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Results for “spatial spread”

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PubMed2004

The effects of spatial movement and group interactions on disease dynamics of social animals.

The effects of spatial movements of infected and susceptible individuals on disease dynamics is not well understood. Empirical studies on the spatial spread of disease and behaviour of infected individuals are few and theoretical studies may be useful to explore different scenarios. Hence due to lack of detail in empirical studies, theoretical models have become necessary tools in investigating the disease influence in host-pathogen systems. In this paper we developed and analysed a spatially explicit model of two interacting social groups of animals of the same species. We investigated how the movement scenarios of susceptible and infected individuals together with the between-group contact parameter affect the survival rate of susceptible individuals in each group. This work can easily be applied to various host-pathogen systems. We define bounds on the number of susceptibles which avoid infection once the disease has died out as a function of the initial conditions and other model parameters. For example, once disease has passed through the populations, a larger diffusion coefficient for each group can result in higher population levels when there is no between-group interaction but in lower levels when there is between-group interaction. Numerical simulations are used to demonstrate these bounds and behaviours and to describe the different outcomes in ecological terms.

Animals↗

PubMed2003

Multichannel surface EMG: basic aspects and clinical utility.

The generation of the surface electromyogram (sEMG) is described with regard to the properties of the single muscle fiber action potential as source, the physical aspects of volume conduction and recording configuration, and the properties and firing pattern of motor units (MUs). The spatial aspect of the motor unit action potential (MUP) is emphasized in relation to the results of high-density, multichannel sEMG measurements. The endplate zone, depth, size, and position of MUs can be estimated. The use of muscle fiber conduction velocity measurements in channelopathies and the changes in pathological fatigue are described. Using the unique patterns of spatial spread of MUPs over the skin (MU fingerprint), MU classification and the determination of firing moments is done noninvasively. Clinical applications of high-density sEMG measurements are reviewed. Emerging possibilities provided by MUP size and fingerprint measurements in neuromuscular disease and motor control are discussed. We conclude that multichannel sEMG adds unique, and sometimes indispensable, spatial information to our knowledge of the motor unit.

Action Potentials↗

PubMed2005

Effect of peri-modiolar cochlear implant positioning on auditory nerve responses: a neural response telemetry study.

CONCLUSIONS: There was no evidence that a reduction in current was needed for nerve stimulation as a result of modiolar placement of a cochlear implant. However, modiolus hugging did reduce the spread of excitation for the basal and apical electrodes. This improved stimulation selectivity may result in improved speech discrimination by implant users. OBJECTIVE: To test the effect of modiolar placement of a cochlear implant on stimulation thresholds, and to confirm whether peri-modiolar electrode placement resulted in the hypothesized reduced spread of excitation. MATERIAL AND METHODS: Auditory nerve responses were measured by means of neural response telemetry (NRT) in 14 subjects. All subjects received a Nucleus CI24R(CS) Contour implant. For each subject, the stimulation threshold and response growth rate were determined on all the odd-numbered electrodes, using a masker-and-probe paradigm. In addition, the spatial spread of excitation was measured on electrodes 1, 6, 11, 16 and 20, using a variable-masker paradigm. All NRT measurements were performed intra-operatively, both before and after peri-modular placement of the electrode by removal of surgical stylet. RESULTS: Removal of the stylet had no significant effect on the threshold and growth rate of NRT responses. It caused a reduction in the spread of excitation for electrodes 1, 6 and 20, but not for electrodes 11 and 16.

Adolescent↗

PubMed2002

The metapopulation dynamics of an infectious disease: tuberculosis in possums.

An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide formulas for individual patch basic reproduction numbers and discuss their connection with the basic reproduction ratio for the system. The model is applied to the problem of spatial spread of bovine tuberculosis in a possum population. The temporal dynamics of infection are investigated for some generic networks of migration links, and the basic reproduction ratio is computed-its value is not greatly different from that for a homogeneous model. Three scenarios are considered for the control of bovine tuberculosis in possums where the spatial aspect is shown to be crucial for the design of disease management operations.

Animal Migration↗

PubMed2003

Wavelet analysis of nonstationary fluctuations of Monte Carlo-simulated excitatory postsynaptic currents.

