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1.
In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reason to divide the human population into two age classes is for practical purpose, as vaccination is usually concentrated in one age class. We assume that a constant rate of individuals in the child-class is vaccinated. We analyze a threshold number which is equivalent to the basic reproduction number. If there is an undeliberate vaccination to infectious children, which worsens their condition as the time span of being infectious increases, then paradoxically, vaccination can be counter productive. The paradox, stating that vaccination makes the basic reproduction number even bigger, can occur if the worsening effect is greater than a certain threshold, a function of the human demographic and epidemiological parameters, which is independent of the level of vaccination. However, if the worsening effect is to increase virulence so that one will develop symptoms, then the vaccination is always productive. In both situations, screening should take place before vaccination. In general, the presence of class division has obscured the known rule of thumb for vaccination.  相似文献   

2.
Two weakly coupled oscillators are studied and the existence of n:m phase-locked solutions is shown. With the use of a slow time scale, the problem is reduced to a two-dimensional system on an invariant attracting torus. This system is further reduced to a one-dimensional dynamical system. Fixed points of this system correspond to n:m phase-locked solutions. The method is applied to a forced oscillator, linearly coupled - systems, and a pair of integrate and fire neuron models.  相似文献   

3.
Viral hepatitis A, as other endemic diseases, represents a public health priority worldwide. To study long-time scale human pathogens through individual-based simulations, the development of a dynamic network of contacts is required. In this work, we introduce an individual-based model accounting for the birth and death of the individuals, the generation of new households, and the educational career of the individuals, in order to investigate viral hepatitis A dynamics in the most affected Italian areas. Intervention options such as targeted vaccination, social distancing measures (e.g., closure of day care centers and kindergartens) and improvements in standards of living and hygiene are evaluated. Results show that a very low vaccination coverage is sufficient to control hepatitis A in Italy, while its elimination is not possible since new cases are continuously imported from high endemicity areas outside the country. Finally, the considered social distancing measures can be counterproductive since the fraction of recovered individuals does not decline while the age at infection increases, thus augmenting the probability of developing acute symptoms.  相似文献   

4.
Motivated by a neuronal modeling problem, a bivariate Wiener process with two independent components is considered. Each component evolves independently until one of them reaches a threshold value. If the first component crosses the threshold value, it is reset while the dynamics of the other component remains unchanged. But, if this happens to the second component, the first one has a jump of constant amplitude; the second component is then reset to its starting value and its evolution restarts. Both processes evolve once again until one of them reaches again its boundary. In this work, the coupling of the first exit times of the two connected processes is studied.  相似文献   

5.
We deal with the following question: Can the consumption of contaminated bush meat, the funeral practices and the environmental contamination explain the recurrence and persistence of Ebola virus disease outbreaks in Africa? We develop an SIR-type model which, incorporates both the direct and indirect transmissions in such a manner that there is a provision of Ebola viruses. We prove that the full model has one (endemic) equilibrium which is locally asymptotically stable whereas, it is globally asymptotically stable in the absence of the Ebola virus shedding in the environment. For the sub-model without the provision of Ebola viruses, the disease dies out or stabilizes globally at an endemic equilibrium. At the endemic level, the number of infectious is larger for the full model than for the sub-model without provision of Ebola viruses. We design a nonstandard finite difference scheme, which preserves the dynamics of the model. Numerical simulations are provided.  相似文献   

6.
Although many infectious diseases of humans and wildlife are transmitted via an environmental reservoir, the theory of environmental transmission remains poorly elaborated. Here we introduce an SIR-type multi-strain disease transmission model with perfect cross immunity where environmental transmission is broadly defined by three axioms. We establish the conditions under which a multi-strain endemic state is invaded by another strain which is both directly and environmentally transmitted. We discuss explicit forms for environmental transmission terms and apply our newly derived invasion conditions to a two-strain system. Then, we consider the case of two strains with matching basic reproduction numbers (i.e., R0), one directly transmitted only and the other both directly and environmentally transmitted, invading each other's endemic state. We find that the strain which is only directly transmitted can invade the endemic state of the strain with mixed transmission. However, the endemic state of the first strain is neutrally stable to invasion by the second strain. Thus, our results suggest that environmental transmission makes the endemic state less resistant to invasion.  相似文献   

7.
We propose a seven variable model with time delay in one of the variables for the cell cycle in higher eukaryotes. The model consists of four important phosphorylation-dephosphorylation (P-D) cycles that govern the cell cycle, namely Pre-MPF-MPF, Cdc25P-Cdc25, Wee1P-Wee1 and APCP-APC. Other variables are cyclin, free cyclin dependent kinase (Cdk) and mass. The mass acts as a G2/M checkpoint and the checkpoint is represented by a saddle node loop bifurcation. The key feature of the model is that a time lag has been introduced in the activation of anaphase promoting complex (APC) by maturation promoting factor (MPF). This is effected by treating MPF as a time-delayed variable in the activation step of APC. The time lag acts as a spindle checkpoint. Absence of time delay induces a bistability in our model. Time delay also brings about variability in G1 phase timings. The model also reproduces the mutant phenotype experiments on wee1 cells. Stochasticity has been introduced in the model to simulate the dependence of the cycle time on cell birth length. Mutant phenotypes in the stochastic model reproduce the experimental observations better than the deterministic model.  相似文献   

