◽  
Temperature Variations ◽  
Host Parasite Interactions ◽  
Effects Of Ph ◽  
Chordodes Nobilii ◽  
Increasing Temperature ◽  
Host Parasite

Abstract The different stages of the life cycle of parasites are important components of ecosystems. Changes in environmental conditions may affect free-living stages, host–parasite interactions and ecosystem functioning. The larvae of Chordodes nobilii, which belongs to the parasitic phylum Nematomorpha, are susceptible to extreme temperatures and different pollutants, but the effects of pH and moderate temperature variations have not been evaluated yet. Our objective was to assess the effect of temperature, pH and their interaction on the infectivity of C. nobilii larvae to Aedes aegypti larvae over time. Larvae were treated with factorial combinations of temperature (18, 23 and 28°C), pH (7, 8 and 9) and time periods (24 and 48 h). Results show a highly significant interaction among all variables. The highest infectivity was recorded at 18°C and pH 7 at 24 and 48 h, and the lowest one at 28°C and pH 8 at 24 and 48 h. Infectivity differed significantly among the three temperatures only at pH 8 and 48 h, decreasing with increasing temperature. Our study is the first report of the effect of pH on a Nematomorpha species and suggests that the infectivity of C. nobilii larvae may be affected negatively by an increase in temperature and its interaction with pH and time. Since parasites must be considered for a better understanding of the effects of stressors on freshwater ecosystems, our results may help in the design and analysis of studies of anthropogenic impact.

Population interactions between a parasitic castrator, Probopyrus pandalicola (Isopoda: Bopyridae), and one of its freshwater shrimp hosts, Palaemonetes paludosus (Decapoda: Caridea)

Parasitology ◽  
1979 ◽  
Vol 79 (3) ◽  
pp. 431-449 ◽  
Author(s):  
J. T. Beck
Keyword(s):  
Host Population ◽  
Acartia Tonsa ◽  
Parasite Control ◽  
Freshwater Shrimp ◽  
Free Swimming ◽  
Host Parasite Interactions ◽  
Population Interactions ◽  
Parasitic Castrator ◽  
Host Parasite ◽  
And Control

SUMMARYFreshwater shrimp, Palaemonetes paludosus, infected by the bopyrid isopod, Probopyrus pandalicola, occurred as far as 33 km upstream in many coastal rivers and canals throughout Florida. Free-swimming isopod larvae and the intermediate copepod host, Acartia tonsa, were collected in the plankton of the Wakulla River, and it appeared that cryptoniscus larvae swam at least as far as 13 km upstream to infect the definitive shrimp host after leaving the copepod in brackish water. In the Wakulla River infection levels ranged from 87·5 to 100%. In contrast, at McBride's Slough infection levels fluctuated from 0·9 to 93·2%. In the St Marks River the frequency of infected shrimp gradually increased from 0% upstream to 96%, 6 km further downstream. A significantly greater percentage of female than male hosts were infected, but only females of size classes less than 31 mm long had a greater frequency of infection. Female P. pandalicola were greatly under-dispersed (coefficient of dispersion (s2/x¯) less than 1) throughout the host population; 99·6% of the infected hosts carried only 1 female parasite. Control of P. pandalicola at the infrapopulation level is probably accomplished by some mode of intraspecific competition, and control at the suprapopulation level occurs through an upstream limitation of the transmission range of the cryptoniscus larval stage. Host–parasite interactions appear to be unstable.

scholarly journals Temperature during the free-living phase of an ectoparasite influences the emergence pattern of the infective phase

Parasitology ◽  
2013 ◽  
Vol 140 (11) ◽  
pp. 1357-1367 ◽  
Author(s):  
M. AMAT-VALERO ◽  
M. A. CALERO-TORRALBO ◽  
F. VALERA
Keyword(s):  
Environmental Influence ◽  
Abiotic Factors ◽  
Life Cycles ◽  
Detailed Knowledge ◽  
Free Living ◽  
Emergence Period ◽  
Host Parasite Interactions ◽  
Emergence Rate ◽  
Emergence Date ◽  
Host Parasite

