Evaluation of the Number of Visits to Chinese Medical Institutions Using a Logistic Differential Equation Model

In this study, we established a two-dimensional logistic differential equation model to study the number of visits in Chinese PHCIs and hospitals based on the behavior of patients. We determine the model's equilibrium points and analyze their stability and then use China medical services data to fit the unknown parameters of the model. Finally, the sensitivity of model parameters is evaluated to determine the parameters that are susceptible to influence the system. The results indicate that the system corresponds to the zero-equilibrium point, the boundary equilibrium point, and the positive equilibrium point under different parameter conditions. We found that, in order to substantially increase visits to PHCIs, efforts should be made to improve PHCI comprehensive capacity and maximum service capacity.

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Analysis of the interaction among weed, inorganic fertilizer and herbivore in paddy ecosystem in fallow season

International Journal of Biomathematics ◽

10.1142/s1793524517501200 ◽

2017 ◽

Vol 10 (08) ◽

pp. 1750120 ◽

Cited By ~ 4

Author(s):

Meihong Xiang ◽

Zhaohua Wu ◽

Tiejun Zhou

Keyword(s):

Hopf Bifurcation ◽

Equilibrium Point ◽

Equation Model ◽

Inorganic Fertilizer ◽

Stable Region ◽

Positive Equilibrium ◽

Bifurcation Phenomenon ◽

Bifurcation Phenomena ◽

Paddy Ecosystem ◽

Positive Equilibrium Point

Paddy growth is influenced by the amount of inorganic fertilizer in paddy ecosystem in fallow season. To discover the interaction among weed, inorganic fertilizer and herbivore in the system, we put forward a differential equation model and investigate its properties. Results show that the system has a weed and herbivore extinct equilibrium and a herbivore extinct equilibrium. The two equilibria are proven to be unstable using the center manifold method. Under certain conditions, the system also has a positive equilibrium point. We give the stable region and the unstable region of the positive equilibrium point, which are determined by some parameters. We find that the system has the Hopf bifurcation phenomenon, and give the critical value of Hopf bifurcation by taking a system parameter as the bifurcation parameter. By comparing the equilibrium states between a paddy ecosystem with herbivore and one without herbivore, we find that the content of inorganic fertilizer can be improved by putting herbivore into a paddy field. An example is given to illustrate the feasibility of the results. Numerical simulation shows that Hopf bifurcation phenomena exist in the system.

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Two mathematical approaches to study the phosphorus eutrophication of a wetland in Puerto Rico

Inge CUC ◽

10.17981/ingecuc.15.1.2019.06 ◽

2019 ◽

Vol 15 (1) ◽

pp. 63-76

Author(s):

Marlio Paredes Gutiérrez ◽

Brenda Carolina Torres Velasquez ◽

Yashira Marie Sanchez Colon ◽

Fred Charles Schaffner Gibbs

Keyword(s):

Differential Equation ◽

Puerto Rico ◽

Equilibrium Point ◽

Nutrient Recycling ◽

Soluble Reactive Phosphorus ◽

Equation Model ◽

Cluster Method ◽

Differential Equation Model ◽

International Standard ◽

Bottom Substrate

Introduction: Laguna Cartagena (LC), a wetland in Lajas, Puerto Rico, has been negatively impacted by nutrients, mainly phosphorus run-off from agricultural activities until the end of sugar cane cultivation in the late 1900s. This led to P concentration remain high at hypereutrophic state that was irremediable even after a 5-fold reduction in source water nutrient concentration. Objective: The main goal of this research paper is to apply two different mathematical approaches to assess the eutrophication level of a wetland in Puerto Rico. Method: Grey Cluster Method (GCM) was used to classify LC’s eutrophic state by applying the International and Chinese trophic standards and two parameters, total phosphorous (TP) and total nitrogen (TN). Mean TP and TN from LC consolidated bottom substrate and flocculence samples were used to classify LC. To address whether LC can recover, soluble reactive phosphorus (SRP) and TP from LC inlet, outlet and center water samples were used to model (differential equation) the input and loss of phosphorus in LC and determine whether an equilibrium point exists. GCM analysis classified LC as a eutrophic wetland using the International standard and hypereutrophic using the Chinese standard. Results: Trophic state classification did not vary with use of consolidated bottom substrate versus flocculence samples. The differential equation model showed that SRP and TP levels within LC were higher than levels of SRP and TP entering LC, which could be caused by a nutrient recycling process within LC that may predict failure of remediation efforts. An equilibrium point was found at the eutrophic level, which means that even if there is a reduction in phosphorus input, there will not be a change in LC’s eutrophic state. Conclusions: Chinese trophic standard indicated LC was in a hypertrophic state. Similar results were found using the international standard. The differential equation model showed that LC is irreversible.