8.
We studied the detailed structure of a neuronal network model in which the spontaneous spike activity is correctly optimized to match the experimental data and discuss the reliability of the optimized spike transmission. Two stochastic properties of the spontaneous activity were calculated: the spike-count rate and synchrony size. The synchrony size, expected to be an important factor for optimization of spike transmission in the network, represents a percentage of observed coactive neurons within a time bin, whose probability approximately follows a power-law. We systematically investigated how these stochastic properties could matched to those calculated from the experimental data in terms of the log-normally distributed synaptic weights between excitatory and inhibitory neurons and synaptic background activity induced by the input current noise in the network model. To ensure reliably optimized spike transmission, the synchrony size as well as spike-count rate were simultaneously optimized. This required changeably balanced log-normal distributions of synaptic weights between excitatory and inhibitory neurons and appropriately amplified synaptic background activity. Our results suggested that the inhibitory neurons with a hub-like structure driven by intensive feedback from excitatory neurons were a key factor in the simultaneous optimization of the spike-count rate and synchrony size, regardless of different spiking types between excitatory and inhibitory neurons.  相似文献   

9.
Experimental populations of 20 Gyrodactylus alexanderi Mizelle &; Kritsky, 1967, on 19 isolated Gasterosteus aculeatus at 15°C increased for 2 weeks to a mean of 61, then decreased in 2 further weeks to a mean of 9. Fish that lost their fluke infestations were refractory to further infestation for about 3 weeks.The chief factors affecting fluke abundance were measured, including reproduction and mortality rates of flukes on fish, rate of shedding by the fish, mortality rates of flukes while off fish, and the rate of reattachment of the flukes. Data on these individual factors were combined to form a simple deterministic model which simulated the population changes on isolated fish. This was later made more realistic by the introduction of a random variable. When the model was tested in a multiple-host situation it predicted results close to those observed experimentally.  相似文献   

10.
The receptive fields of cells in the lateral geniculate nucleus (LGN) are shaped by their diverse set of impinging inputs: feedforward synaptic inputs stemming from retina, and feedback inputs stemming from the visual cortex and the thalamic reticular nucleus. To probe the possible roles of these feedforward and feedback inputs in shaping the temporal receptive-field structure of LGN relay cells, we here present and investigate a minimal mechanistic firing-rate model tailored to elucidate their disparate features. The model for LGN relay ON cells includes feedforward excitation and inhibition (via interneurons) from retinal ON cells and excitatory and inhibitory (via thalamic reticular nucleus cells and interneurons) feedback from cortical ON and OFF cells. From a general firing-rate model formulated in terms of Volterra integral equations, we derive a single delay differential equation with absolute delay governing the dynamics of the system. A freely available and easy-to-use GUI-based MATLAB version of this minimal mechanistic LGN circuit model is provided. We particularly investigate the LGN relay-cell impulse response and find through thorough explorations of the model’s parameter space that both purely feedforward models and feedback models with feedforward excitation only, can account quantitatively for previously reported experimental results. We find, however, that the purely feedforward model predicts two impulse response measures, the time to first peak and the biphasic index (measuring the relative weight of the rebound phase) to be anticorrelated. In contrast, the models with feedback predict different correlations between these two measures. This suggests an experimental test assessing the relative importance of feedforward and feedback connections in shaping the impulse response of LGN relay cells.  相似文献   

11.
A kinetic model was proposed for dynein, a motor protein, complexed with microtubule fragments. The model explains the experimental observations of oscillatory movements in surprisingly simple axoneme fragments perfused with an ATP solution. This is the first model explaining the oscillatory activity of dynein as determined by a cooperative interaction of two dynein heads in the axoneme. The oscillation shape, frequency, and amplitude obtained for the model are close to the corresponding parameters determined experimentally.  相似文献   

12.
A natural language parser implemented entirely in simulated neurons is described. It produces a semantic representation based on frames. It parses solely using simulated fatiguing Leaky Integrate and Fire neurons, that are a relatively accurate biological model that is simulated efficiently. The model works on discrete cycles that simulate 10 ms of biological time, so the parser has a simple mapping to psychological parsing time. Comparisons to human parsing studies show that the parser closely approximates this data. The parser makes use of Cell Assemblies and the semantics of lexical items is represented by overlapping hierarchical Cell Assemblies so that semantically related items share neurons. This semantic encoding is used to resolve prepositional phrase attachment ambiguities encountered during parsing. Consequently, the parser provides a neurally-based cognitive model of parsing.  相似文献   

