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1.
Vaccination and antiviral treatment are two important prevention and control measures for the spread of influenza. However,
the benefit of antiviral use can be compromised if drug-resistant strains arise. In this paper, we develop a mathematical
model to explore the impact of vaccination and antiviral treatment on the transmission dynamics of influenza. The model includes
both drug-sensitive and resistant strains. Analytical results of the model show that the quantities ℛ
SC
and ℛ
RC
, which represent the control reproduction numbers of the sensitive and resistant strains, respectively, provide threshold
conditions that determine the competitive outcomes of the two strains. These threshold conditions can be used to gain important
insights into the effect of vaccination and treatment on the prevention and control of influenza. Numerical simulations are
also conducted to confirm and extend the analytic results. The findings imply that higher levels of treatment may lead to
an increase of epidemic size, and the extent to which this occurs depends on other factors such as the rates of vaccination
and resistance development. This suggests that antiviral treatment should be implemented appropriately. 相似文献
2.
Parasite and predator play significant role in trophic interaction, productivity and stability of an ecosystem. In this paper,
we have studied a host-parasite-predator interaction that incorporates incubation delay. How the qualitative and quantitative
behaviors of the system alter with the incubation delay have been discussed both from mathematical and biological point of
views. It is observed that for a lower infection rate, the system is stable for all delays; but for a higher infection rate,
there exists a threshold value of the delay above which the system is unstable and below which the system is stable leading
to the persistence of all the species. Also, the instability arising from the incubation delay may be controlled if somehow
the growth rate of predator population is increased. Numerical studies have also been performed to illustrate different analytical
findings.
Research is supported by UGC, India; F No. 32-173/2006(SR). 相似文献
3.
This paper studies a class of dynamical systems that model multi-species ecosystems. These systems are ‘resource bounded’
in the sense that species compete to utilize an underlying limiting resource or substrate. This boundedness means that the
relevant state space can be reduced to a simplex, with coordinates representing the proportions of substrate utilized by the
various species. If the vector field is inward pointing on the boundary of the simplex, the state space is forward invariant
under the system flow, a requirement that can be interpreted as the presence of non-zero exogenous recruitment. We consider
conditions under which these model systems have a unique interior equilibrium that is globally asymptotically stable. The
systems we consider generalize classical multi-species Lotka–Volterra systems, the behaviour of which is characterized by
properties of the community (or interaction) matrix. However, the more general systems considered here are not characterized
by a single matrix, but rather a family of matrices. We develop a set of ‘explicit conditions’ on the basis of a notion of
‘uniform diagonal dominance’ for such a family of matrices, that allows us to extract a set of sufficient conditions for global
asymptotic stability based on properties of a single, derived matrix. Examples of these explicit conditions are discussed. 相似文献
4.
5.
Martin Bock Amit Kumar Tyagi Jan-Ulrich Kreft Wolfgang Alt 《Bulletin of mathematical biology》2010,72(7):1696-1731
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however,
so far only with flat hyper-surfaces as cell-cell contact borders. In order to reproduce the experimentally observed piecewise
spherical boundary shapes, we develop a consistent theoretical framework of multiplicatively weighted distance functions,
defining generalized finite Voronoi neighborhoods around cell bodies of varying radius, which serve as heterogeneous generators
of the resulting model tissue. The interactions between cells are represented by adhesive and repelling force densities on
the cell contact borders. In addition, protrusive locomotion forces are implemented along the cell boundaries at the tissue
margin, and stochastic perturbations allow for non-deterministic motility effects. Simulations of the emerging system of stochastic
differential equations for position and velocity of cell centers show the feasibility of this Voronoi method generating realistic
cell shapes. In the limiting case of a single cell pair in brief contact, the dynamical nonlinear Ornstein–Uhlenbeck process
is analytically investigated. In general, topologically distinct tissue conformations are observed, exhibiting stability on
different time scales, and tissue coherence is quantified by suitable characteristics. Finally, an argument is derived pointing
to a tradeoff in natural tissues between cell size heterogeneity and the extension of cellular lamellae. 相似文献
6.