SUMMARYUnderstanding the population dynamics and co-evolution of host–parasite systems requires detailed knowledge of their phenology which, in turn, requires a deep knowledge of the effect of abiotic factors on the life cycles of organisms. Temperature is known to be a key environmental influence that participates in the regulation of diapause. Yet, not much is known about the effect of temperature on the free-living stages of true parasites and how it may influence host–parasite interactions. Here we experimentally study the effect of ambient temperature on overwintering pupae ofCarnus hemapterus(Diptera, Carnidae), an ectoparasitic fly of various bird species. We also test whether chilling is a prerequisite for completion of diapause in this species. In the course of three winter seasons we experimentally exposed carnid pupae from nests of various host species to spring temperatures with and without chilling and recorded the emergence patterns in experimental and control groups. Experimental groups showed an advanced emergence date, a lower emergence rate and, consequently, a protracted emergence period. Chilling had no obvious effect on the start of emergence but it did advance the mean emergence date, shortened the length of the emergence period when compared with the control treatment and increased the emergence rate when compared with the spring treatment. This study identifies an environmental cue, namely temperature during the free-living stage, affecting the emergence of a widespread parasite and demonstrates the plasticity of diapause in this parasite. Our findings are of potential significance in understanding host–parasite interactions.

The distribution of echinostome parasites in ponds and implications for larval anuran survival

Parasitology ◽  
2017 ◽  
Vol 144 (6) ◽  
pp. 801-811 ◽  
Author(s):  
JOHN A. MARINO ◽  
MANJA P. HOLLAND ◽  
EARL E. WERNER
Keyword(s):  
Community Dynamics ◽  
Field Survey ◽  
Host Population ◽  
Intermediate Hosts ◽  
Enclosure Experiment ◽  
Host Parasite Interactions ◽  
Fitness Consequences ◽  
Prevalence Proportion ◽  
Population And Community Dynamics ◽  
Host Parasite

SUMMARYParasites can influence host population dynamics, community composition and evolution. Prediction of these effects, however, requires an understanding of the influence of ecological context on parasite distributions and the consequences of infection for host fitness. We address these issues with an amphibian – trematode (Digenea: Echinostomatidae) host–parasite system. We initially performed a field survey of trematode infection in first (snail) and second (larval green frog, Rana clamitans) intermediate hosts over 5 years across a landscape of 23 ponds in southeastern Michigan. We then combined this study with a tadpole enclosure experiment in eight ponds. We found echinostomes in all ponds during the survey, although infection levels in both snails and amphibians differed across ponds and years. Echinostome prevalence (proportion of hosts infected) in snails also changed seasonally depending on host species, and abundance (parasites per host) in tadpoles depended on host size and prevalence in snails. The enclosure experiment demonstrated that infection varied at sites within ponds, and tadpole survival was lower in enclosures with higher echinostome abundance. The observed effects enhance our ability to predict when and where host–parasite interactions will occur and the potential fitness consequences of infection, with implications for population and community dynamics, evolution and conservation.

scholarly journals Hidden paths to endless forms most wonderful: parasite-blind diversification of host quality

2021 ◽  
Vol 288 (1949) ◽  
Author(s):  
Lisa Freund ◽  
Marie Vasse ◽  
Gregory J. Velicer
Keyword(s):  
Host Population ◽  
Host Quality ◽  
Evolution Theory ◽  
Evolutionary Diversification ◽  
Adaptive Landscapes ◽  
Host Parasite Interactions ◽  
Parasite Evolution ◽  
Host Evolution ◽  
Host Parasite ◽  
Selective Environment

Evolutionary diversification can occur in allopatry or sympatry, can be driven by selection or unselected, and can be phenotypically manifested immediately or remain latent until manifested in a newly encountered environment. Diversification of host–parasite interactions is frequently studied in the context of intrinsically selective coevolution, but the potential for host–parasite interaction phenotypes to diversify latently during parasite-blind host evolution is rarely considered. Here, we use a social bacterium experimentally adapted to several environments in the absence of phage to analyse allopatric diversification of host quality—the degree to which a host population supports a viral epidemic. Phage-blind evolution reduced host quality overall, with some bacteria becoming completely resistant to growth suppression by phage. Selective-environment differences generated only mild divergence in host quality. However, selective environments nonetheless played a major role in shaping evolution by determining the degree of stochastic diversification among replicate populations within treatments. Ancestral motility genotype was also found to strongly shape patterns of latent host-quality evolution and diversification. These outcomes show that (i) adaptive landscapes can differ in how they constrain stochastic diversification of a latent phenotype and (ii) major effects of selection on biological diversification can be missed by focusing on trait means. Collectively, our findings suggest that latent-phenotype evolution should inform host–parasite evolution theory and that diversification should be conceived broadly to include latent phenotypes.