13.
A genetically structured mathematical model of the trp operon based on known molecular interactions of aporepressor, corepressor, and inducer is proposed. The model simulates, both qualitatively and quantitatively, the influence of these regulatory species on the extent of repression and expression of cloned gene products. It shows that at low aporepressor concentration, full repression is not possible even with high tryptophan levels, resulting in leaky expression. Calculations based on the model enabled predictions of optimum levels of aporepressor and tryptophan for effective repression and, concurrently, the beta-indoleacrylic acid concentrations required for induction for both low and high plasmid copy number clones. Using the model we attempted to provide explanations for seemingly anomalous and sometimes contradictory observations by researchers when working with the trp promoter. (c) 1993 John Wiley & Sons, Inc.  相似文献   

14.
15.
1. The ecosystem response of Lake Tanganyika was studied using a four-component, nutrient–phytoplankton–zooplankton–detritus, phosphorus-based ecosystem model coupled to a nonlinear, reduced-gravity, circulation model. The ecosystem model, an improved version of the earlier eco-hydrodynamics model developed for Lake Tanganyika, was used to estimate the annual primary production of Lake Tanganyika and its spatial and temporal variability. The simulations were driven with the National Centres for Environmental Protection (NCEP) records for winds and solar radiation forcing.
2. The simulated annual cycles of the four ecosystem variables and the daily net primary production were compared with the observations. The comparison showed that simulations reproduced realistically the general features of the annual cycles of epilimnial phosphate, net primary production and plankton dynamics.
3. The climatic simulations for the years 1970–2006 yielded a daily averaged integrated upper layer net production ranging from 0.11 to 1.78 g C m−2 day−1 and daily averaged chlorophyll- a (chl- a ) from 0.16 to 4.3 mg m−3. Although the nutrient concentrations in the epilimnion during the strong wind years were high, the net production was low, which is partly because of the greater vertical mixing, produced by strong winds, exposing the phytoplankton to low light conditions in deeper waters. The simulated annual net production and chl- a agreed quite well with observed production available in the literature.
4. We envisage using this model to predict the future scenarios of primary productivity in the lake.  相似文献   

16.
A disease transmission model in a nonconstant population   总被引:9,自引:0,他引:9  
A general SIRS disease transmission model is formulated under assumptions that the size of the population varies, the incidence rate is nonlinear, and the recovered (removed) class may also be directly reinfected. For a class of incidence functions it is shown that the model has no periodic solutions. By contrast, for a particular incidence function, a combination of analytical and numerical techniques are used to show that (for some parameters) periodic solutions can arise through homoclinic loops or saddle connections and disappear through Hopf bifurcations.Supported in part by NSERC grant A-8965, the University of Victoria Committee on Faculty Research & Travel, and the Institute for Mathematics and its Applications, Minneapolis, MN, with funds provided by NSF  相似文献   

17.
This paper develops a simple mathematical model of the sitting of capillary sprouts on an existing blood vessel during the initiation of tumour-induced angiogenesis. The model represents an inceptive attempt to address the question of how unchecked sprouting of the parent vessel is avoided at the initiation of angiogenesis, based on the idea that feedback regulation processes play the dominant role. No chemical interaction between the proangiogenic and antiangiogenic factors is assumed. The model is based on corneal pocket experiments, and provides a mathematical analysis of the initial spacing of angiogenic sprouts.  相似文献   

18.
Mechanical transmission of pathogens by biting insects is a non-specific phenomenon in which pathogens are transmitted from the blood of an infected host to another host during interrupted feeding of the insects. A large range of pathogens can be mechanically transmitted, e.g. hemoparasites, bacteria and viruses. Some pathogens are almost exclusively mechanically transmitted, while others are also cyclically transmitted. For agents transmitted both cyclically and mechanically (mixed transmission), such as certain African pathogenic trypanosomes, the relative impact of mechanical versus cyclical transmission is essentially unknown. We have developed a mathematical model of pathogen transmission by a defined insect population to evaluate the importance of mechanical transmission. Based on a series of experiments aimed at demonstrating mechanical transmission of African trypanosomes by tabanids, the main parameters of the model were either quantified (host parasitaemia, mean individual insect burden, initial prevalence of infection) or estimated (unknown parameters). This model allows us to simulate the evolution of pathogen prevalence under various predictive circumstances, including control measures and could be used to assess the risk of mechanical transmission under field conditions. If adjustments of parameters are provided, this model could be generalized to other pathogenic agents present in the blood of their hosts (Bovine Leukemia virus, Anaplasma, etc.) or other biting insects such as biting muscids (stomoxyines) and hippoboscids.  相似文献   

19.
Avian influenza virus reveals persistent and recurrent outbreaks in North American wild waterfowl, and exhibits major outbreaks at 2-8 years intervals in duck populations. The standard susceptible-infected- recovered (SIR) framework, which includes seasonal migration and reproduction, but lacks environmental transmission, is unable to reproduce the multi-periodic patterns of avian influenza epidemics. In this paper, we argue that a fully stochastic theory based on environmental transmission provides a simple, plausible explanation for the phenomenon of multi-year periodic outbreaks of avian flu. Our theory predicts complex fluctuations with a dominant period of 2 to 8 years which essentially depends on the intensity of environmental transmission. A wavelet analysis of the observed data supports this prediction. Furthermore, using master equations and van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how the outbreak period varies with the environmental transmission.  相似文献   

20.
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