Bistability in apoptosis, or programmed cell death, is crucial for the healthy functioning of multicellular organisms. The
aim in this study is to show the presence of bistability in a mitochondria-dependent apoptosis model under nitric oxide effects
using chemical reaction network theory. The model equations are a set of coupled ordinary differential equations arising from
the assumed mass action kinetics. Whether these equations have a capacity for bistability (cell survival and apoptosis) is
determined using a modular approach in which the model is decomposed into modules. Each module contains only a subset of the
whole model and is analyzed separately. It is seen that bistability in a module is preserved throughout the whole model after
adding the remaining reactions in the pathway on these modules. It is also found that inhibitor effect of some proteins and
the appearance of a reacting protein in a later stage as a product is a desired feature but not sufficient for bistability
(in the absence of cooperativity effects). On the whole model, two apoptotic and two cell survival states are obtained depending
on the initial cell conditions. The results suggest that the antiapoptotic effects of nitric oxide species are responsible
for the bistable character of the apoptotic pathway when cooperativity is not assumed in the apoptosome formation. 相似文献
7.
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity.
It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It
is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists,
it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is performed
using DDE-BIFTOOL and traceDDE to investigate different dynamical regimes in the model using numerical continuation for different
values of system parameters and different integral kernels. 相似文献
8.
Logan JD 《Bulletin of mathematical biology》2008,70(1):1-20
Studies document the fact that temperature changes strongly affect interactions in many consumer-resource systems through
altered, or shifted, phenologies. The mistiming of events, such as migration or emergence times, or the contraction or expansion
of development times can upset the normal synchronization and lead to increased or decreased predation events. In this paper,
we formulate a continuous time, phenologically-structured model of predator-prey interactions that is driven by temperature
variations. It is particularly applicable to arthropod interactions because their development rates are so strongly temperature
related. The model takes the form of a system of partial differential-integral equations for the species’ population densities
in development-time variables. In special cases, the model is analytically tractable and we find a closed-form solution. By
calculating density variations under different temperature regimes, the model gives a quantitative method for assessing the
effects of global temperature change on consumer-resource interactions. 相似文献
9.
Miranda I. Teboh-Ewungkem Chandra N. Podder Abba B. Gumel 《Bulletin of mathematical biology》2010,72(1):63-93
A mathematical model is developed to assess the role of gametocytes (the infectious sexual stage of the malaria parasite)
in malaria transmission dynamics in a community. The model is rigorously analysed to gain insights into its dynamical features.
It is shown that, in the absence of disease-induced mortality, the model has a globally-asymptotically stable disease-free
equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number (denoted by ℛ0), is less than unity. Further, it has a unique endemic equilibrium if ℛ0>1. The model is extended to incorporate an imperfect vaccine with some assumed therapeutic characteristics. Theoretical analyses
of the model with vaccination show that an imperfect malaria vaccine could have negative or positive impact (in reducing disease
burden) depending on whether or not a certain threshold (denoted by ∇) is less than unity. Numerical simulations of the vaccination model show that such an imperfect anti-malaria vaccine (with
a modest efficacy and coverage rate) can lead to effective disease control if the reproduction threshold (denoted by ℛvac) of the disease is reasonably small. On the other hand, the disease cannot be effectively controlled using such a vaccine
if ℛvac is high. Finally, it is shown that the average number of days spent in the class of infectious individuals with higher level
of gametocyte is critically important to the malaria burden in the community. 相似文献
10.