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On Stationary Solutions Of Delay Differential Equations: A Model Of Local Translation In Synapses

Математическая биология и биоинформатика ◽

10.17537/2019.14.554 ◽

2019 ◽

Vol 14 (2) ◽

pp. 554-569 ◽

Cited By ~ 1

Author(s):

V.A. Likhoshvai ◽

T.M. Khlebodarova

Keyword(s):

Equilibrium Point ◽

Relative Stability ◽

Equilibrium Points ◽

Stationary Solutions ◽

Translation System ◽

Positive Equilibrium ◽

Absolute Instability ◽

Local Translation ◽

Delayed Arguments ◽

Positive Equilibrium Point

The results of analytical analysis of stationary solutions of a differential equation with two delayed arguments τ1 and τ2 are presented. Such equations are used in modeling of molecular-genetic systems where the delay of arguments appear naturally. Conditions of existence of non-negative solutions are described, and dependence of stability of these solutions on the values of delayed arguments is studied. This stability theory allows to give complete characterization of these solutions for all values of the parameters of the model, and ensures instability of a positive equilibrium point for any values of the delays τ2 ≥ τ1 ≥ 0 in the case when it is unstable for τ2 = τ1 = 0 (absolute instability). If this positive equilibrium point is stable only for τ2 = τ1 = 0, then this domain τ2 ≥ τ1 ≥ 0 is the domain of absolute instability as well. For positive equilibrium points which are stable at τ2 = τ1 = 0, we find domains of absolute stability were the equilibrium points remain stable for all values of the parameters τ1 and τ2. The domains of relative stability, where these points become unstable for some values of these parameters are also described. We show that when the efficiency of translation, and non-linearity and complexity of its regulation mechanisms grow, the domains of the absolute and relative stability of the positive equilibrium point shrink, while the domains of its instability expand. So, enhanced activity of the local translation system can be a factor of its instability and that of the risk of neuro-psychical diseases related to distortions of plasticity of the synapse and memory, where importance of stability of the proteome in the synapse is postulated.

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A Bayes Regularized Ordinary Differential Equation Model for the Inference of Gene Regulatory Networks

Handbook of Research on Computational Methodologies in Gene Regulatory Networks ◽

10.4018/978-1-60566-685-3.ch006 ◽

2010 ◽

pp. 139-168

Author(s):

Nicole Radde ◽

Lars Kaderali

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Regulatory Networks ◽

Quantitative Description ◽

Simulated Data ◽

Equation Model ◽

Model Parameters ◽

Ordinary Differential Equation Model ◽

Differential Equation Model ◽

Stochastic Framework

Differential equation models provide a detailed, quantitative description of transcription regulatory networks. However, due to the large number of model parameters, they are usually applicable to small networks only, with at most a few dozen genes. Moreover, they are not well suited to deal with noisy data. In this chapter, we show how to circumvent these limitations by integrating an ordinary differential equation model into a stochastic framework. The resulting model is then embedded into a Bayesian learning approach. We integrate the-biologically motivated-expectation of sparse connectivity in the network into the inference process using a specifically defined prior distribution on model parameters. The approach is evaluated on simulated data and a dataset of the transcriptional network governing the yeast cell cycle.

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Dynamics of a prey predator disease model with Holling type functional response and stochastic perturbation

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.37 ◽

2020 ◽

pp. 471-488

Author(s):

M. N. Srinivas ◽

G. Basava Kumar ◽

V. Madhusudanan

Keyword(s):

Equilibrium Point ◽

Disease Model ◽

Stochastic Perturbation ◽

Positive Equilibrium ◽

Type Ii ◽

Asymptotically Stable ◽

Unique Positive Solution ◽

Stochastic Nature ◽

Research Article ◽

Positive Equilibrium Point

The present research article constitutes Holling type II and IV diseased prey predator ecosystem and classified into two categories namely susceptible and infected predators.We show that the system has a unique positive solution. The deterministic and stochastic nature of the dynamics of the system is investigated. We check the existence of all possible steady states with local stability. By using Routh-Hurwitz criterion we showed that the positive equilibrium point $E_{7}$ is locally asymptotically stable if $x^{*} > \sqrt{m_{1}}$ .Moreover condition of the global stability of positive equilibrium point $E_{7}$ are also entrenched with help of Lyupunov theorem. Some Numerical simulations are carried out to illustrate our analytical findings.

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