Tracking spectral changes of rapidly varying signals is a demanding task. In this study, we explore on Monte Carlo-simulated glutamate-activated AMPA patch and synaptic currents whether a wavelet analysis offers such a possibility. Unlike Fourier methods that determine only the frequency content of a signal, the wavelet analysis determines both the frequency and the time. This is owing to the nature of the basis functions, which are infinite for Fourier transforms (sines and cosines are infinite), but are finite for wavelet analysis (wavelets are localized waves). In agreement with previous reports, the frequency of the stationary patch current fluctuations is higher for larger currents, whereas the mean-variance plots are parabolic. The spectra of the current fluctuations and mean-variance plots are close to the theoretically predicted values. The median frequency of the synaptic and nonstationary patch currents is, however, time dependent, though at the peak of synaptic currents, the median frequency is insensitive to the number of glutamate molecules released. Such time dependence demonstrates that the "composite spectra" of the current fluctuations gathered over the whole duration of synaptic currents cannot be used to assess the mean open time or effective mean open time of AMPA channels. The current (patch or synaptic) versus median frequency plots show hysteresis. The median frequency is thus not a simple reflection of the overall receptor saturation levels and is greater during the rise phase for the same saturation level. The hysteresis is due to the higher occupancy of the doubly bound state during the rise phase and not due to the spatial spread of the saturation disk, which remains remarkably constant. Albeit time dependent, the variance of the synaptic and nonstationary patch currents can be accurately determined. Nevertheless the evaluation of the number of AMPA channels and their single current from the mean-variance plots of patch or synaptic currents is not highly accurate owing to the varying number of the activatable AMPA channels caused by desensitization. The spatial nonuniformity of open, bound, and desensitized AMPA channels, and the time dependence and spatial nonuniformity of the glutamate concentration in the synaptic cleft, further reduce the accuracy of estimates of the number of AMPA channels from synaptic currents. In conclusion, wavelet analysis of nonstationary fluctuations of patch and synaptic currents expands our ability to determine accurately the variance and frequency of current fluctuations, demonstrates the limits of applicability of techniques currently used to evaluate the single channel current and number of AMPA channels, and offers new insights into the mechanisms involved in the generation of unitary quantal events at excitatory central synapses.

Algorithms↗

PubMed1999

Numerical simulation of Ca2+ "sparks" in skeletal muscle.

A three dimensional (3D) model of Ca(2+) diffusion and binding within a sarcomere of a myofibril, including Ca(2+) binding sites troponin, parvalbumin, sarcoplasmic reticulum Ca(2+) pump, and fluorescent Ca(2+)-indicator dye (fluo-3), was developed to numerically simulate laser scanning confocal microscope images of Ca(2+) "sparks" in skeletal muscle. Diffusion of free dye (D), calcium dye (CaD), and Ca(2+) were included in the model. The Ca(2+) release current was assumed to last 8 ms, to arise within 4 x 10(-5) microm(3) at the triad and to be constant during release. Line scan confocal fluorescence images of Ca(2+) sparks were simulated by 3D convolution of the calculated distribution of CaD with a Gaussian kernel approximating the point spread function of the microscope. Our results indicate that the amplitude of the simulated spark is proportional to the Ca(2+) release current if all other model parameters are constant. For a given release current, the kinetic properties and concentrations of the binding sites and the diffusion parameters of D, CaD, and Ca(2+) all have significant effects on the simulated Ca(2+) sparks. The simulated sparks exhibited similar amplitudes and temporal properties, but less spatial spread than experimentally observed sparks.

Adenosine Triphosphate↗

PubMed1996

Ca2+ diffusion and sarcoplasmic reticulum transport both contribute to [Ca2+]i decline during Ca2+ sparks in rat ventricular myocytes.