Benjamin H. Beck Hyunggoon Kim Rebecca O’Brien Martin R. Jadus G. Yancey Gillespie Gretchen A. Cloud Neil T. Hoa Catherine P. Langford Richard D. Lopez Lualhati E. Harkins Lawrence S. Lamb Jr. 《PloS one》2015,10(5)
Human γδ T cells are potent effectors against glioma cell lines in vitro and in human/mouse xenograft models of glioblastoma, however, this effect has not been investigated in an immunocompetent mouse model. In this report, we established GL261 intracranial gliomas in syngeneic WT C57BL/6 mice and measured circulating γδ T cell count, phenotype, Vγ/Vδ repertoire, tumor histopathology, NKG2D ligands expression, and T cell invasion at day 10–12 post-injection and at end stage. Circulating γδ T cells transiently increased and upregulated Annexin V expression at post-tumor day 10–12 followed by a dramatic decline in γδ T cell count at end stage. T cell receptor repertoire showed no changes in Vγ1, Vγ4, Vγ7 or Vδ1 subsets from controls at post-tumor day 10–12 or at end stage except for an end-stage increase in the Vδ4 population. Approximately 12% of γδ T cells produced IFN-γ. IL-17 and IL-4 producing γδ T cells were not detected. Tumor progression was the same in TCRδ-/- C57BL/6 mice as that observed in WT mice, suggesting that γδ T cells exerted neither a regulatory nor a sustainable cytotoxic effect on the tumor. WT mice that received an intracranial injection of γδ T cells 15m following tumor placement showed evidence of local tumor growth inhibition but this was insufficient to confer a survival advantage over untreated controls. Taken together, our findings suggest that an early nonspecific proliferation of γδ T cells followed by their depletion occurs in mice implanted with syngeneic GL261 gliomas. The mechanism by which γδ T cell expansion occurs remains a subject for further investigation of the mechanisms responsible for this immune response in the setting of high-grade glioma. 相似文献
11.
Hanna T. M. Eskola Stefan A. H. Geritz Mats Gyllenberg 《Bulletin of mathematical biology》2011,73(6):1312-1332
We study the evolution of an individual’s reproductive strategy in a mechanistic modeling framework. We assume that the total
number of juveniles one adult individual can produce is a finite constant, and we study how this number should be distributed
during the season, given the types of inter-individual interactions and mortality processes included in the model. The evolution
of the timing of reproduction in this modeling framework has already been studied earlier in the case of equilibrium resident
dynamics, but we generalize the situation to also fluctuating population dynamics. We find that, as in the equilibrium case,
the presence or absence of inter-juvenile aggression affects the functional form of the evolutionarily stable reproductive
strategy. If an ESS exists, it can have an absolutely continuous part only if inter-juvenile aggression is included in the
model. If inter-juvenile aggression is not included in the model, an ESS can have no continuous parts, and only Dirac measures
are possible. 相似文献
12.
Since its conception in 1952, the Turing paradigm for pattern formation has been the subject of numerous theoretical investigations.
Experimentally, this mechanism was first demonstrated in chemical reactions over 20 years ago and, more recently, several
examples of biological self-organisation have also been implicated as Turing systems. One criticism of the Turing model is
its lack of robustness, not only with respect to fluctuations in the initial conditions, but also with respect to the inclusion
of delays in critical feedback processes such as gene expression. In this work we investigate the possibilities for Turing
patterns on growing domains where the morphogens additionally regulate domain growth, incorporating delays in the feedback
between signalling and domain growth, as well as gene expression. We present results for the proto-typical Schnakenberg and
Gierer–Meinhardt systems: exploring the dynamics of these systems suggests a reconsideration of the basic Turing mechanism
for pattern formation on morphogen-regulated growing domains as well as highlighting when feedback delays on domain growth
are important for pattern formation. 相似文献
13.
This paper is concerned with early development of transformed epithelial cells (TECs) in the presence of fibroblasts in the
tumor micro-environment. These two types of cells interact by means of cytokines such as transforming growth factor (TGF-β) and epidermal growth factor (EGF) secreted, respectively, by the TECs and the fibroblasts. As this interaction proceeds,
TGF-β induces fibroblasts to differentiate into myofibroblasts which secrete EGF at a larger rate than fibroblasts. We monitor
the entire process in silico, in a setup which mimics experiments in a Tumor Chamber Invasion Assay, where a semi-permeable
membrane coated by extracellular matrix (ECM) is placed between two chambers, one containing TECs and another containing fibroblasts.
We develop a mathematical model, based on a system of PDEs, that includes the interaction between TECs, fibroblasts, myofibroblasts,
TGF-β, and EGF, and we show how model parameters affect tumor progression. The model is used to generate several hypotheses on
how to slow tumor growth and invasion. In an Appendix, it is proved that the mathematical model has a unique global in-time
solution. 相似文献
14.
