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

Inge CUC ◽  
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.

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

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Xiaoxia Zhao ◽  
Wei Li ◽  
Yanyang Wang ◽  
Lihong Jiang
Keyword(s):  
Differential Equation ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Equation Model ◽  
Positive Equilibrium ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Differential Equation Model ◽  
Number Of Visits ◽  
Positive Equilibrium Point

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.

scholarly journals A spatially varying stochastic differential equation model for animal movement

2018 ◽  
Vol 12 (2) ◽  
pp. 1312-1331 ◽  
Author(s):  
James C. Russell ◽  
Ephraim M. Hanks ◽  
Murali Haran ◽  
David Hughes
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Animal Movement ◽  
Equation Model ◽  
Differential Equation Model ◽  
Spatially Varying

Time Fractional Differential Equation Model With Random Derivative Order

2009 ◽  
Author(s):  
Hongguang Sun ◽  
Yangquan Chen ◽  
Wen Chen
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Diffusion Processes ◽  
Time Derivative ◽  
Equation Model ◽  
Differential Equation Model ◽  
New Model ◽  
Potential Applications ◽  
Fractional Differential ◽  
Derivative Order

This paper proposes a new type of fractional differential equation model, named time fractional differential equation model, in which noise term is included in the time derivative order. The new model is applied to anomalous relaxation and diffusion processes suffering noisy field. The analysis and numerical simulation results show that our model can well describes the feature of these processes. We also find that the scale parameter and the frequency of the noise play a crucial role in the behaviors of these systems. At the end, we recognize some potential applications of this new model.

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