scholarly journals Annual environmental variation influences host tolerance to parasites

2019 ◽  
Vol 286 (1897) ◽  
pp. 20190049 ◽  
Author(s):  
Sabrina M. McNew ◽  
Sarah A. Knutie ◽  
Graham B. Goodman ◽  
Angela Theodosopoulos ◽  
Ashley Saulsberry ◽  
...  
Keyword(s):  
Environmental Conditions ◽  
Environmental Variation ◽  
Host Population ◽  
Variable Environment ◽  
Host Parasite Interactions ◽  
Video Observations ◽  
Single Host ◽  
Parental Provisioning ◽  
Host Tolerance ◽  
Host Parasite

When confronted with a parasite or pathogen, hosts can defend themselves by resisting or tolerating the attack. While resistance can be diminished when resources are limited, it is unclear how robust tolerance is to changes in environmental conditions. Here, we investigate the sensitivity of tolerance in a single host population living in a highly variable environment. We manipulated the abundance of an invasive parasitic fly, Philornis downsi , in nests of Galápagos mockingbirds ( Mimus parvulus ) over four field seasons and measured host fitness in response to parasitism. Mockingbird tolerance to P. downsi varied significantly among years and decreased when rainfall was limited. Video observations indicate that parental provisioning of nestlings appears key to tolerance: in drought years, mockingbirds likely do not have sufficient resources to compensate for the effects of P. downsi . These results indicate that host tolerance is a labile trait and suggest that environmental variation plays a major role in mediating the consequences of host–parasite interactions.

The population dynamics of microparasites and their invertebrate hosts

1981 ◽  
Vol 291 (1054) ◽  
pp. 451-524 ◽  
Keyword(s):  
Vertical Transmission ◽  
Laboratory Data ◽  
Host Population ◽  
Pest Species ◽  
Free Living ◽  
Specific Level ◽  
Dynamical Interaction ◽  
Death Rates ◽  
Forest Insects ◽  
Host Parasite

We show how directly transmitted microparasites, broadly defined to include viruses, bacteria, protozoans and fungi, may regulate natural populations of invertebrate hosts. The study combines elements of conventional epidemiology (where the host population is assumed constant) with elements of prey-predator studies (which conventionally emphasize how prey and predator populations may be regulated by their interaction). To this end, we construct simple models embodying the essentials of the dynamical interaction between invertebrate hosts and their directly transmitted microparasites. In successive refinements, these models include the effects of recovery and disease-induced mortality, castration or diminished reproduction of infected hosts, vertical transmission, latent periods of infection, stress-related pathogenicity, the interplay between disease and other density-dependent constraints on host population growth, and free-living infective stages. In analysing the dynamical behaviour of these models, we focus on : the possible regulation of the host population by the parasite; the basic reproductive rate of the parasite, and the way in which it affects the dynamics and the evolution of the host-parasite association; and the threshold host density and its implications for endemic or epidemic maintenance of the infection. These are examined in the light of synoptic compilations of field and laboratory data on: birth rates (and disease-induced reduction thereof), natural death rates and disease-induced death rates of hosts; latent periods and efficiencies of vertical transmission of pathogens; the rate of production and lifetime of free-living infective stages; and some characteristics of long-term cycles and of epidemic outbreaks of disease in forest insects. In particular, our models suggest that the baculovirus and microsporidian infections of many temperate forest insects will tend to produce stable cycles in host abundance and in prevalence of infection, with periods in the range 5-12 years. Enough is known about the European larch budmoth and an associated granulosis virus for us to undertake a detailed comparison between theory and data that strongly suggests that the observed 9-10 year cycles are driven by the host-parasite interaction. We also discuss the possible control of invertebrate pest species by pathogens, showing how our models could guide laboratory or field studies, to help estimate whether a given pathogen is capable of regulating the target pest population, and, if so, roughly what quantity is needed to effect a specific level of (local) control. Throughout, the emphasis is on the biological ingredients of the models, and on the biological conclusions to be drawn; mathematical details are given in appendixes.

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