1. We sought to evaluate the contribution of the sarcoplasmic reticulum (SR) Ca2+ pump (vs. diffusion) to the kinetics of [Ca24]i decline during Ca2+ sparks, which are due to spontaneous local SR Ca2+ release, in isolated rat ventricular myocytes measured using fluo-3 and laser scanning confocal microscopy. 2. Resting Ca2+ sparks were compared before (control) and after the SR Ca2(+)-ATPase was either completely blocked by 5 microM thapsigargin (TG) or stimulated by isoprenaline. Na(+)-Ca2+ exchange was blocked using Na(+)-free, Ca(2+)-free solution (0 Na+, O Ca2+) and conditions were arranged so that the SR Ca2+ content was the same under all conditions when Ca2+ sparks were measured. 3. The control Ca2+ spark amplitude (281 +/- 13 nM) was not changed by TG (270 +/- 21 nM) or isoprenaline (302 +/- 10 nM). However, the time constant of [Ca2+]i decline was significantly slower in the presence of TG (29.3 +/- 4.3 ms) compared with control (21.6 +/- 1.5 ms) and faster with isoprenaline (14.5 +/- 0.9 ms), but in all cases was much faster than the global [Ca2+]i decline during a control twitch (177 +/- 10 ms). 4. The spatial spread of Ca2+ during the Ca2+ spark was also influenced by the SR Ca2+ pump. The apparent 'space constant' of the Ca2+ sparks was longest when the SR Ca2+ pump was blocked, intermediate in control and shortest with isoprenaline. 5. We conclude that while Ca2+ diffusion from the source of Ca2+ release is the dominant process in local [Ca2+]i decline during the Ca2+ spark, Ca2+ transport by the SR contributes significantly to both the kinetics and spatial distribution of [Ca2+]i during the Ca2+ spark.

Adrenergic beta-Agonists↗

PubMed1990

Calcium wave evoked by activation of endogenous or exogenously expressed receptors in Xenopus oocytes.

The mRNA encoding the cloned substance K receptor was microinjected into Xenopus laevis oocytes. After expression of the mRNA, Ca2+ was imaged in the oocytes with a digital imaging fluorescence microscopy system using the Ca2(+)-sensitive dyes fura-2 and fluo-3. Application of substance K caused a dose-related wave of Ca2+ mobilization to spread from a focus and to elevate the Ca2+ concentration in the oocyte. Activation of endogenous muscarinic or angiotensin II receptors in noninjected oocytes evoked a similar response. The Ca2+ rise in oocytes induced by substance K was due to internal Ca2+ mobilization and was independent of external Ca2+, since it occurred in Ca2(+)-free medium fortified with 2 mM EGTA. The Ca2+ imaging was well correlated with ion current measurements of voltage-clamped oocytes. Imaging, in addition to detecting the spatial spread of Ca2+ across the cell, was at least as sensitive as voltage clamping and much faster when screening oocytes for the expression of receptor mRNAs that stimulate Ca2+ mobilization. While it is known that fertilization of Xenopus eggs causes a spreading wave of Ca2+ mobilization, we found that activation of either native or newly expressed receptors in oocytes causes a similar change in Ca2+ distribution.

Animals↗

PubMed2004

Characteristics of prolonged Ca2+ release events associated with the nuclei in adult cardiac myocytes.

Confocal microscopy was used to study the properties of nuclear Ca2+ regulation in adult ventricular myocytes. Prolonged nuclear Ca2+ release (PNCR) events were identified in both intact and permeabilized rat myocytes. PNCR occurred spontaneously and was restricted to localized regions at the ends of the elongated nuclei. Typically, PNCR took the form of a rapid rise in [Ca2+] followed by a maintained plateau. The mean duration of PNCR (1.78+/-0.19 seconds) was markedly greater than the half decay time for cytosolic Ca2+ sparks (31.2+/-0.56 ms) obtained under the same conditions. The PNCR width at half maximum amplitude (5.0+/-0.2 microm) was also significantly greater than that of cytosolic Ca2+ sparks (2.6+/-0.05 microm) obtained under the same conditions. Experiments involving the use of syto-11 to accurately locate the nuclei demonstrated that PNCR originates from the nuclear envelope or a closely associated structure. The spatial spread of PNCR was asymmetrical, with greater diffusion of Ca2+ toward the center of the nucleus than the cytosol. Both PNCR and Ca2+ sparks were abolished by interventions that deplete SR Ca2+ stores or inhibit RYR activation. Experiments on intact, electrically stimulated cells revealed that diffusion of Ca2+ from the ends of the nucleus toward the center is a prominent feature of the nucleoplasmic Ca2+ transient. The possibility that recruitment of Ca2+ release sites involved in PNCR might influence the temporal and spatial characteristics of the nucleoplasmic [Ca2+] transient is considered.

Animals↗

PubMed2005

Secondary spinal cord hypoperfusion of circumscribed areas after injury in rats.