We studied from 1998 to 2002 the fine-scale vegetation dynamics of a poorly regenerated vacuum-mined bog located in southern
Quebec. We selected mined sites that have been abandoned for 14 years and monitored the vascular and non-vascular plants,
and some hydrological characteristics. We focussed our study on the monitoring of cotton-grass (Eriophorum vaginatum L.) tussocks. Major changes in the plant cover were observed during the five-year period, such as a decrease (26–31%) in
the number of cotton-grass tussocks and an increase in the ericaceous shrub cover. The water table level (lower than 40 cm
below the soil surface) and frost heaving appear to be the main factors explaining the failure of cotton-grass and of other
typical bog plant species to colonize abandoned mined surfaces. The ericaceous shrub cover, although increasing, was still
sparse even after two decades of abandonment, and it may take several additional decades before a complete shrub cover establishes
itself. While the natural revegetation process of this vacuum-mined bog is still dynamic after two decades of abandonment,
there is no evidence to suggest that vegetation assemblages will eventually resemble those of undisturbed peatlands. 相似文献
15.
16.
17.
We describe and analyze a mathematical model for schistosomiasis in which infected snails are distinguished from susceptible
through increased mortality and no reproduction. We based the model on the same derivation as Anderson and May (J. Anim. Ecol.
47:219–247, 1978), Feng and Milner (A New Mathematical Model of Schistosomiasis, Mathematical Models in Medical and Health Science, Nashville,
TN, 1997. Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, pp. 117–128, 1998), and May and Anderson (J. Anim. Ecol. 47:249–267, 1978), but used logistic growth both in human and snail hosts. We introduce a parameter r, the effective coverage of medical treatment/prevention to control the infection. We determine a reproductive number for
the disease directly related to its persistence and extinction. Finally, we obtain a critical value for r that indicates the minimum treatment effort needed in order to clear out the disease from the population. 相似文献
18.
The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1
infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a “healthy”
steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV
therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment
periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality
condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead
to the long-term control of HIV by the strong immune response after discontinuation of therapy. 相似文献
19.
Epidemic transmission is one of the critical density-dependent mechanisms that affect species viability and dynamics. In a
predator-prey system, epidemic transmission can strongly affect the success probability of hunting, especially for social
animals. Predators, therefore, will suffer from the positive density-dependence, i.e., Allee effect, due to epidemic transmission
in the population. The rate of species contacting the epidemic, especially for those endangered or invasive, has largely increased
due to the habitat destruction caused by anthropogenic disturbance. Using ordinary differential equations and cellular automata,
we here explored the epidemic transmission in a predator-prey system. Results show that a moderate Allee effect will destabilize
the dynamics, but it is not true for the extreme Allee effect (weak or strong). The predator-prey dynamics amazingly stabilize
by the extreme Allee effect. Predators suffer the most from the epidemic disease at moderate transmission probability. Counter-intuitively,
habitat destruction will benefit the control of the epidemic disease. The demographic stochasticity dramatically influences
the spatial distribution of the system. The spatial distribution changes from oil-bubble-like (due to local interaction) to
aggregated spatially scattered points (due to local interaction and demographic stochasticity). It indicates the possibility
of using human disturbance in habitat as a potential epidemic-control method in conservation. 相似文献
20.
Smoking has long being associated with tuberculosis. We present a tuberculosis dynamics model taking into account the fact that some people in the population are smoking in order to assess the effects of smoking on tuberculosis transmission. The epidemic thresholds known as the reproduction numbers and equilibria for the model are determined and stabilities analyzed. Qualitative analysis of the model including positivity and persistence of solutions are presented. The model is numerically analyzed to assess the effects of smoking on the transmission dynamics of tuberculosis. Numerical simulations of the model show that smoking enhances tuberculosis transmission, progression to active disease and in a population of smokers, tuberculosis cannot be controlled even when treatment success is assumed to be as high as 88%. Further, analysis of the reproduction numbers indicates that the number of active tuberculosis cases increases as the number of smokers increase. 相似文献