OBJECTIVES: The evaluation of the spatial spread of ischemia following spinal cord injury (SCI) is important for planning therapeutic strategies for secondary injury. The purpose of this study was to investigate in detail the change in regional spinal cord blood flow (rSCBF) after SCI. METHODS: Thirty-four male Wistar rats were used, for which laminectomies of the T11-13 vertebrae were performed. SCI was produced by a directed impact through a laminectomy site at the level of the Th12 using a pneumatic impact device. We measured the sequential and spatial changes of rSCBF using a laser Doppler scanning technique before and after SCI in rats not only at the injured myelomere but also at the circumferent myelomeres. SCBF mapping was carried out before and after SCI on each site. RESULTS: After SCI, the rSCBF value gradually decreased for each site for the SCI group (n=26), while it globally decreased at the epicenter. Moreover, a decrease in SCBF was observed at the caudal and rostral sites. The mean value of the %SCBF 120 minutes after SCI for each site was 63.6+/-2.3% (Th11), 74.4+/-4.5% (Th12), 75.8+/-3.2% (Th13), and was significantly lower for the rostral site compared with the caudal site (p<0.05, one-way analysis of variance). DISCUSSION: This study found that SCBF is significantly decreased not only at the injured myelomere but also at the circumferent myelomeres. Circumferentially extending ischemia after SCI is related to secondary injury after SCI. The improvement in SCBF after SCI, therefore, can be attributed to the treatment of SCI.

Analysis of Variance↗

PubMed2000

Ca(2+) signals mediated by Ins(1,4,5)P(3)-gated channels in rat ureteric myocytes.

Localized Ca(2+)-release signals (puffs) and propagated Ca(2+) waves were characterized in rat ureteric myocytes by confocal microscopy. Ca(2+) puffs were evoked by photorelease of low concentrations of Ins(1,4,5)P(3) from a caged precursor and by low concentrations of acetylcholine; they were also observed spontaneously in Ca(2+)-overloaded myocytes. Ca(2+) puffs showed some variability in amplitude, time course and spatial spread, suggesting that Ins(1,4,5)P(3)-gated channels exist in clusters containing variable numbers of channels and that within these clusters a variable number of channels can be recruited. Immunodetection of Ins(1,4,5)P(3) receptors revealed the existence of several spots of fluorescence in the confocal cell sections, supporting the existence of clusters of Ins(1,4,5)P(3) receptors. Strong Ins(1,4,5)P(3) photorelease and high concentrations of acetylcholine induced Ca(2+) waves that originated from an initiation site and propagated in the whole cell by spatial recruitment of neighbouring Ca(2+)-release sites. Both Ca(2+) puffs and Ca(2+) waves were blocked selectively by intracellular applications of heparin and an anti-Ins(1,4,5)P(3)-receptor antibody, but were unaffected by ryanodine and intracellular application of an anti-ryanodine receptor antibody. mRNAs encoding for the three subtypes of Ins(1,4,5)P(3) receptor and subtype 3 of ryanodine receptor were detected in these myocytes, and the maximal binding capacity of [(3)H]Ins(1,4,5)P(3) was 10- to 12-fold higher than that of [(3)H]ryanodine. These results suggest that Ins(1,4,5)P(3)-gated channels mediate a continuum of Ca(2+) signalling in smooth-muscle cells expressing a high level of Ins(1,4,5)P(3) receptors and no subtypes 1 and 2 of ryanodine receptors.

Acetylcholine↗

PubMedDate not supplied

Comparison of violet versus red laser exposures on visual search performance in humans.

Previous research suggests that the visual impairment of a violet laser is not highly localized on the retina, because the lens absorbs most short-wavelength visible light and partly retransmits it as a diffuse fluorescence at approximately 500 nm. The present study investigated whether a 405 nm violet diode laser more greatly impairs visual search performance in humans than does a 670 nm red diode laser, depending on target eccentricity. Participants had to locate a square among 15 diamonds spread throughout a visual search display while being exposed to a violet or red laser beam that was either continuous or flickering and presented either on-axis or 33 degrees off-axis. Whereas the continuous on-axis violet and red lasers had comparable effects on search performance when the target was located near the center of the beam, the violet laser disrupted processing of eccentric targets more than did the red laser. The search decrements were reduced for both lasers when the beams were flickered or presented off-axis. Both the bluish appearance and greater spatial spread of effect of the violet laser suggest that the unique impairment caused by a violet laser beam derives from its induced lens fluorescence.

Adult↗

PubMed2006

PKCalpha: a versatile key for decoding the cellular calcium toolkit.

Conventional protein kinases C (cPKCs) play an essential role in signal transduction and are believed to integrate both global Ca(2+) transients and diacylglycerol signals. We provide evidence that PKCalpha is a ubiquitous readout sensor for the cellular Ca(2+) toolkit, including highly restricted elementary Ca(2+) release. Threshold stimulations of cells with Ca(2+)-mobilizing agonists resulted in PKCalpha translocation events with limited spatial spreads (<4 microm) comprising two groups of lifetimes; brief events (400-1,500 ms) exclusively mediated by Ca(2+)-C2 domain membrane interactions and long-lasting events (>4 s) resulting from longer DAG-C1a domain-mediated membrane interactions. Although upon uncaging NP-EGTA, which is a caged Ca(2+) compound, WT-PKCalpha displayed rapid membrane translocations within <250 ms, PKCalpha constructs with C2 domains mutated in their Ca(2+)-binding region lacked any Ca(2+)-dependent translocation. Flash photolysis of diazo-2, a photosensitive caged Ca(2+) buffer, revealed a biphasic membrane dissociation (slow and fast period) of WT-PKCalpha. The slow phase was absent in cells expressing PKCalpha-constructs containing mutated C1a-domains with largely reduced DAG binding. Thus, two groups of PKCalpha membrane interactions coexist; C2- and C1a-mediated interactions with different lifetimes but rapid interconversion. We conclude that PKCalpha can readout very fast and, spatially and temporally, very complex cellular Ca(2+) signals. Therefore, cPKCs are important transducers for the ubiquitous cellular Ca(2+) signaling toolkit.

Animals↗

PubMed1997

Allozyme polymorphism and geographic variation in the small brown planthopper, Laodelphax striatellus (Homoptera: Delphacidae).

The small brown planthopper, Laodelphax striatellus, immigrates annually into Japan over the East China Sea from the Asian mainland. It is not known whether this long-distance dispersal has any effect on the genetic structure of Japanese L. striatellus populations. The dispersal of L. striatellus is suspected to be relevant to the population dynamics of infection with the parasitic bacterium Wolbachia, which causes cytoplasmic incompatibility in L. striatellus. Wolbachia infection has spread within and among Japanese L. striatellus populations due to this cytoplasmic incompatibility. In the present study, the geographic differences among II L. striatellus populations from Japan and Taiwan was investigated using allozyme polymorphism. FST values on three enzyme loci (GPI, PGM, and AK) indicated a geographically differentiated population structure. Significant differentiation was found even among populations located along the course of the long-distance dispersal. The results indicated that long-range dispersal of L. striatellus does not occur regularly over the main islands of Japan and that it does not have a large effect on the population structure of L. striatellus. This conclusion is in agreement with the geographically variable life history of L. striatellus adapted to local climates. The short-term rice stripe epidemic, which is vectored by L. striatellus, in northwestern Kyushu, Japan, during 1985 and 1986 corresponds to these results. Based on the present findings, short-distance dispersal was considered to drive the spatial spread of Wolbachia infection among L. striatellus populations.

Alleles↗

PubMed2003

Sequence-dependent solution structure and motions of 13 TATA/TBP (TATA-box binding protein) complexes.

The TATA element is a well-known example of a DNA promoter sequence recognized by the TATA box binding protein (TBP) through its intrinsic motion and deformability. Although TBP recognizes the TATA element octamer unusually (through the minor groove, which lacks the distinctive features of the major groove), single base-pair replacements alter transcriptional activity. Recent crystallographic experiments have suggested that TATA/TBP complexes differing by a single base pair retain substantial structural similarity despite their functional differences in activating transcription. To investigate the subtle role of sequence-dependent motion within the TATA element and certain aspects of its effect on assembly of the transcriptional complex, we examine 5-ns dynamics trajectories of 13 variant TATA/TBP complexes differing from each other by a single base pair. They include the wild-type (WT) adenovirus 2 major late promoter (AdMLP) TATA element, TATAAAAG (the octamer specifies positions -31 to -24 with respect to the transcription initiation site), and the variants A31 (i.e., AATAAAAG), T30, A29, C29, G28, T28, T27, G26, T26, C25, T25, and T24. Our simulated TATA/TBP complexes develop sequence-dependent structure and motion trends that may lead to favorable orientations for high-activity variants (with respect to binding TFIIA, TFIIB, and other transcription factors), while conversely, accelerate dissociation of low-activity TATA/TBP complexes. The motions that promote favorable geometries for preinitiation complexes include small rotations between TBP's N- and C-terminal domains, sense strand DNA backbone "slithering," and rotations in TBP's H2 and H2' helices. Low-activity variants tend to translate the H1 and H1' helices and withdraw the intercalating phenylalanines. These cumulative DNA and protein motions lead to a spatial spread of complex orientations up to 4 A; this is associated with an overall bend of the variant TATA/TBP complexes that spans 93 degrees to 110 degrees (107 degrees for the crystal reference). Taken together, our analyses imply larger differences when these local structural and bending changes are extended to longer DNA (upstream and downstream) and suggest that specific local TATA/TBP motions (e.g., shifts in TBP helices and TATA bases and backbone) play a role in modulating the formation and maintenance of the transcription initiation complex.

Base Sequence↗

PubMed2004

Role of glial amino acid transporters in synaptic transmission and brain energetics.

This article reviews how the uptake of neurotransmitter by glial amino acid transporters limits the spatial spread of transmitter to preserve the independent operation of nearby synapses, temporally shapes postsynaptic currents, and regulates the effects of tonic transmitter release. We demonstrate the importance of amino acid uptake and recycling mechanisms for preventing the loss of energetically costly neurotransmitter from the brain, and also examine the suggestion that glutamate uptake into glia plays a key role in regulating the energy production of the brain. Finally, we assess the role of glial amino acid transporters in transmitter recycling pathways.

Amino Acid Transport Systems↗

PubMed2005

The Orbitrap: a new mass spectrometer.

Research areas such as proteomics and metabolomics are driving the demand for mass spectrometers that have high performance but modest power requirements, size, and cost. This paper describes such an instrument, the Orbitrap, based on a new type of mass analyzer invented by Makarov. The Orbitrap operates by radially trapping ions about a central spindle electrode. An outer barrel-like electrode is coaxial with the inner spindlelike electrode and mass/charge values are measured from the frequency of harmonic ion oscillations, along the axis of the electric field, undergone by the orbitally trapped ions. This axial frequency is independent of the energy and spatial spread of the ions. Ion frequencies are measured non-destructively by acquisition of time-domain image current transients, with subsequent fast Fourier transforms (FFTs) being used to obtain the mass spectra. In addition to describing the Orbitrap mass analyzer, this paper also describes a complete Orbitrap-based mass spectrometer, equipped with an electrospray ionization source (ESI). Ions are transferred from the ESI source through three stages of differential pumping using RF guide quadrupoles. The third quadrupole, pressurized to less than 10(-3) Torr with collision gas, acts as an ion accumulator; ion/neutral collisions slow the ions and cause them to pool in an axial potential well at the end of the quadrupole. Ion bunches are injected from this pool into the Orbitrap analyzer for mass analysis. The ion injection process is described in a simplified way, including a description of electrodynamic squeezing, field compensation for the effects of the ion injection slit, and criteria for orbital stability. Features of the Orbitrap at its present stage of development include high mass resolution (up to 150,000), large space charge capacity, high mass accuracy (2-5 ppm), a mass/charge range of at least 6000, and dynamic range greater than 10(3). Applications based on electrospray ionization are described, including characterization of transition-metal complexes, oligosaccharides, peptides, and proteins. Use is also made of the high-resolution capabilities of the Orbitrap to confirm the presence of metaclusters of serine octamers in ESI mass spectra and to perform H/D exchange experiments on these ions in the storage quadrupole.

Alcohol Dehydrogenase↗

PubMed1986

The asymptotic speed of propagation of the deterministic non-reducible n-type epidemic.

A model has been formulated in to describe the spatial spread of an epidemic involving n types of individuals, when triggered by the introduction of infectives from outside. Wave solutions for such a model have been investigated in and have been shown only to exist at certain speeds. This paper establishes that the asymptotic speed of propagation, as defined in Aronson and Weinberger, of such an epidemic is in fact c0, the minimum speed at which wave solutions exist. This extends the known result for the one-type and host-vector epidemics.

Biometry↗